Statistical Characterization of NP-Complete Problems
نویسنده
چکیده
NP-complete problems fall into a range of difficulty and it is of considerable interest to identify the general characteristics of these problems that account for this difference. A method for measuring problem difficulty is developed based on the amount of time it takes to find an optimal solution. This reveals that there are layers of difficulty and that any NP-complete problem can be separated into an easy part and a hard part where solving the hard part involves a search of the first few levels of the decision tree. The difficulty of solving a particular problem is then related to how constrained the system is which is related to both the number of optimal solutions and the ratio of optimal solutions to suboptimal solutions. The results show that the least difficult problems are either highly overconstrained or highly underconstrained systems while the most difficult appear to be in the region of being slightly underconstrained.
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