We study the problem k-SET SPLITTING in fixed parameter complexity. We show that the problem can be solved in time O∗(2.6494k), improving on the best currently known running time of O∗(8k). This is done by showing that a non-trivial instance must have a small minimal SET COVER, and using this to reduce the problem to a series of small instances of MAX SAT. We also give a linear kernel containin...

In this paper we demonstrate a general method of designing constant-factor approximation algorithms for some discrete optimization problems with cardinality constraints. The core of the method is a simple deterministic (\pipage") procedure of rounding of linear relaxations. By using the method we design a (1 ? (1 ? 1=k) k)-approximation algorithm for the maximum coverage problem where k is the ...

In this paper we investigate the parametrized complexity of the problems MaxSat and MaxCut using the framework developed by Downey and Fellowss7]. Let G be an arbitrary graph having n vertices and m edges, and let f be an arbitrary CNF formula with m clauses on n variables. We improve Cai and Chen's O(2 2k m) time algorithm for determining if at least k clauses of of a c-CNF formula f can be sa...

Remarkable breakthroughs have been made recently in obtaining approximate solutions to some fundamental NP-hard problems, namely Max-Cut, Max k-Cut, Max-Sat, Max-Dicut, Max-bisection, k-vertex coloring, maximum independent set, etc. All these breakthroughs involve polynomial time randomized algorithms based upon semidefinite programming, a technique pioneered by Goemans and Williamson. In this ...

We consider the performance of two classic approximation algorithms which work by scanning the input and greedily constructing a solution. We investigate whether running these algorithms on a random permutation of the input can increase their performance ratio. We obtain the following results: 1. Johnson’s approximation algorithm for MAX-SAT is one of the first approximation algorithms to be ri...

In this study, turning operation of Monel K500 copper-nickel super-alloy was evaluated. Ceramic cutting tools with two different cutting noses (conventional and wiper) were utilized. At first, the experimental tests were designed by using central composite design method. After implementation of the tests, the statistical models for output data (surface roughness, cutting force, and flank wear) ...

during the last years, the concept of input congestion and technical ineff-ciency in data envelopment analysis (dea), have been investigated by manyresearchers. the motivation of this paper is to present models which obtain thedecreased output value due to input congestion and technical ineciency. more-over, we extend the models to estimate input congestion, technical ineciencyand output red...

Consider a network of pipes joining a set of intakes (the source) to a separate set of outlets (the e n sink), so that liquid flows from the intakes, through the network, to the outlets. A cross-section of th etwork, separating the intakes on one side from the outlets on the other, is called a cut. A minimal t c cut is one that, roughly speaking, slices through a set of pipes whose combined cap...