Related papers: Neighbors
Classic computational models of collective motion suggest that simple local averaging rules can promote many observed group level patterns. Recent studies, however, suggest that rules simpler than local averaging may be at play in real…
The stable matching problem is a prototype model in economics and social sciences where agents act selfishly to optimize their own satisfaction, subject to mutually conflicting constraints. A stable matching is a pairing of adjacent…
The locker puzzle is a game played by multiple players against a referee. It has been previously shown that the best strategy that exists cannot succeed with probability greater than 1-ln2 \approx 0.31, no matter how many players are…
We characterize the graphs for which the independence number equals the packing number. As a consequence we obtain simple structural descriptions of the graphs for which (i) the distance-$k$-packing number equals the distance-$2k$-packing…
A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. A dominating set is connected if the subgraph induced by its vertices is connected. The connected domatic partition problem asks for…
This paper presents the design of deep learning architectures which allow to classify the social relationship existing between two people who are walking in a side-by-side formation into four possible categories --colleagues, couple, family…
In the classic circle packing problem, one asks whether a given set of circles can be packed into a given container. Packing problems like this have been shown to be $\mathsf{NP}$-hard. In this paper, we present new sufficient conditions…
In 1995 T. Matsui considered a special family 0/1-polytopes for which the problem of recognizing the non-adjacency of two arbitrary vertices is NP-complete. In 2012 the author of this paper established that all the polytopes of this family…
In this work we investigate the problem of order batching and picker routing in storage areas. These are labour and capital intensive problems, often responsible for a substantial share of warehouse operating costs. In particular, we…
We discuss some stability problems when each agent of a linear flock on the line interacts with its two nearest neighbors (one on either side).
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…
For every positive integer $n$, we find a complete classification for planar graphs according to the collection of numbers of common neighbours for every $n$-tuple of distinct vertices. Our results expand the literature on planar graphical…
We study the evolution of cooperation in populations where individuals play prisoner's dilemma on a network. Every node of the network corresponds on an individual choosing whether to cooperate or defect in a repeated game. The players…
Divide and Conquer is a well known algorithmic procedure for solving many kinds of problem. In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. Finding the distance of the closest pair is an…
In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general case, since any subset sum problem can be solved upon…
In this note, we investigate an infinite one parameter family of circle packings, each with a set of three mutually tangent circles. We use these to generate an infinite set of circle packings with the Apollonian property. That is, every…
In the analysis of social networks many relatively loose and heuristic definitions of 'community' abound. In this paper the concept of closely knit communities is studied as defined by the property that every pair of its members are…
Evolution of cooperation in the prisoner's dilemma game is studied where initially all players are linked via a regular graph, having four neighbors each. Simultaneously with the strategy evolution, players are allowed to make new…
A matching is compatible to two or more labeled point sets of size $n$ with labels $\{1,\dots,n\}$ if its straight-line drawing on each of these point sets is crossing-free. We study the maximum number of edges in a matching compatible to…
In voting contexts, some new candidates may show up in the course of the process. In this case, we may want to determine which of the initial candidates are possible winners, given that a fixed number $k$ of new candidates will be added. We…