Publications related to Online Matching with General Arrivals

A Distributed Augmenting Path Approach for the Bottleneck Assignment Problem

We develop an algorithm to solve the bottleneck assignment problem (BAP) that is amenable to having computation distributed over a network of agents. This consists of exploring how each component of the algorithm can be distributed, with a focus on one com ...

Ieee-Inst Electrical Electronics Engineers Inc2024

How to Match in Modern Computational Settings

Buddhima Ruwanmini Gamlath Gamlath Ralalage

This thesis focuses on the maximum matching problem in modern computational settings where the algorithms have to make decisions with partial information. First, we consider two stochastic models called query-commit and price-of-information where the algo ...

EPFL2021

Faster Monotone Min-Plus Product, Range Mode, and Single Source Replacement Paths

Adam Teodor Polak

One of the most basic graph problems, All-Pairs Shortest Paths (APSP) is known to be solvable in n^{3-o(1)} time, and it is widely open whether it has an O(n^{3-ε}) time algorithm for ε > 0. To better understand APSP, one often strives to obtain subcubic t ...

Schloss Dagstuhl -- Leibniz-Zentrum für Informatik2021

Minimum-Error Classes for Matching Parts

Thomas Alois Weber

This paper examines the binning of two types of parts with random characteristics, so that a componentwise monotonic evaluation criterion exhibits a minimum deviation to a given target value over all possible realizations. The optimal matching classes are ...

2021

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

On subgraphs of C-2k-free graphs and a problem of Kuhn and Osthus

Abhishek Methuku

Let c denote the largest constant such that every C-6-free graph G contains a bipartite and C-4-free subgraph having a fraction c of edges of G. Gyori, Kensell and Tompkins showed that 3/8

2020

Space Efficient Approximation to Maximum Matching Size from Uniform Edge Samples

Mikhail Kapralov, Slobodan Mitrovic, Ashkan Norouzi Fard, Jakab Tardos

Given a source of iid samples of edges of an input graph G with n vertices and m edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in G? Moreover, is it possible to obtain such an estimate in a sm ...

ASSOC COMPUTING MACHINERY2020

Symbolic Algorithms for Token Swapping

Giovanni De Micheli, Mathias Soeken, Bruno Schmitt Antunes

We study different symbolic algorithms to solve two related reconfiguration problems on graphs: the token swapping problem and the permutation routing via matchings problem. Input to both problems is a connected graph with labeled vertices and a token in e ...

2020

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

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

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

Matthias Grossglauser, Osman Emre Dai, Negar Kiyavash

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

Weighted Matchings via Unweighted Augmentations

Slobodan Mitrovic, Ola Nils Anders Svensson, 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

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

Ordered Graphs And Large Bi-Cliques In Intersection Graphs Of Curves

János Pach, Istvan Tomon

An ordered graph G(

COMENIUS UNIV2019

Ordered graphs and large bi-cliques in intersection graphs of curves

János Pach, Istvan Tomon

An ordered graph G(

ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD2019

An Optimal Space Lower Bound for Approximating MAX-CUT

Mikhail Kapralov

We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. At one extreme, there is a trivial 2-approximation for this problem that uses only O(log n) space, namely, count the number of edges and output hal ...

ASSOC COMPUTING MACHINERY2019

Distributed Coloring of Graphs with an Optimal Number of Colors

Etienne Michel François Bamas

This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e. with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so far has focused on ...

SCHLOSS DAGSTUHL, LEIBNIZ CENTER INFORMATICS2019

Robust Adaptive Decision Making: Bayesian Optimization and Beyond

Ilija Bogunovic

The central task in many interactive machine learning systems can be formalized as the sequential optimization of a black-box function. Bayesian optimization (BO) is a powerful model-based framework for \emph{adaptive} experimentation, where the primary go ...

EPFL2019

On some problems related to 2-level polytopes

Manuel Francesco Aprile

In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes ...

EPFL2018