We investigate the approximability properties of several weighted problems, by comparing them with the respective unweighted problems. For an appropriate (and very general) definition of niceness, we show that if a nice weighted problem is hard to approximate within r, then its polynomially bounded weighted version is hard to approximate within r \Gamma o(1). Then we turn our attention to specific problems, and we show that the unweighted

this paper we shrink the gap for the Max 3-Set Splitting problem and its generalization Max k-Set Splitting from both ends, finding new lower bounds and new upper bounds. In the Max k-Set Splitting problem, the instance consists of subsets of size k of a finite set of elements. The problem is to partition the elements into two parts, such that as many subsets as possible will be split, i.e. contain elements from both parts. The problem was shown to be NP-complete by Lov'asz [11]. Recently it was shown to be Apx-complete [15]. We also consider another generalization of Max 3-Set Splitting, namely

We investigate the approximability properties of several weighted problems, by comparing them with the respective unweighted problems. For an appropriate (and very general) definition of niceness, we show that if a nice weighted problem is hard to approximate within r, then its polynomially bounded weighted version is hard to approximate within r − o(1). Then we turn our attention to specific problems, and we show that the unweighted versions of Min Vertex Cover, Min Sat, Max Cut, Max DiCut, Max 2Sat, and Max Exact kSat are exactly as hard to approximate as their weighted versions. We note in passing that Min Vertex Cover is exactly as hard to approximate as Min Sat. In order to prove the reductions for Max 2Sat, Max Cut, Max DiCut, and Max E3Sat we introduce the new notion of “mixing ” set and we give an explicit construction of such sets. These reductions give new non-approximability results for these problems. 1

We construct new approximation algorithms for Max Set Splitting and Max Not-All-Equal Sat, which when combined with existing algorithms give the best approximation results so far for these problems. Furthermore, when analyzing our combination of approximation algorithms, we introduce a novel technique, which improves the analysis of the performance ratio of such algorithms. In contrast with previous techniques we use a linear program to find an upper bound on the performance ratio. This linear program can also be used to see which of the contributing algorithms it is possible to exclude from the combined algorithm without affecting its performance ratio.

this paper the performance of the Hamming-based Reactive Tabu Search algorithm (H-RTS) previously proposed for the Maximum Satisfiability problem is studied for the different Maximum k--Conjunctive Constraint Satisfaction problem. In addition, the use of non-oblivious functions recently proposed in the framework of approximation algorithms is investigated

The aim of the project is to develop, analyze and implement...