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A Distributed Augmenting Path Approach for the Bottleneck Assignment Problem

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Improved Ramsey-type results for comparability graphs

Istvan Tomon, Dániel József Korándi

Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is ...

CAMBRIDGE UNIV PRESS2020

Weighted Matchings via Unweighted Augmentations

Ola Nils Anders Svensson, Slobodan Mitrovic, Buddhima Ruwanmini Gamlath Gamlath Ralalage

We design a generic method to reduce the task of finding weighted matchings to that of finding short augmenting paths in unweighted graphs. This method enables us to provide efficient implementations for approximating weighted matchings in the massively pa ...

ASSOC COMPUTING MACHINERY2019

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

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

Generalized Turan problems for disjoint copies of graphs

Abhishek Methuku

Given two graphs H and F, the maximum possible number of copies of H in an F-free graph on n vertices is denoted by ex(n, H, F). We investigate the function ex(n, H, kF), where kF denotes k vertex disjoint copies of a fixed graph F. Our results include cas ...

ELSEVIER2019

Tight Bounds for Online Edge Coloring

David Wajc

Vizing's celebrated theorem asserts that any graph of maximum degree Delta admits an edge coloring using at most Delta + 1 colors. In contrast, Bar-Noy, Motwani and Naor showed over a quarter century ago that the trivial greedy algorithm, which uses 2 Delt ...

IEEE COMPUTER SOC2019

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

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

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

Extension complexity of stable set polytopes of bipartite graphs

Yuri Faenza, Manuel Francesco Aprile

The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that affinely projects to P. Let G be a bipartite graph with n vertices, m edges, and no isolated vertices. Let STAB(G) be the convex hull of the stable sets of G. ...

Springer2017