TY - JOUR

T1 - Steiner diagrams and $k$-star hubs

AU - Blasum, U.

AU - Hochstättler, W.

AU - Oertel, P.

AU - Woeginger, G.J.

PY - 2007

Y1 - 2007

N2 - 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 -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 -complete for k3. An efficient algorithm for the case k=2 is given.

AB - 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 -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 -complete for k3. An efficient algorithm for the case k=2 is given.

U2 - 10.1016/j.jda.2006.06.001

DO - 10.1016/j.jda.2006.06.001

M3 - Article

SN - 1570-8667

VL - 5

SP - 622

EP - 634

JO - Journal of Discrete Algorithms

JF - Journal of Discrete Algorithms

IS - 3

ER -