Toward systematic generation of 3COL instances based on minimal unsolvable structures

In this paper, the authors propose a method of systematically generating 3-colorable (3COL) graph instances for which a great deal of time and effort are required to obtain a solution (or to determine solvability). This method, which differs from the conventional approach of selecting hard instances from among randomly generated instances, aims to reliably generate hard problems by repeatedly embedding 3COL minimal unsolvable structures in the initial graph. The generated instances conform to various conditions of problems for which the solution searches that had been identified conventionally are extremely difficult. Also, the authors use several solution search algorithms to experimentally verify that the required effort is an exponential order of the number of vertices. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(12): 27–35, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20359