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In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…

Machine Learning · Computer Science 2024-10-08 Morris Yau , Nikolaos Karalias , Eric Lu , Jessica Xu , Stefanie Jegelka

We revisit the coalition structure generation problem in which the goal is to partition the players into exhaustive and disjoint coalitions so as to maximize the social welfare. One of our key results is a general polynomial-time algorithm…

Computer Science and Game Theory · Computer Science 2011-06-21 Haris Aziz , Bart de Keijzer

We consider two optimization problems in planar graphs. In Maximum Weight Independent Set of Objects we are given a graph $G$ and a family $\mathcal{D}$ of objects, each being a connected subgraph of $G$ with a prescribed weight, and the…

Data Structures and Algorithms · Computer Science 2018-07-23 Michał Pilipczuk , Erik Jan van Leeuwen , Andreas Wiese

An important objective in scheduling literature is to minimize the sum of weighted flow times. We are given a set of jobs where each job is characterized by a release time, a processing time, and a weight. Our goal is to find a preemptive…

Data Structures and Algorithms · Computer Science 2022-08-08 Alexander Armbruster , Lars Rohwedder , Andreas Wiese

The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each…

Data Structures and Algorithms · Computer Science 2009-07-13 Paola Bonizzoni , Gianluca Della Vedova , Riccardo Dondi

Capacitated network bargaining games are popular combinatorial games that involve the structure of matchings in graphs. We show that it is always possible to stabilize unit-weight instances of this problem (that is, ensure that they admit a…

Discrete Mathematics · Computer Science 2024-09-05 Laura Sanità , Lucy Verberk

The game of Cops and Robber is traditionally played on a finite graph. The purpose of this note is to introduce and analyze the game that is played on an arbitrary geodesic space. The game is defined in such a way that it preserves the…

Combinatorics · Mathematics 2021-12-07 Bojan Mohar

A rotor walk in a directed graph can be thought of as a deterministic version of a Markov Chain, where a pebble moves from vertex to vertex following a simple rule until a terminal vertex, or sink, is reached. The ARRIVAL problem, as…

Computer Science and Game Theory · Computer Science 2022-05-03 David Auger , Pierre Coucheney , Loric Duhaze

This paper is about computing constrained approximate Nash equilibria in polymatrix games, which are succinctly represented many-player games defined by an interaction graph between the players. In a recent breakthrough, Rubinstein showed…

Computer Science and Game Theory · Computer Science 2017-05-09 Argyrios Deligkas , John Fearnley , Rahul Savani

In this paper, we resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPAD-complete, along with the domains of practical significance:…

Computational Complexity · Computer Science 2009-04-10 Shiva Kintali , Laura J. Poplawski , Rajmohan Rajaraman , Ravi Sundaram , Shang-Hua Teng

We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…

Data Structures and Algorithms · Computer Science 2024-11-26 Antonios Antoniadis , Marek Eliáš , Adam Polak , Moritz Venzin

We consider the {\em Capacitated Domination} problem, which models a service-requirement assignment scenario and is also a generalization of the well-known {\em Dominating Set} problem. In this problem, given a graph with three parameters…

Discrete Mathematics · Computer Science 2015-05-18 Mong-Jen Kao , Han-Lin Chen

We study strategic games on weighted directed graphs, in which the payoff of a player is defined as the sum of the weights on the edges from players who chose the same strategy, augmented by a fixed non-negative integer bonus for picking a…

Computer Science and Game Theory · Computer Science 2021-03-15 Krzysztof R. Apt , Sunil Simon , Dominik Wojtczak

We study the efficient approximability of basic graph and logic problems in the literature when instances are specified hierarchically as in \cite{Le89} or are specified by 1-dimensional finite narrow periodic specifications as in…

Computational Complexity · Computer Science 2007-05-23 Madhav V. Marathe , Harry B. Hunt , Richard E. Stearns , Venkatesh Radhakrishnan

The problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in…

Discrete Mathematics · Computer Science 2024-03-05 Hanna Furmańczyk , Tytus Pikies , Inka Sokołowska , Krzysztof Turowski

We study the algorithmic complexity of Maker-Breaker games played on the edge sets of general graphs. We mainly consider the perfect matching game and the $H$-game. Maker wins if she claims the edges of a perfect matching in the first, and…

Computational Complexity · Computer Science 2024-11-18 Eric Duchêne , Valentin Gledel , Fionn Mc Inerney , Nicolas Nisse , Nacim Oijid , Aline Parreau , Miloš Stojaković

We define a general framework of partition games for formulating two-player pebble games over finite structures. We show that one particular such game, which we call the invertible-map game, yields a family of polynomial-time approximations…

Logic in Computer Science · Computer Science 2015-03-20 Anuj Dawar , Bjarki Holm

We study the biased $(1:b)$ Maker--Breaker positional games, played on the edge set of the complete graph on $n$ vertices, $K_n$. Given Breaker's bias $b$, possibly depending on $n$, we determine the bounds for the minimal number of moves,…

Combinatorics · Mathematics 2023-06-22 Mirjana Mikalački , Miloš Stojaković

The Maker-Breaker connectivity game and Hamilton cycle game belong to the best studied games in positional games theory, including results on biased games, games on random graphs and fast winning strategies. Recently, the Connector-Breaker…

Combinatorics · Mathematics 2023-06-02 Dennis Clemens , Pranshu Gupta , Yannick Mogge

Turn-based discounted-sum games are two-player zero-sum games played on finite directed graphs. The vertices of the graph are partitioned between player 1 and player 2. Plays are infinite walks on the graph where the next vertex is decided…

Computer Science and Game Theory · Computer Science 2024-05-21 Ali Asadi , Krishnendu Chatterjee , Raimundo Saona , Jakub Svoboda