On the P-Coverage Problem on the Real Line

In this paper we consider the p-coverage problem on the real line. We first give a detailed description of an algorithm to solve the coverage problem without the upper bound p on the number of open facilities. Then we analyze how the structure of the optimal solution changes if the setup costs of the facilities are all decreased by the same amount. This result is used to develop a parametric approach to the p-coverage problem which runs in O (pn log n) time, n being the number of clients.Economics ;

Treewidth: Computational Experiments.

Many NP-complete graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for diverse optimization problems. To apply a tree decomposition approach, the treewidth of the graph has to be determined, independently of the application at hand. Although for fixed k, linear time algorithms exist to solve the decision problem ``treewidth at most k, their practical use is very limited. The computational tractability of treewidth has been rarely studied so far. In this paper, we compare four heuristics and two lower bounds for instances from applications such as the frequency assignment problem and the vertex coloring problem. Three of the heuristics are based on well-known algorithms to recognize triangulated graphs. The fourth heuristic recursively improves a tree decomposition by the computation of minimal separating vertex sets in subgraphs. Lower bounds can be computed from maximal cliques and the minimum degree of induced subgraphs. A computational analysis shows that the treewidth of several graphs can be identified by these methods. For other graphs, however, more sophisticated techniques are necessary.operations research and management science;

The partial constraint satisfaction problem : facets and lifting theorems

In this paper the partial constraint satisfaction problem (PCSP) is introduced and formulated as a {0,1}-programming problem. We define the partial constraint satisfaction polytope as the convex hull of feasible solutions for this programming problem. As examples of the class of problems studied we mention the frequency assignment problem and the maximum satisfiability problem. Lifting theorems are presented and some classes of facet-defining valid inequalities for PCSP are given. Computational results show that these valid inequalities reduce the gap between LP-value and IP-value substantially.mathematical applications;