We investigate the computational complexity of the following problem. We are given a graph in which each vertex has an initial and a target color. Each pair of adjacent vertices can swap their current colors. Our goal is to perform the minimum number of swaps so that the current and target colors agree at each vertex. When the colors are chosen from {1, 2, . . . , c}, we call this problem c-Col...

A coloring of a hypergraph is a mapping of vertices to colors such that no hyperedge is monochromatic. We are interested in the problem of coloring 2-colorable hypergraphs. For the special case of graphs (hypergraphs of dimension 2) this can easily be done in linear time. The problem for general hypergraphs is much more difficult since a result of Lovász implies that the problem is NP-hard even...

Existing color constancy methods cannot handle both uniformly colored surfaces and highly textured surfaces in a single integrated framework. Statistics-based methods require many surface colors and become error prone when there are only a few surface colors. In contrast, dichromatic-based methods can successfully handle uniformly colored surfaces but cannot be applied to highly textured surfac...

Color preference is an important aspect of visual experience, but little is known about why people in general like some colors more than others. Previous research suggested explanations based on biological adaptations [Hurlbert AC, Ling YL (2007) Curr Biol 17:623-625] and color-emotions [Ou L-C, Luo MR, Woodcock A, Wright A (2004) Color Res Appl 29:381-389]. In this article we articulate an eco...

We study the rendezvous problem for two robots moving in the plane (or on a line). Robots are autonomous, anonymous, oblivious, and carry colored lights that are visible to both. We consider deterministic distributed algorithms in which robots do not use distance information, but try to reduce (or increase) their distance by a constant factor, depending on their lights’ colors. We give a comple...

The increased demand for minimally invasive placement of intravascular medical devices has led to increased procedure-related complications, including retention of all or part of the implanted device. A number of risk factors can predispose to unintentionally retained vascular devices (uRVD); most are technical in etiology. Despite best efforts to insert and remove vascular devices properly, uR...

Motivated by the frequency assignment problem we study the ddistant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A d-distant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have different colors. The d-distant chromatic number of H, denoted χd(H), is the minimum number of col...

Even within the framework of the leading logarithmic approximation the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the planar limit case where the problem becomes integrable. We consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly sol...

848 NOTICES OF THE AMS VOLUME 45, NUMBER 7 E very planar map of connected countries can be colored using four colors in such a way that countries with a common boundary segment (not just a point) receive different colors. It is amazing that such a simply stated result resisted proof for one and a quarter centuries, and even today it is not yet fully understood. In this article I concentrate on ...