论文信息 - Worst-Case Performance of Some Heuristics for Steiner's Problem in Directed Graphs

Worst-Case Performance of Some Heuristics for Steiner's Problem in Directed Graphs

Abstract Steiner's problem in directed graphs is to find a minimum-cost subgraph of a given directed graph such that a directed path from a root node to every vertex of a set of specified vertices exists. According to the NP-hardness of the problem one is interested in developing efficient heuristic algorithms to find good approximate solutions. In this paper we investigate the worst-case performance of some heuristics and study their comparability by means of some examples.

Stefan Voß | S. Voß

[1] Peter Widmayer,et al. An Approximation Algorithms for Steiner's Problem in Graphs , 1986, WG.

[2] Choukhmane El-Arbi. Une heuristique pour le problème de l'arbre de Steiner , 1978 .

[3] R. Prim. Shortest connection networks and some generalizations , 1957 .

[4] A. Volgenant,et al. Reducing the hierarchical network design problem , 1989 .

[5] Robert E. Tarjan,et al. Efficient algorithms for finding minimum spanning trees in undirected and directed graphs , 1986, Comb..

[6] Dana S. Richards,et al. Steiner tree problems , 1992, Networks.

[7] Makoto Imase,et al. Worst-Case Performance of Rayward-Smith's Steiner Tree Heuristic , 1988, Inf. Process. Lett..

[8] Stefan Voss,et al. Steiner-Probleme in Graphen , 1990 .

[9] Stefan Voß,et al. Steiner's Problem in Graphs: Heuristic Methods , 1992, Discret. Appl. Math..

[10] Pawel Winter,et al. Steiner problem in networks: A survey , 1987, Networks.

[11] J. Plesník. A bound for the Steiner tree problem in graphs , 1981 .

[12] Kurt Mehlhorn,et al. A Faster Approximation Algorithm for the Steiner Problem in Graphs , 1988, Inf. Process. Lett..

[13] Richard T. Wong,et al. A dual ascent approach for steiner tree problems on a directed graph , 1984, Math. Program..

[14] J. Plesnik. WORST-CASE RELATIVE PERFORMANCES OF HEURISTICS FOR THE STEINER PROBLEM IN GRAPHS , 1991 .