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;

A dynamic programming algorithm for the local access network expansion problem

Technological innovations and growing consumer demand have led to a variety of design and expansion problems in telecommunication networks. In particular, local access net- works have received a lot of attention, since they account for approximately 60% of total investments in communication facilities. In this paper we consider the Local Access Network Expansion Problem, in which growing demand can be satisfied by expanding cable capacities and/or installing concentrators in the network. The problem is known to be NP-hard. We present a pseudo-polynomial dynamic programming algorithm, with time complexity O( nB²) and storage requirements O( nB ), where n refers to the size of the network, and B to an upper bound on concentrator capacity. The cost structure in the network is assumed to be decomposable, but may be non-convex, non-concave, and node and edge dependent otherwise. Computational results indicate that the algorithm is very efficient and can solve medium to large scale problems to optimality within (fractions of) seconds to minutes.mathematical economics and econometrics ;