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Weighted Matchings via Unweighted Augmentations

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New Graph Algorithms via Polyhedral Techniques

Jakub Tarnawski

In this thesis we give new algorithms for two fundamental graph problems. We develop novel ways of using linear programming formulations, even exponential-sized ones, to extract structure from problem instances and to guide algorithms in making progress. S ...

EPFL2019

Construction of Polar Codes With Sublinear Complexity

Rüdiger Urbanke, Seyed Hamed Hassani, Marco Mondelli

Consider the problem of constructing a polar code of block length N for a given transmission channel W. Previous approaches require one to compute the reliability of the N synthetic channels and then use only those that are sufficiently reliable. However, ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Analysis of a Canonical Labeling Algorithm for the Alignment of Correlated Erdős-Rényi Graphs

Matthias Grossglauser, Negar Kiyavash, Osman Emre Dai

Graph alignment in two correlated random graphs refers to the task of identifying the correspondence between vertex sets of the graphs. Recent results have characterized the exact information-theoretic threshold for graph alignment in correlated Erdös-Rény ...

Association for Computing Machinery (ACM)2019

Anytime Heuristic for Weighted Matching Through Altruism-Inspired Behavior

Boi Faltings, Aris Filos Ratsikas, Panayiotis Danassis

We present a novel anytime heuristic (ALMA), inspired by the human principle of altruism, for solving the assignment problem. ALMA is decentralized, completely uncoupled, and requires no communication between the participants. We prove an upper bound on th ...

2019

Online Matching with General Arrivals

Ola Nils Anders Svensson, Mikhail Kapralov, Buddhima Ruwanmini Gamlath Gamlath Ralalage, Andreas Maggiori, David Wajc

The online matching problem was introduced by Karp, Vazirani and Vazirani nearly three decades ago. In that seminal work, they studied this problem in bipartite graphs with vertices arriving only on one side, and presented optimal deterministic and randomi ...

IEEE COMPUTER SOC2019

When Stuck, Flip a Coin

Slobodan Mitrovic

Many modern services need to routinely perform tasks on a large scale. This prompts us to consider the following question: How can we design efficient algorithms for large-scale computation? In this thesis, we focus on devising a general strategy to addr ...

EPFL2018

Finding Perfect Matchings in Bipartite Hypergraphs

Chidambaram Annamalai

Haxell's condition [14] is a natural hypergraph analog of Hall's condition, which is a well-known necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell's condition holds it forces the existence of a perf ...

SPRINGER HEIDELBERG2018

Round Compression for Parallel Matching Algorithms

Slobodan Mitrovic, Aleksander Madry

For over a decade now we have been witnessing the success of massive parallel computation (MPC) frameworks, such as MapReduce, Hadoop, Dryad, or Spark. One of the reasons for their success is the fact that these frameworks are able to accurately capture th ...

ASSOC COMPUTING MACHINERY2018

Improved Massively Parallel Computation Algorithms for MIS, Matching, and Vertex Cover

Slobodan Mitrovic, Mohsen Ghaffari

We present O(log log n)-round algorithms in the Massively Parallel Computation (MPC) model, with a(n) memory per machine, that compute a maximal independent set, a 1 + epsilon approximation of maximum matching, and a 2 + epsilon approximation of minimum ve ...

ASSOC COMPUTING MACHINERY2018

The weighted stable matching problem

Linda Farczadi

We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be NP-hard in general ...

2017