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The k-median problem is a well-known strongly NP-hard combinatorial optimization problem of both theoretical and practical significance. The previous best approximation ratio for this problem is 2.611+ǫ (Bryka et al. 2014) based on an (1, 1.95238219) bi-factor approximation algorithm for the classical facility location problem (FLP). This work offers an… (More)

This paper considers the problem of preemptive on-line scheduling for two uniform processors in which one of the processors has speed 1 and the other has speed s¿1. The objective is to minimize the makespan. A best possible algorithm with competitive ratio of (1 + s) 2 =(1 + s + s 2) is proposed for this problem.

We consider the facility location problem with submodular penalties (FLPSP), introduced by Hayrapetyan et al. (Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 933–942, 2005), who presented a 2.50-approximation algorithm that is non-combinatorial because this algorithm has to solve the LP-relaxation of an integer… (More)

We consider the facility location problem with submodular penalty (FLPSP) and the facility location problem with linear penalty (FLPLP), two extensions of the classical facility location problem (FLP). First, we introduce a general algorithmic framework for a class of covering problems with submodular penalty, extending the recent result of Geunes et al.… (More)

A notorious open problem in the field of rendezvous search is to decide the rendezvous value of the symmetric rendezvous search problem on the line, when the initial distance apart between the two players is 2. We show that the symmetric rendezvous value is within the interval (4.1520, 4.2574), which considerably improves the previous best known result… (More)

We propose a cost-sharing scheme for the k-level facility location game that is cross-monotonic, competitive, and 6-approximate cost recovery. This extends the recent result for the 1-level facility location game of Pál and Tardos.

The maximum residual flow problem with one-arc destruction is shown to be solvable in strongly polynomial time in [Aneja et al., Networks, 38 (2001), 194-198.]. However the status of the corresponding problem with more than one-arc destruction is left open therein. We resolve the status of the two-arc destruction problem by demonstrating that it is already… (More)