Algorithms for finding optimum trees: Description, use and evaluation

This work is devoted to the problem of finding an optimum spanning tree in an undirected graph. Both min-sum and min-max trees are sought. The five algorithms considered are among the most well-known proposed in the literature. They are described in sect. 1 as thoroughly as possible, using a simplified Pascal language; all min-sum algorithms are derived from a unique prototype formulation. In sect. 2, the algorithms are implemented in PFORT to enhance their portability and ad hoc data structures are utilized in order to obtain subroutines as efficient as possible. Finally, in sect. 3, the programs are evaluated, comparing their performances in handling several classes of randomly generated graphs. Various observations are reported, and some indications for choosing the most suitable algorithm in each case are provided.

[1]  Alan M. Frieze,et al.  On the value of a random minimum spanning tree problem , 1985, Discret. Appl. Math..

[2]  R. V. Slyke,et al.  Computing minimum spanning trees efficiently , 1972, ACM Annual Conference.

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

[4]  Paolo M. Camerini.  The Min-Max Spanning Tree Problem and Some Extensions , 1978, Inf. Process. Lett..

[5]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[6]  Robert E. Tarjan,et al.  Data structures and network algorithms , 1983, CBMS-NSF regional conference series in applied mathematics.

[7]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[8]  Barbara G. Ryder,et al.  The pfort verifier , 1974, Softw. Pract. Exp..

[9]  Robert E. Tarjan,et al.  Efficiency of a Good But Not Linear Set Union Algorithm , 1972, JACM.

[10]  Donald B. Johnson,et al.  Priority Queues with Update and Finding Minimum Spanning Trees , 1975, Inf. Process. Lett..

[11]  Michael Ian Shamos,et al.  Geometric complexity , 1975, STOC.

[12]  M. Fischetti,et al.  A hybrid algorithm for finding thekth smallest ofn elements in O(n) time , 1988 .

[13]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[14]  Zvi Galil,et al.  Efficient Implementation of Graph Algorithms Using Contraction , 1984, FOCS.

[15]  Giorgio Gallo,et al.  Shortest path algorithms , 1988, Handbook of Optimization in Telecommunications.

[16]  Robert E. Tarjan,et al.  Finding Minimum Spanning Trees , 1976, SIAM J. Comput..

[17]  Andrew Chi-Chih Yao,et al.  An O(|E| log log |V|) Algorithm for Finding Minimum Spanning Trees , 1975, Inf. Process. Lett..