ACM Transactions on

Algorithms (TALG)

Latest Articles

Agnostic Learning in Permutation-Invariant Domains

We generalize algorithms from computational learning theory that are successful under the uniform distribution on the Boolean hypercube {0,... (more)

Maximizing k-Submodular Functions and Beyond

We consider the maximization problem in the value oracle model of functions defined on k-tuples of sets that are submodular in every orthant and... (more)

Improved Approximation Algorithms for Matroid and Knapsack Median Problems and Applications

We consider the matroid median problem [Krishnaswamy et al. 2011], wherein we are given a set of facilities with opening costs and a matroid on the... (more)

A Linear-Size Logarithmic Stretch Path-Reporting Distance Oracle for General Graphs

Thorup and Zwick [2001a] proposed a landmark distance oracle with the following properties. Given an n-vertex undirected graph G = (V, E) and a... (more)

Compressed Cache-Oblivious String B-Tree

In this article, we study three variants of the well-known prefix-search problem for strings, and we design solutions for the cache-oblivious model which improve the best known results. Among these contributions, we close (asymptotically) the classic problem, which asks for the detection of the set of strings that share the longest common prefix... (more)

Data Structures for Path Queries

Consider a tree T on n nodes, each having a weight drawn from [1‥σ]. In this article, we study the problem of supporting various path queries over the tree T. The path counting query asks for the number of the nodes on a query path whose weights are in a query range, while the path reporting query requires to report these nodes. The path... (more)

Approximation Algorithms for Movement Repairmen

In the Movement Repairmen (MR) problem, we are given a metric space (V, d) along with a set R of k repairmen r1, r2, …, rk with their start depots s1, s2, …, sk ∈ V and speeds v1, v2, …, vk ⩾ 0, respectively, and a set C of m clients c1, c2, …, cm having start locations s′1, s′2, …, s′m... (more)

On Hierarchical Routing in Doubling Metrics

We study the problem of routing in doubling metrics and show how to perform hierarchical routing in such metrics with small stretch and compact routing tables (i.e., with a small amount of routing information stored at each vertex). We say that a metric (X, d) has doubling dimension dim(<i<X</i<) at most α if every ball can be... (more)


In Memoriam: David S. Johnson

About TALG

The ACM Transactions on Algorithms (TALG) publishes original research of the highest quality dealing with algorithms that are inherently discrete and finite, and having mathematical content in a natural way, either in the objective or in the analysis.

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Forthcoming Articles
Nearest-Neighbor Searching Under Uncertainty II

Nearest-neighbor (NN) search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases, location-based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest neighbor queries in a probabilistic framework in which the location of each input point is specified as a probability density function. We present efficient algorithms for (i) computing all points that are nearest neighbors of a query point with nonzero probability; (ii) estimating, within a specified additive error, the probability of a point being the nearest neighbor of a query point; (iii) using it to return the point that maximizes the probability being the nearest neighbor, or all the points with probabilities greater than some threshold to be the NN.

Adaptive and Approximate Orthogonal Range Counting

We present three new results on one of the most basic problems in geometric data structures, 2-D orthogonal range counting. All the results are in the $w$-bit word RAM model. - It is well known that there are linear-space data structures for 2-D orthogonal range counting with worst-case optimal query time O(log n / loglog n). We give an O(n loglog n)-space adaptive data structure that improves the query time to O(loglog n+log k / loglog n), where k is the output count. When k=O(1), our bounds match the state of the art for the 2-D orthogonal range emptiness problem [Chan, Larsen, and Patrascu, SoCG 2011]. - We give an O(n loglog n)-space data structure for approximate 2-D orthogonal range counting that can compute a (1+delta)-factor approximation to the count in O(loglog n) time for any fixed constant delta>0. Again, our bounds match the state of the art for the 2-D orthogonal range emptiness problem. - Lastly, we consider the 1-D range selection problem, where a query in an array involves finding the kth least element in a given subarray. This problem is closely related to 2-D 3-sided orthogonal range counting. Recently, Jorgensen and Larsen [SODA 2011] presented a linear-space adaptive data structure with query time O(loglog n + log k / loglog n). We give a new linear-space structure that improves the query time to O(1 + log k / loglog n), exactly matching the lower bound proved by Jorgensen and Larsen.

An Improved Approximation for k-median, and Positive Correlation in Budgeted Optimization

Dependent rounding is a useful technique for optimization problems with hard budget constraints. This framework naturally leads to \emph{negative correlation} properties. However, what if an application naturally calls for dependent rounding on the one hand, and desires \emph{positive} correlation on the other? More generally, we develop algorithms that guarantee the known properties of dependent rounding, but also have nearly best-possible behavior -- near-independence, which generalizes positive correlation -- on ``small" subsets of the variables. The recent breakthrough of Li \& Svensson for the classical $k$-median problem has to handle positive correlation in certain dependent-rounding settings, and does so implicitly. We improve upon Li-Svensson's approximation ratio for $k$-median from $2.732 + \epsilon$ to $2.611 + \epsilon$ by developing an algorithm that improves upon various aspects of their work. Our dependent-rounding approach helps us improve the dependence of the runtime on the parameter $\epsilon$ from Li-Svensson's $N^{O(1/\epsilon^2)}$ to $N^{O((1/\epsilon) \log(1/\epsilon))}$.

Inapproximability of the Multi-level Uncapacitated Facility Location Problem

Tight lower bound for the channel assignment problem

We study the complexity of the Channel Assignment problem. An open problem asks whether Channel Assignment admits an $O(c^n)$-time algorithm, for a constant $c$ independent of the weights on the edges. We answer this question in the negative i.e. we show that there is no $2^{o(n\log n)}$-time algorithm solving Channel Assignment unless the Exponential Time Hypothesis fails. Note that the currently best known algorithm works in time $O^*(n!) = 2^{O(n\log n)}$ so our lower bound is tight.

On Uniform Capacitated k-Median Beyond the Natural LP Relaxation

In this paper, we study the uniform capacitated k-median problem. In the problem, we are given a set F of potential facility locations, a set C of clients, a metric d over F \cup C, an upper bound k on the number of facilities we can open and an upper bound u on the number of clients each facility can serve. We need to open a subset S \subseteq F of k facilities and connect clients in C to facilities in S so that each facility is connected by at most u clients. The goal is to minimize the total connection cost over all clients. Obtaining a constant approximation algorithm for this problem is a notorious open problem; most previous works gave constant approximations by either violating the capacity constraints or the cardinality constraint. Notably, all these algorithms are based on the natural LP-relaxation for the problem. The LP-relaxation has unbounded integrality gap, even when we are allowed to violate the capacity constraints or the cardinality constraint by a factor of 2-\eps. Our result is an \exp(O(1/\eps^2))-approximation algorithm for the problem that violates the cardinality constraint by a factor of 1+\eps. This is already beyond the capability of the natural LP relaxation, as it has unbounded integrality gap even if we are allowed to open (2-\eps)k facilities. Indeed, our result is based on a novel LP for this problem. We hope that this LP is the first step towards a constant approximation for capacitated k-median.

Tabulating Pseudoprimes and Tabulating Liars

This paper presents new algorithms for two problems related to the Miller-Rabin-Selfridge primality test. The first problem is to tabulate strong pseudoprimes to a fixed base $a$. Tabulating up to $x$ requires $O(x)$ multiplications, where previous methods required $O(x \log{x})$ multiplications. The second problem is to find all strong liars and witnesses, given a fixed odd composite $n$. This appears to be unstudied, and an algorithm is presented that requires $O(n (\log\log{n})^2)$ multiplications. Although interesting in their own right, a notable application is the search for sets of composites with no reliable witness.

Deletion Without Rebalancing in Binary Search Trees

We address the vexing issue of deletions in balanced trees. Rebalancing after a deletion is generally more complicated than rebalancing after an insertion. Textbooks neglect deletion rebalancing, and many B-tree-based database systems do not do it. We describe a relaxation of AVL trees in which rebalancing is done after insertions but not after deletions, yet access time remains logarithmic in the number of insertions. For many applications of balanced trees, our structure offers performance competitive with that of classical balanced trees. With the addition of periodic rebuilding, the performance of our structure is theoretically superior to that of many if not all classic balanced tree structures. Our structure needs lglg(m) + 1 bits of balance information per node, where m is the number of insertions and lg is the base-two logarithm, or lglg(n) + O(1) with periodic rebuilding, where n is the number of nodes. An insertion takes up to two rotations and O(1) amortized time, the same as in standard AVL trees. Using an analysis that relies on an exponential potential function, we show that rebalancing steps occur with a frequency that is exponentially small in the height of the affected node. Our techniques apply to other types of balanced trees, notably B-trees, as we show in a companion paper, and in particular red-black trees, which can be viewed as a special case of B-trees.

Waste Makes Haste: Bounded Time algorithms for Envy-Free Cake Cutting with Free Disposal

We consider the classic problem of envy-free division of a heterogeneous good ("cake") among several agents. It is known that, when the allotted pieces must be connected, the problem cannot be solved by a finite algorithm for 3 or more agents. Even when the pieces may be disconnected, no bounded-time algorithm is known for 5 or more agents. The impossibility result, however, assumes that the entire cake must be allocated. In this paper we replace the entire-allocation requirement with a weaker partial-proportionality requirement: the piece given to each agent must be worth for it at least a certain positive fraction of the entire cake value. We prove that this version of the problem is solvable in bounded time even when the pieces must be connected. We present bounded-time envy-free cake-cutting algorithms for: (1) giving each of $n$ agents a connected piece with a positive value; (2) giving each of 3 agents a connected piece worth at least 1/3; (3) giving each of 4 agents a connected piece worth at least 1/7; (4) giving each of 4 agents a disconnected piece worth at least 1/4; (5) giving each of $n$ agents a disconnected piece worth at least $(1-\epsilon)/n$ for any positive $\epsilon$.

Smoothed Analysis of the 2-Opt Algorithm for the General TSP

2-Opt is a simple local search heuristic for the traveling salesperson problem, which performs very well in experiments both with respect to running time and solution quality. In contrast to this, there are instances on which 2-Opt may need an exponential number of steps to reach a local optimum. To understand why 2-Opt usually finds local optima quickly in experiments, we study its expected running time in the model of smoothed analysis, which can be considered as a less pessimistic variant of worst-case analysis in which the adversarial input is subject to a small amount of random noise. In our probabilistic input model an adversary chooses an arbitrary graph~$G$ and additionally a probability density function for each edge according to which its length is chosen. We prove that in this model the expected number of local improvements is~$O(mn\phi(\log m)^3\cdot 4^{3\sqrt{\ln{m}}})=m^{1+o(1)}n\phi$, where~$n$ and~$m$ denote the number of vertices and edges of~$G$, respectively, and~$\phi$ denotes an upper bound on the density functions.

Space-Constrained Interval Selection

We study streaming algorithms for the interval selection problem: finding a maximum cardinality subset of disjoint intervals on the line. A deterministic $2$-approximation streaming algorithm for this problem is developed, together with an algorithm for the special case of proper intervals, achieving improved approximation ratio of $3/2$. We complement these upper bounds by proving that they are essentially best possible in the streaming setting: it is shown that an approximation ratio of $2 - \epsilon$ (or $3 / 2 - \epsilon$ for proper intervals) cannot be achieved unless the space is linear in the input size. In passing, we also answer an open question of Adler and Azar (J.\ Scheduling 2003) regarding the space complexity of constant-competitive randomized preemptive online algorithms for the same problem.

Semi-Streaming Set Cover

This paper studies the set cover problem under the semi-streaming model. The underlying set system is formalized in terms of a hypergraph $G = (V, E)$ whose edges arrive one-by-one and the goal is to construct an edge cover $F \subseteq E$ with the objective of minimizing the cardinality (cost in the weighted case) of $F$. We consider a parameterized relaxation of this problem, where given some $0 \leq \epsilon < 1$, the goal is to construct an edge $(1 - \epsilon)$-cover, namely, a subset of edges incident to all but an $\epsilon$-fraction of the vertices (or their benefit in the weighted case). The key limitation imposed on the algorithm is that its space is limited to (poly)logarithmically many bits per vertex. Our main result is an asymptotically tight trade-off between $\epsilon$ and the approximation ratio: We design a semi-streaming algorithm that on input hypergraph $G$, constructs a succinct data structure $\mathcal{D}$ such that for every $0 \leq \epsilon < 1$, an edge $(1 - \epsilon)$-cover that approximates the optimal edge \mbox{($1$-)cover} within a factor of $f(\epsilon, n)$ can be extracted from $\mathcal{D}$ (efficiently and with no additional space requirements), where \[ f(\epsilon, n) = \left\{ \begin{array}{ll} O (1 / \epsilon), & \text{if } \epsilon > 1 / \sqrt{n} \\ O (\sqrt{n}), & \text{otherwise} \end{array} \right. \, . \] In particular for the traditional set cover problem we obtain an $O(\sqrt{n})$-approximation. This algorithm is proved to be best possible by establishing a family (parameterized by $\epsilon$) of matching lower bounds.

Sparse Fault-Tolerant BFS Structures

A {\em fault-tolerant} structure for a network is required to continue functioning following the failure of some of the network's edges or vertices. This paper considers {\em breadth-first search (BFS)} spanning trees, and addresses the problem of designing a sparse {\em fault-tolerant} BFS structure, or {\em FT-BFS structure} for short, namely, a sparse subgraph $T$ of the given network $G$ such that subsequent to the failure of a single edge or vertex, the surviving part $T'$ of $T$ still contains a BFS spanning tree for (the surviving part of) $G$. Our main results are as follows. We present an algorithm that for every $n$-vertex graph $G$ and source node $s$ constructs a (single edge failure) FT-BFS structure rooted at $s$ with $O(n \cdot \min\{Depth(s), \sqrt{n}\})$ edges, where $Depth(s)$ is the depth of the BFS tree rooted at $s$. This result is complemented by a matching lower bound. We then consider {\em fault-tolerant multi-source BFS structures}, or {\em FT-MBFS structure} for short, aiming to provide (following a failure) a BFS tree rooted at each source $s\in S$ for some subset of sources $S\subseteq V$. Finally, we propose an $O(\log n)$ approximation algorithm for constructing FT-BFS and FT-MBFS structures.

An Improved Approximation Algorithm for the Edge-Disjoint Paths Problem with Congestion Two

Minimum Latency Submodular Cover

We study the Minimum Latency Submodular Cover problem (MLSC), which consists of a metric $(V,d)$ with source $r\in V$ and $m$ monotone submodular functions $f_1, f_2, ..., f_m: 2^V \rightarrow [0,1]$. The goal is to find a path originating at $r$ that minimizes the total cover time of all functions. This generalizes well-studied problems, such as Submodular Ranking [AzarG11] and Group Steiner Tree [GargKR00]. We give a polynomial time $O(\log \frac{1}{\eps} \cdot \log^{2+\delta} |V|)$-approximation algorithm for MLSC, where $\epsilon>0$ is the smallest non-zero marginal increase of any $\{f_i\}_{i=1}^m$ and $\delta>0$ is any constant. We also consider the Latency Covering Steiner Tree problem (LCST), which is the special case of \mlsc where the $f_i$s are multi-coverage functions. This is a common generalization of the Latency Group Steiner Tree [GuptaNR10, ChakrabartyS11] and Generalized Min-sum Set Cover [AzarGY09, BansalGK10] problems. We obtain an $O(\log^2|V|)$-approximation algorithm for LCST. Finally we study a natural stochastic extension of the Submodular Ranking problem, and obtain an adaptive algorithm with an $O(\log 1/ \eps)$ approximation ratio, which is best possible. This result also generalizes some previously studied stochastic optimization problems, such as Stochastic Set Cover [GoemansV06] and Shared Filter Evaluation [MunagalaSW07,LiuPRY08].

2-Edge Connectivity in Directed Graphs

Edge and vertex connectivity are fundamental concepts in graph theory. While they have been thoroughly studied in the case of undirected graphs, surprisingly not much has been investigated for directed graphs. In this paper we study 2-edge connectivity problems in directed graphs and, in particular, we consider the computation of the following natural relation: We say that two vertices v and w are 2-edge-connected if there are two edge-disjoint paths from v to w and two edge-disjoint paths from w to v. This relation partitions the vertices into blocks such that all vertices in the same block are 2-edge-connected. Differently from the undirected case, those blocks do not correspond to the 2-edge-connected components of the graph. The main result of this paper is an algorithm for computing the 2-edge-connected blocks of a directed graph in linear time. Besides being asymptotically optimal, our algorithm improves significantly over previous bounds. Once the 2-edge-connected blocks are available, we can test in constant time if two vertices are 2-edge-connected. Additionally, when two query vertices v and w are not 2-edge-connected, we can produce in constant time a witness of this property. We are also able to compute in linear time a sparse certificate for this relation, i.e., a subgraph of the input graph that has O(n) edges and maintains the same 2-edge-connected blocks as the input graph, where n is the number of vertices.

How good is multi-pivot quicksort?

Multi-Pivot Quicksort refers to variants of classical quicksort where in the partitioning step k pivots are used to split the input into k + 1 segments. For many years, multi-pivot quicksort was regarded as impractical, but in 2009 a 2-pivot approach by Yaroslavskiy, Bentley, and Bloch was chosen as the standard sorting algorithm in Sun's Java 7. In 2014 at ALENEX, Kushagra et al. introduced an even faster algorithm that uses three pivots. This paper studies what possible advantages multi-pivot quicksort might offer in general. The contributions are as follows: Natural comparison-optimal algorithms for multi-pivot quicksort are devised and analyzed. The analysis shows that the benefits of using multiple pivots with respect to the average comparison count are marginal and these strategies are inferior to simpler strategies such as the well known median-of-k approach. A substantial part of the partitioning cost is caused by rearranging elements. A rigorous analysis of an algorithm for rearranging elements in the partitioning step is carried out, observing mainly how often array cells are accessed during partitioning. The algorithm behaves best if 3 or 5 pivots are used. Experiments show that this translates into good cache behavior and is closest to predicting observed running times of multi-pivot quicksort algorithms. Finally, it is studied how choosing pivots from a sample affects sorting cost.

On the Tradeoff between Stability and Fit

In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments, and must decide how to respond to a new set of constraints, given that each change from the current assignment comes at a price. That is, we would like to maximize the fitness or efficiency of our system, but we need to balance it with the changeout cost from the previous state. We provide a precise formulation for this tradeoff and analyze the resulting {\em stable extensions} of some fundamental problems in measurement and analytics. Our main technical contribution is a stable extension of PPS (probability proportional to size) weighted random sampling, with applications to monitoring and anomaly detection problems. We also provide a general framework that applies to top-k, minimum spanning tree, and assignment. In both cases, we are able to provide exact solutions, and discuss efficient incremental algorithms that can find new solutions as the input changes.

Better Balance by Being Biased: A 0.8776-Approximation for Max Bisection

Dynamic Facility Location via Exponential Clocks

The dynamic facility location problem is a generalization of the classic facility location problem proposed by Eisenstat, Mathieu, and Schabanel to model the dynamics of evolving social/infrastructure networks. The generalization lies in that the distance metric between clients and facilities changes over time. This leads to a trade-off between optimizing the classic objective function and the "stability" of the solution: there is a switching cost charged every time a client changes the facility to which it is connected. While the standard linear program (LP) relaxation for the classic problem naturally extends to this problem, traditional LP-rounding techniques do not, as they are often sensitive to small changes in the metric resulting in frequent switches. We present a new LP-rounding algorithm for facility location problems, which yields the first constant approximation algorithm for the dynamic facility location problem. Our algorithm installs competing exponential clocks on the clients and facilities, and connect every client by the path that repeatedly follows the smallest clock in the neighborhood. The use of exponential clocks gives rise to several properties that distinguish our approach from previous LP-roundings for facility location problems. In particular, we use no clustering and we allow clients to connect through paths of arbitrary lengths. In fact, the clustering-free nature of our algorithm is crucial for applying our LP-rounding approach to the dynamic problem.


Publication Years 2005-2016
Publication Count 524
Citation Count 3028
Available for Download 524
Downloads (6 weeks) 1557
Downloads (12 Months) 15099
Downloads (cumulative) 202784
Average downloads per article 387
Average citations per article 6
First Name Last Name Award
Lars Arge ACM Distinguished Member (2009)
Moses S Charikar ACM Paris Kanellakis Theory and Practice Award (2012)
Anne Condon ACM Doctoral Dissertation Award
Series Winner (1988) ACM Doctoral Dissertation Award
Series Winner (1988)
Graham R. Cormode ACM Distinguished Member (2013)
Constantinos Daskalakis ACM Doctoral Dissertation Award (2008)
Xiaotie Deng ACM Senior Member (2006)
Martin Dietzfelbinger ACM Distinguished Member (2011)
Pedro F Felzenszwalb ACM Grace Murray Hopper Award (2013)
Michael T Goodrich ACM Distinguished Member (2006)
Leonidas J Guibas ACM AAAI Allen Newell Award (2007)
Venkatesan Guruswami ACM Doctoral Dissertation Award (2002)
Piotr Indyk ACM Paris Kanellakis Theory and Practice Award (2012)
Charles E Leiserson ACM-IEEE CS Ken Kennedy Award (2014)
ACM Paris Kanellakis Theory and Practice Award (2013)
ACM Doctoral Dissertation Award (1982)
Kurt Mehlhorn ACM Paris Kanellakis Theory and Practice Award (2010)
Mukesh Mohania ACM Distinguished Member (2011)
Noam Nissan ACM Doctoral Dissertation Award
Series Winner (1990) ACM Doctoral Dissertation Award
Series Winner (1990)
Omer Reingold ACM Grace Murray Hopper Award (2005)
Sandeep K Shukla ACM Distinguished Member (2012)
ACM Senior Member (2007)
David Steurer ACM Doctoral Dissertation Award
Honorable Mention (2011) ACM Doctoral Dissertation Award
Honorable Mention (2011)
Madhu Sudan ACM Doctoral Dissertation Award (1993)
Subhash Suri ACM Distinguished Member (2007)
Robert E Tarjan ACM Paris Kanellakis Theory and Practice Award (1999)
ACM A. M. Turing Award (1986)
Salil P Vadhan ACM Doctoral Dissertation Award (2000)
Jeffrey S Vetter ACM Distinguished Member (2012)
ACM Gordon Bell Prize
Performance (2010)
Jennifer L Welch ACM Distinguished Member (2012)

First Name Last Name Paper Counts
MohammadTaghi Hajiaghayi 12
Dániel Marx 11
Guy Kortsarz 10
Erik Demaine 8
Uri Zwick 8
Robert Tarjan 7
Mikkel Thorup 7
Samir Khuller 7
Gonzalo Navarro 6
Magnús Halldórsson 6
Pankaj Agarwal 6
Zeev Nutov 6
Haim Kaplan 6
Moshe Lewenstein 6
Noga Alon 6
Rohit Khandekar 5
Ke Yi 5
David Eppstein 5
David Peleg 5
Chandra Chekuri 5
Andrzej Pelc 5
Kirk Pruhs 5
Hadas Shachnai 5
Micha Sharir 5
Raphael Yuster 5
Joseph Naor 5
Inge Gørtz 5
Venkatesh Raman 5
Saket Saurabh 5
Michael Elkin 5
Yossi Azar 5
Shay Solomon 5
S Muthukrishnan 5
Liam Roditty 5
Maxim Sviridenko 5
Nikhil Bansal 5
Anupam Gupta 5
Telikepalli Kavitha 4
Thore Husfeldt 4
Glencora Borradaile 4
Fedor Fomin 4
Dana Ron 4
Ashish Goel 4
Daniel Lokshtanov 4
Oren Weimann 4
Baruch Schieber 4
Timothy Chan 4
Graham Cormode 4
Guy Even 4
Viswanath Nagarajan 4
Sudipto Guha 4
Paolo Ferragina 4
Mohammad Salavatipour 4
Philip Klein 4
Susanne Albers 4
Ignaz Rutter 4
Seth Pettie 4
Sariel Har-Peled 4
Kurt Mehlhorn 4
Asaf Levin 4
Andrew McGregor 3
Adi Rosén 3
Dror Rawitz 3
Artur Czumaj 3
Alberto Marchetti-Spaccamela 3
Surender Baswana 3
Daniel Berend 3
Harald Räcke 3
Stephen Alstrup 3
Edward Reingold 3
Rob Van Stee 3
Leah Epstein 3
Sanjeev Khanna 3
Amotz Bar-Noy 3
Julia Chuzhoy 3
Dimitrios Thilikos 3
Marek Cygan 3
Harold Gabow 3
Christian Sohler 3
Boris Aronov 3
Pat Morin 3
Gabriel Scalosub 3
Srinivasa Satti 3
Meng He 3
George Karakostas 3
Shai Gutner 3
Baruch Awerbuch 3
Fabrizio Grandoni 3
Wojciech Szpankowski 3
Amol Deshpande 3
Amos Korman 3
Jeff Edmonds 3
Laurent Alonso 3
Kazuo Iwama 3
Sergio Cabello 3
Marek Chrobak 3
Chaitanya Swamy 3
Amit Chakrabarti 3
Rajiv Gandhi 3
David Johnson 3
Danny Segev 3
Stefan Kratsch 3
Zoya Svitkina 3
Dimitrios Michail 3
Refael Hassin 3
Philip Bille 3
Ramamoorthi Ravi 3
Martín Farach-Colton 3
Amin Saberi 3
Yuval Rabani 3
Joseph Cheriyan 3
Morteza Zadimoghaddam 3
Lisa Hellerstein 3
Ioannis Caragiannis 2
Ola Svensson 2
Tami Tamir 2
Anne Driemel 2
Djamal Belazzougui 2
Adrian Vetta 2
Dilys Thomas 2
John Iacono 2
Holeung Chan 2
Kunihiko Sadakane 2
Teofilo Gonzalez 2
Roy Schwartz 2
Jérémy Barbay 2
Milan Ružić 2
Antoine Vigneron 2
R Sritharan 2
Konstantin Makarychev 2
Andréa Richa 2
Leen Stougie 2
Rajeev Raman 2
Rossano Venturini 2
Dariusz Kowalski 2
Katarzyna Paluch 2
Jochen Könemann 2
Holger Dell 2
Magnus Wahlström 2
Cristopher Moore 2
Berthold Vöcking 2
Michael Bender 2
Svante Janson 2
Andreas Björklund 2
Loukas Georgiadis 2
Christoph Ambühl 2
Hiroki Yanagisawa 2
Tobias Jacobs 2
Conrado Martínez 2
Alfredo Viola 2
Don Coppersmith 2
Atri Rudra 2
Zachary Friggstad 2
Stefan Langerman 2
Amihood Amir 2
Joan Boyar 2
Joseph Leung 2
Joe Sawada 2
Peter Korteweg 2
Camil Demetrescu 2
Giuseppe Italiano 2
Alex Kesselman 2
Clifford Stein 2
Kamesh Munagala 2
HoLeung Chan 2
Venkatesan Guruswami 2
Thomas Erlebach 2
MohammadHossein Bateni 2
Irene Finocchi 2
Hans Bodlaender 2
Vijay Kumar 2
Bernhard Haeupler 2
Carmit Hazay 2
Bundit Laekhanukit 2
Thomas Sauerwald 2
An Zhu 2
Lisa Fleischer 2
Rina Panigrahy 2
Lisa Zhang 2
Veli Mäkinen 2
Takwah Lam 2
Lapchi Lau 2
Pierre Fraigniaud 2
Hamid Mahini 2
Subhash Suri 2
James Aspnes 2
Éva Tardos 2
Claire Mathieu 2
Yury Makarychev 2
Hamid Nazerzadeh 2
Matthew Andrews 2
Michael Drmota 2
Bodo Manthey 2
Dimitris Fotakis 2
Michele Flammini 2
Helmut Prodinger 2
Alexandr Andoni 2
Dina Sokol 2
Eduardo Laber 2
Konstantinos Panagiotou 2
Jie Gao 2
Kenichi Kawarabayashi 2
MohammadTaghi Hajiaghayi 2
Christophe Paul 2
Ulrich Meyer 2
Petr Kolman 2
Iftah Gamzu 2
Somnath Sikdar 2
Jesper Nederlof 2
Ioannis Koutis 2
Roberto Grossi 2
Benjamin Raichel 2
Angelika Steger 2
Mingyang Kao 2
Shanghua Teng 2
Jon Feldman 2
Anastasios Sidiropoulos 2
Mikko Koivisto 2
Ignasi Sau 2
Christos Kaklamanis 2
Klaus Jansen 2
Martin Skutella 2
Tomás Feder 2
Cyril Gavoille 2
Julián Mestre 2
Luca Becchetti 2
Mohammad Mahdian 2
Jiří Sgall 2
Dieter Kratsch 2
Geevarghese Philip 2
Thomas Bläsius 2
Dekel Tsur 2
Yoann Dieudonné 2
Suresh Venkatasubramanian 2
Lars Arge 2
Ittai Abraham 2
Allan Borodin 2
Vincenzo Bonifaci 2
Alexander Russell 2
Yishay Mansour 2
Ramakrishna Thurimella 2
Kenneth Clarkson 2
Goran Konjevod 2
Jittat Fakcharoenphol 2
John Hershberger 2
Yonatan Aumann 2
Adam Meyerson 2
Shay Mozes 2
Joan Feigenbaum 2
Shuichi Miyazaki 2
Theis Rauhe 2
Martin Aumüller 1
Sándor Fekete 1
Frank Staals 1
Jeremy Fineman 1
Philip Klein 1
Alexander Golovnev 1
Ryan Williams 1
Johannes Fischer 1
Jérémie Chalopin 1
Yann Disser 1
Vít Jelínek 1
Aaron Williams 1
Krishnaram Kenthapadi 1
Daniel Lemire 1
Mark De Berg 1
Ron Levy 1
Bastian Pochon 1
Gerhard Woeginger 1
Hsienkuei Hwang 1
Gad Landau 1
Shmuel Safra 1
Martin Gairing 1
Kasturi Varadarajan 1
Niv Buchbinder 1
Vanbang Le 1
Alessandro Panconesi 1
Steve Oudot 1
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Rogers Mathew 1
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Fenghui Zhang 1
Anke Truß 1
Roberto De Prisco 1
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Kedar Dhamdhere 1
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Paul Medvedev 1
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Walter Kern 1
Jessica Chang 1
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Ari Freund 1
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Norbert Zeh 1
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F Bruss 1
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Prudence Wong 1
Daniel Golovin 1
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Pedro Felzenszwalb 1
Sambuddha Roy 1
Lusheng Wang 1
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Eric De Verdiere 1
Alexander Schrijver 1
Yuval Ishai 1
Łukasz Jeż 1
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Satish Rao 1
Arie Koster 1
Ely Porat 1
Alexander Hall 1
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Richard Ladner 1
Daming Zhu 1
Peter Grabner 1
Hoyee Cheung 1
Arnaud Labourel 1
Li Ning 1
Daniel Blandford 1
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Justin Thaler 1
Alon Shalita 1
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Huy Nguyeݱn 1
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Shantanu Das 1
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Iam Roditty 1
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J Munro 1
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Richard Geary 1
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William Aiello 1
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David Wood 1
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Mark Pedigo 1
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T Jayram 1
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Yang Liu 1
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Ning Chen 1
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Sen Zhang 1
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Alexander Izsak 1
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Arash Asadpour 1
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Nira Shafrir 1
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Martin Jaggi 1
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Jing Wang 1
Amnon Ta-Shma 1
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Ofer Neiman 1
Mihai P&acaron;trascu 1
Linus Hamilton 1
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Noa Avigdor-Elgrabli 1
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Virginia Vassilevska 1
Elliot Anshelevich 1
Vijaya Ramachandran 1
Michiel Smid 1
Cunquan Zhang 1
ChiaChi Yeh 1
Dahlia Malkhi 1
Paul LaFollette 1
Rajneesh Hegde 1
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William Evans 1
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Tao Jiang 1
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Hiro Ito 1
Jeff Erickson 1
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David Woodruff 1
Marcin Pilipczuk 1
Amin Sayedi-Roshkhar 1
Qin Zhang 1
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Panos Giannopoulos 1
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Xin Han 1
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Mark Ward 1
Konstantin Andreev 1
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Pranjal Awasthi 1
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Igor Razgon 1
Clemens Heuberger 1
SiuWing Cheng 1
Jurek Czyzowicz 1
Shuchi Chawla 1
Amitabh Sinha 1
András Benczúr 1
Claire Mathieu 1
Ning Chen 1
Funda Ergün 1
Marcel Silva 1
Rishi Saket 1
Petteri Kaski 1
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Lukáš Poláček 1
Liam Mencel 1
Dorothea Wagner 1
Moran Feldman 1
Saber Fadaee 1
Fabrizio Frati 1
László Végh 1
Benjamin Doerr 1
N Narayanaswamy 1
Arturo Gonzalez-Gutierrez 1
Shahar Fattal 1
Claire Kenyon 1
Owen Kaser 1
Emden Gansner 1
Jim Pugh 1
Hsueh Lu 1
Michael Fuchs 1
Manuel Kauers 1
Giovanni Manzini 1
Ryan Hayward 1
Jin Zhang 1
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Charles Tresser 1
Kaimin Chung 1
Salil Vadhan 1
Marco Molinaro 1
Luca Foschini 1
Piotr Krysta 1
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Jennifer Welch 1
Xin Chen 1
Claus Jensen 1
Steven Skiena 1
Sangil Oum 1
Alex Scott 1
Phong Nguyêñ 1
Matt DeVos 1
John Carlsson 1
Yusu Wang 1
Leonidas Guibas 1
Jakub Łącki 1
Dömötör Pálvölgyi 1
Bogdan Chlebus 1
Moses Charikar 1
Venkatesh Natarajan 1
Matthew Maxel 1
Yijie Han 1
Michael Krivelevich 1
Hiroshi Fujiwara 1
Eldar Fischer 1
Ying Xu 1
Louis Ibarra 1
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Panagiotis Cheilaris 1
Gruia Călinescu 1
Fabrizio Luccio 1
Xiaotie Deng 1
Juanjo Rué 1
Martin Pál 1
Uriel Feige 1
SéBastien Collette 1
Marcelo De Carvalho 1
Kristian Lichtenberg 1
David Hay 1
Kinsum Mak 1
Renato Werneck 1
Leszek Gąsieniec 1
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Stephen Kobourov 1
Amir Sapir 1
Kobbi Nissim 1
Christina Fragouli 1
Christian Sommer 1
Atlas IV 1
Ekkehard Köhler 1
Mark Petrick 1
George Yuhasz 1
Himanshu Gupta 1
Robert Krauthgamer 1
Mikkel Thorup 1
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Keren Censor 1
Cristiane Sato 1
Jelani Nelson 1
Vitaly Feldman 1
Poshen Loh 1
Joseph Mitchell 1
Valentin Polishchuk 1
Jukka Suomela 1
Marc Van Kreveld 1
Ran Raz 1
Alexander Langer 1
Alexander Kulikov 1
Aravind Srinivasan 1
Ivan Mihajlin 1
Shi Li 1
Siuwing Cheng 1
Hjalte VildhØj 1
Csaba Tóth 1
Donglin Xia 1
Rajesh Chitnis 1
MohammadAmin Fazli 1
Sina Sadeghabad 1
MohammadAli Safari 1
Dannyziyi Chen 1
Jan Kratochvíl 1
Richard Cole 1
M Ramanujan 1
Stanislav Živný 1
Frank Ruskey 1
Shay Kutten 1
Gagan Aggarwal 1
Shimon Shahar 1
Hisao Tamaki 1
Hung Yu 1
Markus Püschel 1
M Paal 1
Lene Favrholdt 1
Vladlen Koltun 1
Gilad Tsur 1
Tomasz Nowicki 1
Avner Magen 1
Karsten Tiemann 1
Sandeep Sen 1
Justus Schwartz 1
Alexey Stepanov 1
Rohan Fernandes 1
Bojan Mohar 1
David Fernández-Baca 1
Ulrich Faigle 1
Reid Andersen 1
Valerie King 1
Constantinos Daskalakis 1
Thomas Rothvoß 1
Yusuke Kobayashi 1
Sebastian Böcker 1
Greg Little 1
Satish Rao 1
Chris Harrelson 1
Oded Lachish 1
Orly Yahalom 1
François Nicolas 1
Nishanth Chandran 1
Mohammad Safari 1
Jens Vygen 1
Shakhar Smorodinsky 1
Mihai Bǎdoiu 1
Bob Sedgewick 1
Francis Chin 1
Nikos Karanikolas 1
Piyush Kurur 1
Alessandro Panconesi 1
Jaikumar Radhakrishnan 1
Julien Clément 1
Pierre Nicodème 1
Balaji Raghavachari 1
Mordecai Golin 1
Guy Louchard 1
Tomasz Radzik 1
Irit Katriel 1
Hu Zhang 1
Sivan Toledo 1
Ge Nong 1
Nicole Megow 1
Erich Kaltofen 1
Piotr Indyk 1
Stefan Hougardy 1
Micah Adler 1
T Chan 1
Martin Hoefer 1
StéPhan Thomassé 1
Danny Hermelin 1
Benjamin Aminof 1
Orna Kupferman 1
Prasad Raghavendra 1
Yi Wu 1
Guillaume Moroz 1
Alex Levin 1

Affiliation Paper Counts
University of Durham 1
Meiji University 1
Medical University of South Carolina 1
National Taiwan Ocean University 1
Georgetown University 1
Shanghai Jiaotong University 1
University College Cork 1
University of Tokyo 1
Rensselaer Polytechnic Institute 1
Indian Institute of Technology, Madras 1
University of Vienna 1
Netanya Academic College 1
Lawrence Livermore National Laboratory 1
University of Melbourne 1
DePaul University 1
Stevens Institute of Technology 1
Kwansei Gakuin University 1
Institute for Advanced Studies 1
Oracle Corporation 1
University of Quebec in Montreal 1
Sant'Anna School of Advanced Studies 1
University of Eastern Piedmont Amedeo Avogadro, Alessandria 1
University of Leoben 1
Siemens AG 1
Ludwig Maximilian University of Munich 1
University of Miami 1
The University of Georgia 1
Wesleyan University Middletown 1
Cisco Systems 1
University of Milan 1
Pavol Jozef safarik University in Kosice 1
California Institute of Technology 1
Utah State University 1
Michigan State University 1
Korea Advanced Institute of Science & Technology 1
University of Wisconsin Madison 1
University of Electro-Communications 1
Saarland University 1
Sobolev Institute of Mathematics of Siberian Branch of the RAS 1
Google Switzerland GmbH 1
NEC Deutschland GmbH 1
Istituto di Scienza e Tecnologie dell'Informazione A. Faedo 1
ORT Braude - College of Engineering 1
Intertrust Technologies Corporation 1
Microsoft Research Cambridge 1
VMware, Inc 1
Laboratoire d'Analyse et Modelisation de Systemes pour l'Aide a la Decision 1
SRI International 1
Harvey Mudd College 1
Emory University 1
University of Michigan 1
Universite Pierre et Marie Curie 1
University of Glasgow 1
University of Stellenbosch 1
Center for Communications Research 1
National Technical University of Athens 1
Toyohashi University of Technology 1
Vanderbilt University 1
Zhejiang University 1
IBM Tokyo Research Laboratory 1
Iowa State University 1
Dalian University of Technology 1
University of G. d'Annunzio Chieti and Pescara 1
J. Craig Venter Institute 1
Ecole Normale Superieure de Lyon 1
Los Alamos National Laboratory 1
University of Western Macedonia 1
National Institutes of Health, Bethesda 1
University of Missouri-Kansas City 1
Sandia National Laboratories, New Mexico 1
Laboratoire d'Informatique, de Robotique et de Microelectronique de Montpellier LIRMM 1
Technical University in Braunschweig 1
Malmo University 1
University of Sao Paulo 1
Vrije Universiteit Amsterdam 1
Hong Kong Polytechnic University 1
Birkbeck University of London 1
Linkoping University 1
Universite Paris 13 1
University of Colorado at Denver 1
Kyushu University 1
BRICS Basic Research in Computer Science 1
National Chiao Tung University Taiwan 1
Lubeck University 1
Duquesne University 1
University of Texas at Austin 1
INRIA Institut National de Rechereche en Informatique et en Automatique 1
Indian Institute of Technology, Bombay 1
Hong Kong Baptist University 1
University of California, Davis 1
Dalle Molle Institute for Artificial Intelligence 1
Federal University of Parana 1
Florida International University 1
University of Witwatersrand 1
Holon Institute of Technology 1
Academia Sinica Taiwan 1
University of New Brunswick 1
University of Tubingen 1
Aegean University 1
George Mason University 1
Universite Bordeaux 1 1
Boston University 1
University of Wisconsin Milwaukee 1
Saint Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences 1
Brandenburg University of Technology Cottbus 1
Hewlett-Packard 1
University of Bristol 1
California State University Northridge 1
Sun Yat-Sen University 1
State University of New York College at Oneonta 1
Johannes Kepler University Linz 1
Pennsylvania State University 2
London School of Economics and Political Science 2
University of Texas at San Antonio 2
Ohio State University 2
University of Rostock 2
Uppsala University 2
Mentor Graphics Corporation 2
University of Ioannina 2
North Carolina State University 2
Instituto Superior Tecnico 2
National Taiwan University 2
Tohoku University 2
University of Dayton 2
University of Texas at Dallas 2
University of Kaiserslautern 2
University of Arizona 2
King's College London 2
Center for Mathematics and Computer Science - Amsterdam 2
University of Trier 2
The Interdisciplinary Center Herzliya 2
Seoul National University 2
City University of Hong Kong 2
University of Denver 2
University of Guelph 2
Dalhousie University 2
Universite de Picardie Jules Verne 2
National University of Singapore 2
University of L'Aquila 2
Graz University of Technology 2
Royal Holloway University of London 2
West Virginia University 2
University of Notre Dame 2
Kasetsart University 2
University of Iowa 2
Universite Paris-Sud XI 2
Eotvos Lorand University 2
Tsinghua University 2
University of Utah 2
University of Freiburg 2
Microsoft 2
University of Oxford 2
Universite Paul Verlaine - Metz 2
St. Louis University 2
Research Organization of Information and Systems National Institute of Informatics 2
University of Chicago 2
University of Aarhus 2
Universite d'Orleans 2
Technical University of Ilmenau 2
Temple University 2
Free University of Berlin 2
University of Cambridge 2
Tata Institute of Fundamental Research 2
University of Nevada, Las Vegas 2
Universite de Caen Basse Normandie 2
Pontifical Catholic University of Rio de Janeiro 2
Indian Institute of Technology, Delhi 2
University of Puerto Rico 2
Universidad de la Republica 2
Microsoft Research Asia 2
Universite de Bordeaux 2
Aalto University 2
Ecole Normale Superieure 3
University of Colorado at Boulder 3
Helsinki Institute for Information Technology 3
Royal Institute of Technology 3
University of Helsinki 3
Johns Hopkins University 3
Nanyang Technological University 3
Northwestern University 3
University of Bonn 3
Johann Wolfgang Goethe University of Frankfurt 3
Harvard University 3
University of Texas-Pan American 3
IBM Research 3
Oregon State University 3
Ecole Polytechnique 3
Texas A and M University 3
University of Connecticut 3
New Jersey Institute of Technology 3
Brooklyn College 3
University of Sydney 3
Laboratoire d'Informatique de l'Ecole Polytechnique 3
Shandong University 3
University of Ljubljana 3
Academy of Sciences of the Czech Republic (Avcr.Cz) 3
University at Buffalo, State University of New York 3
York University Canada 3
University of Iceland 3
Toyota Technological Institute at Chicago 3
King Abdullah University of Science and Technology 3
Aix Marseille Universite 3
Chinese University of Hong Kong 4
University of Victoria 4
IBM India Research Laboratory New Delhi 4
Arizona State University 4
Yale University 4
City University of New York 4
University of Salerno 4
Universitat Politecnica de Catalunya 4
Roma Tre University 4
Indian Institute of Science 4
AT&T Inc. 4
INRIA Lorraine 4
National Tsing Hua University 4
University of Southern Denmark 4
Georgia Institute of Technology 4
University of Twente 4
Universite Montpellier 2 Sciences et Techniques 4
Computer and Automation Research Institute Hungarian Academy of Sciences 4
Virginia Tech 4
University of Athens 4
University of Southern California 4
Karlsruhe Institute of Technology, Campus South 4
Budapest University of Technology and Economics 4
University of Dortmund 4
University of New Mexico 4
Reykjavik University 4
Illinois Institute of Technology 5
Cornell University 5
Alcatel-Lucent Bell Labs 5
IBM Almaden Research Center 5
Purdue University 5
University of Kiel 5
University of Massachusetts Amherst 5
University of Washington Seattle 5
University of Wroclaw 5
Indian Institute of Technology, Kanpur 5
University of Roma Tor Vergata 5
Hungarian Academy of Sciences 5
University of California, Riverside 5
McMaster University 5
Yahoo Research Labs 5
Universite Libre de Bruxelles 6
Humboldt University of Berlin 6
MIT Computer Science and Artificial Intelligence Laboratory 6
Utrecht University 6
The University of British Columbia 6
Dartmouth College 6
Kyoto University 6
University of Pittsburgh 6
Charles University in Prague 6
Vienna University of Technology 6
Simon Fraser University 6
IT University of Copenhagen 6
University of Quebec in Outaouais 6
New York University 6
Columbia University 6
University of California, San Diego 6
University of Leicester 6
Karlsruhe Institute of Technology 6
Polytechnic University - Brooklyn 7
University of California, Irvine 7
University of Toronto 7
The University of Warwick 7
Open University of Israel 7
University Michigan Ann Arbor 7
Stony Brook University 7
University of California, Santa Barbara 7
University of Copenhagen 7
University of Patras 7
University of Illinois at Urbana-Champaign 8
McGill University 8
University of Illinois 8
Universite Paris 7- Denis Diderot 8
Technical University of Denmark 8
University of Warsaw 8
Carleton University 8
University of Liverpool 8
University of California, Los Angeles 8
Sharif University of Technology 8
Lund University 8
Rutgers, The State University of New Jersey 8
University of Pennsylvania 9
Hebrew University of Jerusalem 9
Duke University 9
Technical University of Berlin 9
Universidad de Chile 9
RWTH Aachen University 9
University of Paderborn 9
University of California, Berkeley 9
Swiss Federal Institute of Technology, Zurich 9
Swiss Federal Institute of Technology, Lausanne 9
University of Pisa 9
Friedrich Schiller University Jena 9
University of Bergen 9
University of Alberta 10
Hong Kong University of Science and Technology 11
Brown University 11
Eindhoven University of Technology 11
Princeton University 13
The University of Hong Kong 13
Rutgers University-Camden campus 14
Institute of Mathematical Sciences India 14
University of Roma La Sapienza 14
Microsoft Research 15
Weizmann Institute of Science Israel 16
University of Haifa 18
Google Inc. 18
AT&T Laboratories Florham Park 18
IBM Thomas J. Watson Research Center 18
Stanford University 21
University of Maryland 21
Bar-Ilan University 23
Ben-Gurion University of the Negev 24
Max Planck Institute for Informatics 25
Carnegie Mellon University 25
Massachusetts Institute of Technology 27
University of Waterloo 28
Technion - Israel Institute of Technology 30
Tel Aviv University 69

ACM Transactions on Algorithms (TALG)

Volume 12 Issue 4, August 2016  Issue-in-Progress
Volume 12 Issue 3, June 2016
Volume 12 Issue 2, February 2016
Volume 12 Issue 1, February 2016 Special Issue on SODA'12 and Regular Papers

Volume 11 Issue 4, June 2015
Volume 11 Issue 3, January 2015

Volume 11 Issue 2, November 2014
Volume 11 Issue 1, October 2014
Volume 10 Issue 4, August 2014
Volume 10 Issue 3, June 2014
Volume 10 Issue 2, February 2014
Volume 10 Issue 1, January 2014

Volume 9 Issue 4, September 2013
Volume 9 Issue 3, June 2013 Special Issue on SODA'11
Volume 9 Issue 2, March 2013

Volume 9 Issue 1, December 2012
Volume 8 Issue 4, September 2012
Volume 8 Issue 3, July 2012
Volume 8 Issue 2, April 2012
Volume 8 Issue 1, January 2012

Volume 7 Issue 4, September 2011
Volume 7 Issue 3, July 2011
Volume 7 Issue 2, March 2011

Volume 7 Issue 1, November 2010
Volume 6 Issue 4, August 2010
Volume 6 Issue 3, June 2010
Volume 6 Issue 2, March 2010

Volume 6 Issue 1, December 2009
Volume 5 Issue 4, October 2009
Volume 5 Issue 3, July 2009
Volume 5 Issue 2, March 2009

Volume 5 Issue 1, November 2008
Volume 4 Issue 4, August 2008
Volume 4 Issue 3, June 2008
Volume 4 Issue 2, May 2008
Volume 4 Issue 1, March 2008

Volume 3 Issue 4, November 2007
Volume 3 Issue 3, August 2007
Volume 3 Issue 2, May 2007
Volume 3 Issue 1, February 2007

Volume 2 Issue 4, October 2006
Volume 2 Issue 3, July 2006
Volume 2 Issue 2, April 2006
Volume 2 Issue 1, January 2006

Volume 1 Issue 2, October 2005
Volume 1 Issue 1, July 2005
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