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Exact algorithms based on specific complexity measures for hard problems (2007)
BibTeX
@MISC{Mölle07exactalgorithms,
author = {Daniel Mölle},
title = {Exact algorithms based on specific complexity measures for hard problems},
year = {2007}
}
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Abstract
At present, most of the important computational problems — be they decision, search, or optimization problems — are known to satisfy one of the following two criteria: 1. The problem can be solved in polynomial time with respect to the input size n, where the degree of the polynomial is small enough to guarantee that the problem can be tackled efficiently in practice. In particular, the decision version of the problem is in P. Typical time complexities are O(n log n) and O(n k), k ≤ 3. 2. The problem is NP-hard, and its decision version is NP-complete. We do not know whether the problem can be solved in polynomial time, but it is complex enough to express every other NP-complete problem via polynomial-time transformations. A typical time complexity for this case is O(c n) with c> 1.
