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Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the ...
A topological graph is k-quasi-planar if it does not contain k pairwise crossing edges. An old conjecture states that for every fixed k, the maximum number of edges in a k-quasi-planar graph on n vertices is O(n). Fox and Pach showed that every k-quasi-pla ...
A graph drawn in the plane is called k-quasi-planar if it does not contain k pair-wise crossing edges. It has been conjectured for a long time that for every fixed k, the maximum number of edges of a k-quasi-planar graph with n vertices is O(n). The best k ...
We propose a new formulation of the index coding problem, where instead of demanding a specific message, clients are “pliable” and are happy to receive any one message they do not have. We prove that with this relaxation, although some instances of this pr ...
We consider the assignment of gates to arriving and departing flights at a large hub airport. It is considered to be a highly complex problem even in planning stage when all flight arrivals and departures are assumed to be known precisely in advance. There ...
In this paper, we study the dynamic hybrid berth allocation problem in bulk ports with the objective to minimize the total service times of the vessels. We propose two exact methods based on mixed integer progra mming and generalized set partitionin g, and ...
A topological graph is k-quasi-planar if it does not contain k pairwise crossing edges. A topological graph is simple if every pair of its edges intersect at most once (either at a vertex or at their intersection). In 1996, Pach, Shahrokhi. and Szegedy [16 ...
We deal with some generalizations of the graph coloring problem on classes of perfect graphs. Namely we consider the μ-coloring problem (upper bounds for the color on each vertex), the precoloring extension problem (a subset of vertices colored beforehand) ...
The restricted max-min fair allocation problem (also known as the restricted Santa Claus problem) is one of few problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, Asadpour et al. [1] pro ...
We study two closely related problems in nonpreemptive scheduling of jobs on identical parallel machines. In these two settings there are either fixed jobs or nonavailability intervals during which the machines are not available; in both cases, the objecti ...
