The optimal location of a structured facility in a tree network

Efficient parallel algorithms for finding an optimum path-shaped or tree-shaped facility with a specified size in a tree network are presented. Four kinds of optimization criteria are considered: minimum eccentricity, maximum eccentricity, minimum distancesum, and maximum distancesum. Eight cases are obtained by combining facility shapes and optimization criteria. Optimal parallel algorithms for finding a minimum/maximum distancesum path were presented by B.C. Tansel et al. (1983). The other six cases are studied here. Two of them can be solved optimally in linear time*processor complexity. For the problem of finding a maximum distancesum tree, the algorithm presented is a polynomial time resolution.<<ETX>>

[1]  Peter J. Slater,et al.  A Linear Algorithm for a Core of a Tree , 1980, J. Algorithms.

[2]  Richard Cole,et al.  Approximate Parallel Scheduling. Part I: The Basic Technique with Applications to Optimal Parallel List Ranking in Logarithmic Time , 1988, SIAM J. Comput..

[3]  Pitu B. Mirchandani,et al.  Location on networks : theory and algorithms , 1979 .

[4]  Robert E. Tarjan,et al.  Finding Biconnected Components and Computing Tree Functions in Logarithmic Parallel Time (Extended Summary) , 1984, FOCS.

[5]  Peter J. Slater.  On Locating a Facility to Service Areas within a Network , 1981, Oper. Res..

[6]  A. J. Goldman.  Optimal Center Location in Simple Networks , 1971 .

[7]  David G. Kirkpatrick,et al.  A Simple Parallel Tree Contraction Algorithm , 1989, J. Algorithms.

[8]  P. Slater.  Locating Central Paths in a Graph , 1982 .

[9]  P. J. Slater.  Centrality of paths and vertices in a graph: cores and pits , 1980 .

[10]  Timothy J. Lowe,et al.  Location on Networks: A Survey. Part I: The p-Center and p-Median Problems , 1983 .

[11]  Edward Minieka,et al.  On Finding the Core of a Tree with a Specified Length , 1983, J. Algorithms.

[12]  R. L. Francis,et al.  State of the Art-Location on Networks: A Survey. Part II: Exploiting Tree Network Structure , 1983 .

[13]  Gary L. Miller,et al.  Parallel tree contraction and its application , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[14]  Martine Labbé,et al.  On locating path- or tree-shaped facilities on networks , 1993, Networks.

[15]  Gary L. Miller,et al.  Deterministic Parallel List Ranking , 1988, AWOC.

[16]  Edward Minieka.  The optimal location of a path or tree in a tree network , 1985, Networks.

[17]  S. Hakimi.  Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems , 1965 .