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We consider the problem of scheduling permanent jobs on related machines in an on-line fashion. We design a new algorithm that achieves the competitive ratio of 3+ p 8 5:828 for the deterministic version, and 3:31= ln 2:155 4:311 for its randomized variant, improving the previous competitive ratios of 8 and 2e 5:436. We also prove lower bounds of 2:4380 on(More)
We present a uniied framework for designing polynomial time approximationschemes (PTASs) for \dense" instances of many NP-hard optimization problems, including maximum cut, graph bisection, graph separation , minimumk-way cut with and without speciied sources, and maximum 3-satissability. Dense graphs for us are graphs with minimumdegree (n), although some(More)
We prove a number of improved inaproximability results, including the best up to date explicit approximation thresholds for MIS problem of bounded degree, bounded occurrences MAX-2SAT, and bounded degree Node Cover. We prove also for the rst time inapproxima-bility of the problem of Sorting by Reversals and display an explicit approximation threshold. This(More)
A reversal on a permutation of (1,.. . , n} is a transformation that reverses the order of a block of two or more consecutive elements of the permutation. The problem of determining the smallest number of reversals required to transform a given permutation to the identity (or to sort the permutation by reversals) has been shown to be NP-hard. In this paper(More)
The Steiner tree problem asks for the shortest tree connecting a given set of terminal points in a metric space. We design new approximation algorithms for the Steiner tree problems using a novel technique of choosing Steiner points in dependence on the possible deviation from the optimal solutions. We achieve the best up to now approximation ratios of(More)