From Unsolvable to Solvable: An Exploration of Simple Changes

Susan L. Epstein, Xi Yun

Abstract: This paper investigates how readily an unsolvable constraint satisfaction problem can be reformulated so that it becomes solvable. We investigate small changes in the definitions of the problem's constraints, changes that alter neither the structure of its constraint graph nor the tightness of its constraints. Our results show that structured and unstructured problems respond differently to such changes, as do easy and difficult problems taken from the same problem class. Several plausible explanations for this behavior are discussed.