The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Tabu Search
An Adaptive Large Neighborhood Search for the Pickup and Delivery Problem with Transfers
Transportation Science
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In this paper, two problems derived from reload problems in transport logistics are introduced and studied. Given a transitive digraph G=(V,A,w) with nonnegative arc weights (the transport network) and a set of directed node pairs B (the demand), the objective of the Steiner Diagram Problem is to find an acyclic set of arcs S of minimum cost that contains a directed path for each pair in B. This problem is NP-complete in the general case and has some interesting structural properties that make it polynomially solvable if the size of B is bounded by a constant, the triangle inequality holds in A and A is transitively closed. A special case of this problem is a weighted edge cover problem with k cost functions on the vertices. It is shown that this problem is NP-complete for k=3. An efficient algorithm for the case k=2 is given.