In Search of Exceptionally Difficult Constraint Satisfaction Problems (1994) [4 citations — 3 self]
Abstract:
Abstract: It has been observed by several authors that for many NP problems, a sharp peak in the median cost to find a solution can be seen as an order parameter is varied. More recently it has been observed that individual problems which are very difficult can be found at some distance from the peak in the median cost. This paper investigates these exceptionally difficult problems in the context of binary constraint satisfaction problems, and addresses the following questions: how can problems which are difficult to solve arise in a region where most problems are easy to solve? Are the problems which are difficult to solve inherently harder than similar problems, or does the difficulty depend on the solution method? Experimental results show that some problems are inherently more difficult than other similar problems and that an important factor is the diversity in the set of solutions to the problem. Exceptionally difficult problems can also occur if the search space induced by the search algorithm is unusually large.
Citations
| 629 | Foundations of Constraint Satisfaction – Tsang - 1993 |
| 468 | Where the really hard problems are – Cheeseman, Kanefsky, et al. - 1991 |
| 249 | and easy distributions of SAT problems – Hard - 1992 |
| 94 | An empirical study of phase transitions in binary constraint satisfaction problems – Prosser - 1996 |
| 77 | The hardest constraint problems: A double phase transition – Hogg, Williams - 1994 |
| 75 | Exploiting the deep structure of constraint problems – Williams, Hogg - 1994 |
| 36 | Using deep structure to locate hard problems – Williams, Hogg - 1992 |
| 22 | Locating the Phase Transition in Constraint Satisfaction Problems – Smith, Dyer - 1994 |
| 4 | Easy Problems are Sometimes Hard. Research Paper 642 – Gent, Walsh - 1993 |
