A Dynamic Programming Algorithm for the ATM Network Installation Problem on a Tree

This paper considers the ATM Network Installation Problem on a tree. To install such a communication network, decisions concerning the location of hardware devices, the capacity installation on links, and the routing of demands have to be made simultaneously. The problem is shown to be NP-hard. By exploiting the tree structure we show that the problem can be solved to optimality using a pseudo-polynomial time dynamic programming algorithm. Computational experiments on real-life problem instances indicate that the algorithm is highly efficient.Economics ;

Lifting valid inequalities for the precedence constrained knapsack problem

This paper considers the precedence constrained knapsack problem. More specifically, we are interested in classes of valid inequalities which are facet-defining for the precedence constrained knapsack polytope. We study the complexity of obtaining these facets using the standard sequential lifting procedure. Applying this procedure requires solving a combinatorial problem. For valid inequalities arising from minimal induced covers, we identify a class of lifting coefficients for which this problem can be solved in polynomial time, by using a supermodular function, and for which the values of the lifting coefficients have a combinatorial interpretation. For the remaining lifting coefficients it is shown that this optimization problem is strongly NP-hard. The same lifting procedure can be applied to (1,k)-configurations, although in this case, the same combinatorial interpretation no longer applies. We also consider K-covers, to which the same procedure need not apply in general. We show that facets of the polytope can still be generated using a similar lifting technique. For tree knapsack problems, we observe that all lifting coefficients can be obtained in polynomial time. Computational experiments indicate that these facets significantly strengthen the LP-relaxation.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 ;

Lifting valid inequalities for the precedence constrained knapsack problem

This paper considers the precedence constrained knapsack problem. More specically, we are interested in classes of valid inequalities which are facet-defining for the precedence constrained knapsack polytope. We study the complexity of obtaining these facets using the standard sequential lifting procedure. Applying this procedure requires solving a combinatorial problem. For valid inequalities arising from minimal induced covers, we identify a class of lifting coefficients for which this problem can be solved in polynomial time, by using a supermodular function, and for which the values of the lifting coefficients have a combinatorial interpretation. For the remaining lifting coefficients it is shown that this optimization problem is strongly NP-hard. The same lifting procedure can be applied to (1,k)-configurations, although in this case, the same combinatorial interpretation no longer applies. We also consider K-covers, to which the same procedure need not apply in general. We show that facets of the polytope can still be generated using a similar lifting technique. For tree knapsack problems, we observe that all lifting coecients can be obtained in poly-nomial time. Computational experiments indicate that these facets significantly strengthen the LP-relaxation