Related papers: Lower Bound for the Unique Games Problem
The approach mapping from a matching of bipartite graphs to digraphs has been successfully used for forcing set problem, in this paper, it is extended to uniquely restricted matching problem. We show to determine a uniquely restricted…
In the $d$-Scattered Set problem we are asked to select at least $k$ vertices of a given graph, so that the distance between any pair is at least $d$. We study the problem's (in-)approximability and offer improvements and extensions of…
We consider a simple optimal probabilistic problem solving strategy that searches through potential solution candidates in a specific order. We are interested in what impact has interchanging the order of two solution candidates with…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
The eternal graph colouring problem, recently introduced by Klostermeyer and Mendoza, is a version of the graph colouring game, where two players take turns properly colouring a graph. In this note, we study the eternal game chromatic…
We consider an assignment problem that has aspects of fair division as well as social choice. In particular, we investigate the problem of assigning a small subset from a set of indivisible items to multiple players so that the chosen…
The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…
It is conjectured that the game domination number is at most $3n/5$ for every $n$-vertex graph which does not contain isolated vertices. It was proved in the recent years that the conjecture holds for several graph classes, including the…
This paper considers pairs of optimization problems that are defined from a single input and for which it is desired to find a good approximation to either one of the problems. In many instances, it is possible to efficiently find an…
Priced timed games (PTGs) are two-player zero-sum games played on the infinite graph of configurations of priced timed automata where two players take turns to choose transitions in order to optimize cost to reach target states. Bouyer et…
We provide an algorithm to find the value and an optimal strategy of the solitaire variant of the Ten Thousand dice game in the framework of Markov Control Processes. Once an optimal critical threshold is found, the set of non-stopping…
We introduce a variant of the Localization game in which the cops only have visibility one, along with the corresponding optimization parameter, the one-visibility localization number $\zeta_1$. By developing lower bounds using…
We study parity games in which one of the two players controls only a small number $k$ of nodes and the other player controls the $n-k$ other nodes of the game. Our main result is a fixed-parameter algorithm that solves bipartite parity…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
Pure exploration in multi-armed bandits has emerged as an important framework for modeling decision-making and search under uncertainty. In modern applications, however, one is often faced with a tremendously large number of options. Even…
Learning heuristics for combinatorial optimization problems through graph neural networks have recently shown promising results on some classic NP-hard problems. These are single-level optimization problems with only one player. Multilevel…
We explain a highly efficient algorithm for playing the simplest type of dots and boxes endgame optimally (by which we mean "in such a way so as to maximise the number of boxes that you take"). The algorithm is sufficiently simple that it…
Several distinct techniques have been proposed to design quasi-polynomial algorithms for solving parity games since the breakthrough result of Calude, Jain, Khoussainov, Li, and Stephan (2017): play summaries, progress measures and register…
We investigate the adversarial bandit problem with multiple plays under semi-bandit feedback. We introduce a highly efficient algorithm that asymptotically achieves the performance of the best switching $m$-arm strategy with minimax optimal…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…