The shortest path tour problem (SPTP) consists of finding a shortest path from a given origin node s to a given destination node d in a directed graph with nonnegative arc lengths with the constraint that the optimal path P should successively pass through at least one node from given node subsets T1, T2, . . . , TN , where ⋂N k=1 Tk = ∅. In this paper, it will proved that the SPTP belongs to t...

1994 Zentrum f ur Paralleles Rechnen Universit at zu K oln Weyertal 80 D{50931 K oln Abstract We describe an improved clustering heuristic for the Eucledian Traveling Salesman Problem and its parallelization for a distributed memory machine. A geometric decomposition is used for the clustering{stage and special emphasis has been put on the computation of the global tour through the clusters. Th...

We introduce a new NP-complete problem asking if a “query” hypercube is (not) covered by a set of other “evidence” hypercubes. This comes down to a form of constraint reasoning asking for the satisfiability of a CNF formula where the logical atoms are inequalities over single variables, with possibly infinite variable domains. We empirically investigate the location of the phase transition regi...

Covering arrays have been studied for their applications to drug screening and software and hardware testing. In this paper, we model the problem as a constraint program. Our proposed models exploit non-binary (global) constraints, redundant modelling, channelling constraints, and symmetry breaking constraints. Our initial experiments show that with our best integrated model, we are able to eit...

The hierarchical hub location problem is encountered three-level network that is applied in production-distribution system, education system, emergency medical services, telecommunication network, etc. This paper addresses the hierarchical hub covering problem with single assignment accounting for mandatory dispersion of central hubs restriction as a special case. This formulation with incorpor...

Given a set of polyhedral cones C1, · · · , Ck ⊂ R, and a convex set D, does the union of these cones cover the set D? In this paper we consider the computational complexity of this problem for various cases such as whether the cones are defined by extreme rays or facets, and whether D is the entire R or a given linear subspace R. As a consequence, we show that it is coNP-complete to decide if ...