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We study interval coloring problems and present new upper and lower bounds for several variants. We are interested in four problems, online coloring of intervals with and without bandwidth and a new problem called lazy online coloring again with and without bandwidth. We consider both general interval graphs and unit interval graphs. Specifically, we(More)
In this paper we address the open problem of bounding the price of stability for network design with fair cost allocation for undirected graphs posed in [1]. We consider the case where there is an agent in every vertex. We show that the price of stability is O(log log n). We prove this by defining a particular improving dynamics in a related graph. This(More)
We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be <i>conflict-free</i>, in the sense that in every interval <i>I</i> there is a color that appears exactly once in <i>I.</i> We present several(More)
Secure two-party and multiparty computation has long stood at the center of the foundations of theoretical cryptography. Recently, however, interest has grown regarding the efficiency of such protocols and their application in practice. As a result, there has been significant progress on this problem and it is possible to actually carry out secure(More)
We study online interval coloring problems with bandwidth. We are interested in some variants motivated by bin packing problems. Specifically we consider open-end coloring, cardinality constrained coloring, coloring with vector constraints and finally a combination of both the cardinality and the vector constraints. We construct competitive algorithms for(More)
We present an improved online algorithm for coloring interval graphs with bandwidth. This problem has recently been studied byAdamy and Erlebach and a 195-competitive online strategy has been presented. We improve this by presenting a 10-competitive strategy. To achieve this result, we use variants of an optimal online coloring algorithm due to Kierstead(More)
In the setting of secure multiparty computation, several distrustful parties wish to carry out a distributed computing task on their local private data while satisfying several security properties such as correctness, privacy, independence of inputs and fairness. The aim of secure multiparty computation (MPC) is to enable the parties to carry out the(More)