Splitting a logic program allows us to reduce the task of computing its stable models similar tasks for subprograms. This can be used increase solving performance and prove correctness programs. We generalize conditions under which this technique is applicable, by considering not only dependencies between predicates but also their arguments context. splitting programs commonly in practice previ...

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...

This paper focuses on the problem of scheduling a set of independent jobs with setup times and job splitting, on a set of identical parallel machines such that total tardiness is minimized. In this study, it is assumed that a job can be split into sub-jobs and these sub-jobs can be processed independently on parallel machines. Because the problem is NP-hard, a memetic algorithm (MA) is proposed...

This paper deals with the problem of clustering a data-set. In particular, the bisecting divisive approach is here considered. This approach can be naturally divided into two sub-problems: the problem of choosing which cluster must be divided, and the problem of splitting the selected cluster. The focus here is on the first problem. The contribution of this work is to propose a new simple techn...

Nearest neighbor searching is a fundamental computational problem. A set of n data points is given in real d-dimensional space, and the problem is to preprocess these points into a data structure, so that given a query point, the nearest data point to the query point can be reported efficiently. Because data sets can be quite large, we are primarily interested in data structures that use only O...

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 pre...

This paper studies the solution of both asymmetric and symmetric linear complementarity problems by two-phase methods that consist of an active set prediction phase and an acceleration phase. The prediction phase employs matrix splitting iterations that are tailored to the structure of the linear complementarity problems studied in this paper. In the asymmetric case, the task of pairing an acce...

We extend work of G. Ahlbrandt and M. Ziegler to give a classiication of the nite covers with bre group of prime order p for the projective space over the eld with p elements, and for the Grassmannian of k-sets from a disintegrated set (for k 2 N). AMS classiication: 03C35 and 20B27. This paper is a contribution to the study of the ne detail of the class of (countable) totally categorical struc...

We investigate the problem of approximating the Pareto set of biobjective optimization problems with a given number of solutions. This task is relevant for two reasons: (i) Pareto sets are often computationally hard so approximation is a necessary tradeoff to allow polynomial time algorithms; (ii) limiting explicitly the size of the approximation allows the decision maker to control the expecte...

We study the problem k-SET SPLITTING from a Fixed Parameter point of view. We give a linear kernel of 2k elements and 2k sets and improve on the current best running time for the problem, giving a O∗(4k) algorithm. This is done by reducing the problem to a bipartite graph problem where we use crown decomposition to reduce the graph. We show that this result also gives a good kernel for Max Cut.