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We consider the maximum chromatic number of hypergraphs consisting of cliques that have pairwise small intersections. Designs of the appropriate parameters produce optimal constructions, but these are known to exist only when the number of…
In this paper, we consider a multi-drawing urn model with random addition. At each discrete time step, we draw a sample of m balls. According to the composition of the drawn colors, we return the balls together with a random number of balls…
The goal of this paper is twofold. First and foremost, we aim to experimentally and quantitatively show that the choice of a multiwinner voting rule can play a crucial role on the way minorities are represented. We also test the possibility…
We consider a dynamic collective choice problem where a large number of players are cooperatively choosing between multiple destinations while being influenced by the behavior of the group. For example, in a robotic swarm exploring a new…
Tournament solutions provide methods for selecting the "best" alternatives from a tournament and have found applications in a wide range of areas. Previous work has shown that several well-known tournament solutions almost never rule out…
The multiple extension problem arises frequently in diagnostic and default inference. That is, we can often use any of a number of sets of defaults or possible hypotheses to explain observations or make Predictions. In default inference,…
We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high…
We settle the complexity of the $(\Delta+1)$-coloring and $(\Delta+1)$-list coloring problems in the CONGESTED CLIQUE model by presenting a simple deterministic algorithm for both problems running in a constant number of rounds. This…
A nontrivial trigonometric limit of the three-coloring statistical model with the domain wall boundary conditions is considered. In this limit the functional equations, constructed in the previous paper, are solved and a new determinant…
Statistical tasks such as density estimation and approximate Bayesian inference often involve densities with unknown normalising constants. Score-based methods, including score matching, are popular techniques as they are free of…
Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…
In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation…
We study a two-alternative voting game where voters' preferences depend on an unobservable world state and each voter receives a private signal correlated to the true world state. We consider the collective decision when voters can…
A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…
Ranking is one of the most fundamental problems in machine learning with applications in many branches of computer science such as: information retrieval systems, recommendation systems, machine translation and computational biology.…
We review the statistical mechanics approach to the study of the emerging collective behavior of systems of heterogeneous interacting agents. The general framework is presented through examples is such contexts as ecosystem dynamics and…
The vertex coloring problem to find chromatic numbers is known to be unsolvable in polynomial time. Although various algorithms have been proposed to efficiently compute chromatic numbers, they tend to take an enormous amount of time for…
Petford and Welsh introduced a sequential heuristic algorithm for (approximately) solving the NP-hard graph coloring problem. The algorithm is based on the antivoter model and mimics the behaviour of a physical process based on a…
We determine the limiting distribution of the logarithm of the number of satisfying assignments in the random $k$-uniform hypergraph 2-colouring problem in a certain density regime for all $k\ge 3$ . As a direct consequence we obtain that…
In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The…