Heuristics

Abstract

ESP is known to be nonpreemptive parallel (NP)-hard, so it is important to derive effective heuristics to solve for general cases. An effective heuristic means an algorithm, which can run in time proportional to a low-degree polynomial of n, and whose output tree length does not exceed that of the Steiner minimal trees (SMT) significantly. Such a heuristic tree is readily available in the form of a minimum spanning tree (MST), where an O (n 1og n) algorithm exists and whose length does not exceed that of an SMT. Therefore, the MST naturally becomes the standard, against which other heuristics are compared. This chapter discusses several heuristics. The heuristics either improve on a given MST, or emulate a given MST algorithm. A simulated annealing algorithm and a probabilistic algorithm are discussed. The chapter presents a simple but easily analyzed heuristic. An effective reduction to the Steiner problem in networks is also discussed. © 1992, Elsevier Science & Technology. All rights reserved.