State-Space Transformation for Approximation and Flexible Computation

Abstract

Most combinatorial optimization problems are NP-hard, and require computation exponential to the problem size. How can we solve difficult tree-search problems approximately, using the analytical results of their average-case complexity? The answer to this question leads to a new approximation approach, the topic of this chapter. This new method makes use of the complexity transitions of branch-and-bound on incremental random trees, and is referred to as ε-transformation.

The author thanks American Association for Artificial Intelligence for permission to reprint some of the text and figures in the article “Epsilon-transformation: Exploiting phase transitions to solve combinatorial optimization problems — Initial results” by Weixiong Zhang and Joseph C. Pemberton which appeared in Proceedings of the 12th National Conference on Artificial Intelligence (AAAI-94), Seattle, WA, July 31-August 4, 1994, pp.895–900, and to Elsevier Science for permission to reprint some of the text and figures in the article “Epsilontransformation: Exploiting phase transitions to solve combinatorial optimization problems” by Joseph C. Pemberton and Weixiong Zhang which appeared in Artificial Intelligence, 81(1–2) (1996) 297–325.