Distance, Origin and Category Constrained Paths

Resource Constrained Shortest Paths

The resource constrained shortest path problem (CSP) asks for the computation of a least cost path obeying a set of resource constraints. The problem is NP-complete. We give theoretical and experimental results for CSP. In the theoretical part we present the hull approach, a combinatorial algorithm for solving a linear programming relaxation and prove that it runs in polynomial time in the case...

On Degree Constrained Shortest Paths

Traditional shortest path problems play a central role in both the design and use of communication networks and have been studied extensively. In this work, we consider a variant of the shortest path problem. The network has two kinds of edges, “actual” edges and “potential” edges. In addition, each vertex has a degree/interface constraint. We wish to compute a shortest path in the graph that m...

On Finding Multi-constrained Paths

New emerging distributed multimedia applications provide guaranteed end-to-end quality of service (QoS) and have stringent constraints on delay, delay-jitter, cost, etc. The task of QoS routing is to find a route in the network which has sufficient resources to satisfy the constraints. The delaycost-constrained routing problem is NP-complete. We propose a heuristic algorithm for this problem. T...

Resource constrained shortest paths and extensions

Cost-Constrained Matchings and Disjoint Paths

Let G = (V,E) be a graph, where the edges are weighted with elements from a finite commutative semigroup (S, +), and consider the problem of finding a matching M that covers a given set U of vertices whose cost c(M) (where c(M) is the sum of the weights on the edges of M) satisfies a given constraint, i.e., for a given constraint function Φ mapping S to {0, 1}, Φ(c(M)) = 1. This problem is NP-c...