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Public goods games represent insightful settings for studying incentives for individual agents to make contributions that, while costly for each of them, benefit the wider society. In this work, we adopt the perspective of a central planner…

Artificial Intelligence · Computer Science 2021-10-27 Victor-Alexandru Darvariu , Stephen Hailes , Mirco Musolesi

An incidence of a graph $G$ is a pair $(v,e)$ where $v$ is a vertex of $G$ and $e$ an edge incident to $v$. Two incidences $(v,e)$ and $(w,f)$ are adjacent whenever $v = w$, or $e = f$, or $vw = e$ or $f$. The incidence coloring game [S.D.…

Discrete Mathematics · Computer Science 2013-06-04 Clément Charpentier , Eric Sopena

Based on the geometric {\it Triangle Algorithm} for testing membership of a point in a convex set, we present a novel iterative algorithm for testing the solvability of a real linear system $Ax=b$, where $A$ is an $m \times n$ matrix of…

Numerical Analysis · Mathematics 2020-04-28 Bahman Kalantari , Chun Lau , Yikai Zhang

We investigate the asymptotic behavior of perfect matchings on rail-yard graphs with doubly free boundary conditions and Jack weights. While a special case of this model reduces to the half space Macdonald process with Jack weights…

Probability · Mathematics 2025-05-27 Zhongyang Li , Kaili Shi

We consider the Lion and Man game, i.e., a two-person pursuit-evasion game with equal players' top speeds. We assume that capture radius is positive and chosen in advance. The main aim of the paper is describing pursuer's winning strategies…

Optimization and Control · Mathematics 2019-08-01 Olga Yufereva

We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations of the…

Analysis of PDEs · Mathematics 2021-05-04 Indranil Chowdhury , Olav Ersland , Espen R. Jakobsen

We consider a class of pursuit-evasion problems where an evader enters a directed acyclic graph and attempts to reach one of the terminal nodes. A pursuer enters the graph at a later time and attempts to capture the evader before it reaches…

Combinatorics · Mathematics 2016-09-14 Shreyas Sundaram , Krishnamoorthy Kalyanam , David W. Casbeer

We study distributed protocols for finding all pairs of similar vectors in a large dataset. Our results pertain to a variety of discrete metrics, and we give concrete instantiations for Hamming distance. In particular, we give improved…

Data Structures and Algorithms · Computer Science 2016-11-16 Paul Beame , Cyrus Rashtchian

In this paper we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of…

Quantum Physics · Physics 2018-10-04 M. Chiew , K. de Lacy , C. H. Yu , S. Marsh , J. B. Wang

We introduce the category of optiongraphs and option-preserving maps as a model to study impartial combinatorial games. Outcomes, remoteness, and extended nim-values are preserved under option-preserving maps. We show that the four…

Combinatorics · Mathematics 2025-10-23 Mikhail Baltushkin , Dana C. Ernst , Nándor Sieben

A three-dimensional (3D) integrated guidance and control (IGC) design approach is proposed by using small-gain theorem in this paper. The 3D IGC model is formulated by combining nonlinear pursuer dynamics with the nonlinear dynamics…

Systems and Control · Computer Science 2014-02-25 Han Yan , Mingzhe Hou

In this technical note, we study the controllability of diffusively coupled networks from a graph theoretic perspective. We consider leader-follower networks, where the external control inputs are injected to only some of the agents, namely…

Systems and Control · Computer Science 2016-08-17 A. Yasin Yazicioglu , Waseem Abbas , Magnus Egerstedt

In this study, we employ the established Carleman estimates and propagation estimates of smallness from measurable sets for real analytic functions, along with the telescoping series method, to establish an observability inequality for the…

Optimization and Control · Mathematics 2023-06-16 Yuanhang Liu , Weijia Wu , Donghui Yang , Can Zhang

Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of…

Probability · Mathematics 2007-08-21 Ori Gurel-Gurevich

The paper is concerned with two-person dynamic zero-sum games. We investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity, and the limit of value functions of…

Optimization and Control · Mathematics 2016-07-21 Dmitry Khlopin

Maximising the detection of intrusions is a fundamental and often critical aim of perimeter surveillance. Commonly, this requires a decision-maker to optimally allocate multiple searchers to segments of the perimeter. We consider a scenario…

Machine Learning · Computer Science 2019-11-12 James A. Grant , David S. Leslie , Kevin Glazebrook , Roberto Szechtman , Adam N. Letchford

It is well known that isoperimetric inequalities imply in a very general measure-metric-space setting appropriate concentration inequalities. The former bound the boundary measure of sets as a function of their measure, whereas the latter…

Differential Geometry · Mathematics 2019-12-19 Emanuel Milman

We revisit the algorithmic problem of finding a triangle in a graph (\textsc{Triangle Detection}), and examine its relation to other problems such as \textsc{3Sum}, \textsc{Independent Set}, and \textsc{Graph Coloring}. We obtain several…

Data Structures and Algorithms · Computer Science 2024-02-13 Adrian Dumitrescu

This paper is a contribution to the study of parity games and the recent constructions of three quasipolynomial time algorithms for solving them. We revisit a result of Czerwi\'nski, Daviaud, Fijalkow, Jurdzi\'nski, Lazi\'c, and Parys…

Computer Science and Game Theory · Computer Science 2018-10-22 Thomas Colcombet , Nathanaël Fijalkow

Graph alignment - identifying node correspondences between two graphs - is a fundamental problem with applications in network analysis, biology, and privacy research. While substantial progress has been made in aligning correlated…

Information Theory · Computer Science 2026-03-16 Jakob Maier , Laurent Massoulié