An Empirical Examination of Exact Algorithms for the Cardinality Steiner Problem
چکیده
The Cardinality Steiner Problem (CSP) is a generalization of the well known and easily solved shortest path and minimum spanning tree problems. Despite the polynomial solvability of these and other special cases, the CSP is NP-complete. This complexity notwithstanding, it is a problem of practical concern, having applications in network design, chip layout, data base queries, and phylogeny. It has been an area of considerable research with no less than seven algorithms advanced for its exact solution. However, computational experience with these exact algorithms is limited and does not allow comparative analysis. To provide such an examination, four exact algorithms have been implemented and executed over a wide variety of input which was classified according to various graph theoretic properties. Execution times were measured for individual problems and averages determined for the various problem classifications. The results obtained from this execution alter the previously accepted characterization of these algorithms. In particular, it is shown that the implicit enumeration technique of Shore, Foulds, and Gibbons outperforms the others almost universally. A characterization of those instances for which it performsOpoorly is given and C a means of overcoming this shortcoming suggested. The execution times of the remaining algorithms display little variance for instances of a given graph size. Although it has been stated by several researchers that the dynamic programming technique of Dreyfus and Wagner is more efficient than the similar approach of Levin, it is shown both theoretically and empirically that the opposite is true.