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We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multi-dimensional mean-payoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but…

Computer Science and Game Theory · Computer Science 2021-09-07 Marcin Jurdziński , Ranko Lazić , Sylvain Schmitz

The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold…

Optimization and Control · Mathematics 2016-09-30 Jaehyun Park , Stephen Boyd

We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…

Optimization and Control · Mathematics 2025-01-31 Pavel Dvurechensky , Gabriele Iommazzo , Shimrit Shtern , Mathias Staudigl

This paper presents a technique for approximating, up to any precision, the set of subgame-perfect equilibria (SPE) in discounted repeated games. The process starts with a single hypercube approximation of the set of SPE. Then the initial…

Computer Science and Game Theory · Computer Science 2010-02-10 Andriy Burkov , Brahim Chaib-draa

We develop a new approach for approximating large independent sets when the input graph is a one-sided spectral expander - that is, the uniform random walk matrix of the graph has its second eigenvalue bounded away from 1. Consequently, we…

Data Structures and Algorithms · Computer Science 2024-11-07 Mitali Bafna , Jun-Ting Hsieh , Pravesh K. Kothari

We study a class of zero-sum games between a singular-controller and a stopper over finite-time horizon. The underlying process is a multi-dimensional (locally non-degenerate) controlled stochastic differential equation (SDE) evolving in an…

Optimization and Control · Mathematics 2023-10-31 Andrea Bovo , Tiziano De Angelis , Elena Issoglio

We introduce a new technique for designing fixed-parameter algorithms for cut problems, namely randomized contractions. We apply our framework to obtain the first FPT algorithm for the Unique Label Cover problem and new FPT algorithms with…

Data Structures and Algorithms · Computer Science 2016-07-20 Rajesh Chitnis , Marek Cygan , MohammadTaghi Hajiaghayi , Marcin Pilipczuk , Michał Pilipczuk

A nondeterministic automaton is history-deterministic if its nondeterminism can be resolved by only considering the prefix of the word read so far. Due to their good compositional properties, history-deterministic automata are useful in…

Formal Languages and Automata Theory · Computer Science 2024-02-14 Udi Boker , Karoliina Lehtinen

State-of-the-art methods for solving 2-player zero-sum imperfect information games rely on linear programming or regret minimization, though not on dynamic programming (DP) or heuristic search (HS), while the latter are often at the core of…

Artificial Intelligence · Computer Science 2022-10-27 Aurélien Delage , Olivier Buffet , Jilles S. Dibangoye , Abdallah Saffidine

We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…

Data Structures and Algorithms · Computer Science 2021-01-01 Katarzyna Paluch , Mateusz Wasylkiewicz

We consider two-player zero-sum differential games (ZSDGs), where the state process (dynamical system) depends on the random initial condition and the state process's distribution, and the objective functional includes the state process's…

Optimization and Control · Mathematics 2020-05-26 Jun Moon , Tamer Basar

Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…

Logic in Computer Science · Computer Science 2016-11-29 Romain Brenguier , Guillermo A. Pérez , Jean-François Raskin , Ocan Sankur

This paper focuses on zero-sum stochastic differential games in the framework of forward-backward stochastic differential equations on a finite time horizon with both players adopting impulse controls. By means of BSDE methods, in…

Optimization and Control · Mathematics 2021-04-08 Liangquan Zhang

We propose an implementable, neural network-based structure preserving probabilistic numerical approximation for a generalized obstacle problem describing the value of a zero-sum differential game of optimal stopping with asymmetric…

Numerical Analysis · Mathematics 2025-01-28 Ľubomír Baňas , Giorgio Ferrari , Tsiry Avisoa Randrianasolo

The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in $NP \cap coNP$ which are not known to be in $P$. However, there are some…

Computational Complexity · Computer Science 2014-08-10 David Auger , Pierre COUCHENEY , Yann Strozecki

We prove the existence and uniqueness of viscosity solutions to quasi-variational inequalities (QVIs) with both upper and lower obstacles. In contrast to most previous works, we allow all involved coefficients to depend on the state…

Probability · Mathematics 2024-09-09 Magnus Perninge

In this paper, we study two-player zero-sum turn-based games played on a finite multidimensional weighted graph. In recent papers all dimensions use the same measure, whereas here we allow to combine different measures. Such heterogeneous…

Computer Science and Game Theory · Computer Science 2016-06-22 Véronique Bruyère , Quentin Hautem , Jean-François Raskin

Determining the integrality gap of the linear programming (LP) relaxation of the metric traveling salesman problem (TSP) remains a long-standing open problem. We introduce a transfer principle: when the integer optimum of the…

Optimization and Control · Mathematics 2025-12-08 Toshiaki Yamanaka

We consider a class of nonlocal games that are related to binary constraint systems (BCSs) in a manner similar to the games implicit in the work of Mermin [N.D. Mermin, "Simple unified form for the major no-hidden-variables theorems," Phys.…

Quantum Physics · Physics 2013-10-17 Richard Cleve , Rajat Mittal

We study the complexity of computing equilibria in two classes of network games based on flows - fractional BGP (Border Gateway Protocol) games and fractional BBC (Bounded Budget Connection) games. BGP is the glue that holds the Internet…

Computer Science and Game Theory · Computer Science 2008-12-05 Laura J. Poplawski , Rajmohan Rajaraman , Ravi Sundaram , Shang-Hua Teng