Related papers: Neighbors
For a finite set of integers such that the first few gaps between its consecutive elements equal $a$, while the remaining gaps equal $b$, we study dense packings of its translates on the line. We obtain an explicit lower bound on the…
We survey several old and new problems related to the number of simplicial spheres, the number of neighborly simplicial spheres, the number of centrally symmetric simplicial spheres that are cs-neighborly, and the transversal numbers of…
In the realizable online setting, a learner is tasked with making predictions for a stream of instances, where the correct answer is revealed after each prediction. A learning rule is online consistent if its mistake rate eventually…
The study of several naturally arising "nearest neighbours" random walks benefits from the study of the associated orthogonal polynomials and their orthogonality measure. I consider extensions of this approach to a larger class of random…
Biological and social scientists have long been interested in understanding how to reconcile individual and collective interests in iterated Prisoner's Dilemma. Many effective strategies have been proposed, and they are often categorized…
This paper investigates the potential benefits of cooperation in scenarios where finitely many agents compete for shared resources, leading to congestion and thereby reduced rewards. By appropriate coordination the members of the…
Given a set of n balls each colored with a color, a ball is said to be majority, k-majority, plurality if its color class has size larger than half of the number of balls, has size at least k, has size larger than any other color class;…
In this paper, we consider approximability issues of the following four problems: triangle packing, full sibling reconstruction, maximum profit coverage and 2-coverage. All of them are generalized or specialized versions of set-cover and…
Divorced individuals face complex situations when they have children with different ex-partners, or even more, when their new partners have children of their own. In such cases, and when kids spend every other weekend with each parent, a…
This paper deals with the problem of circle packing, in which the largest radii circle is to be fit in a confined space filled with arbitrary circles of different radii and centers. A circle packing problem is one of a variety of cutting…
In the classical best approximation pair (BAP) problem, one is given two nonempty, closed, convex and disjoint subsets in a finite- or an infinite-dimensional Hilbert space, and the goal is to find a pair of points, each from each subset,…
A geometric graph is a graph whose vertex set is a set of points in the plane and whose edge set contains straight-line segments. A matching in a graph is a subset of edges of the graph with no shared vertices. A matching is called perfect…
Edge-matching problems, also called edge matching puzzles, are abstractions of placement problems with neighborhood conditions. Pieces with colored edges have to be placed on a board such that adjacent edges have the same color. The problem…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is…
We study the knapsack problem with group fairness constraints. The input of the problem consists of a knapsack of bounded capacity and a set of items, each item belongs to a particular category and has and associated weight and value. The…
We investigate an evolutionary prisoner's dilemma game among self-driven agents, where collective motion of biological flocks is imitated through averaging directions of neighbors. Depending on the temptation to defect and the velocity at…
The garbage disposal game involves a finite set of individuals, each of whom updates their garbage by either receiving from or dumping onto others. We examine the case where only social neighbors, whose garbage levels differ by a given…
In the packing-constrained point covering problem, PC^2, one seeks configurations of points in the plane that cannot all be covered by a packing arrangement of unit disks. We consider in particular the problem of finding the minimum number…
This letter studies the problem of cooperative nearest-neighbor control of multi-agent systems where each agent can only realize a finite set of control points. Under the assumption that the underlying graph representing the communication…
We consider inapproximability of the correlation clustering problem defined as follows: Given a graph $G = (V,E)$ where each edge is labeled either "+" (similar) or "-" (dissimilar), correlation clustering seeks to partition the vertices…