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 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)
C+G content (GC content or G+C content) is known to be correlated with genome/chromosome size in bacteria but the relationship for other kingdoms remains unclear. This study analyzed genome size, chromosome size, and base composition in most of the available sequenced genomes in various kingdoms. Genome size tends to increase during evolution in plants and… (More)
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)
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)