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Title:
CSDM: A Tutorial on the Likely Worst-Case Complexities of NP-Complete Problems
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Abstract:
Abstract
The P vs. NP problem has sometimes been unofficially paraphrased as asking whether
it is possible to improve on exhaustive search for such problems as Satisfiability, Clique,
Graph Coloring, etc. However, known algorithms for each of these problems indeed are
substantially better than exhaustive search, if still exponential. Furthermore, although a
polynomial-time algorithm for any one of these problems implies one for all of them, these
improved exponential algorithms are highly specific, and it is unclear what the limit of
improvement should be.
In the past 15 years or so, a complexity theory for exponential complexities has emerged.
Fundamental to this theory are two related hypotheses: the Exponential Time Hypothesis,
that each k-SAT problem requires time 2ckn for 0
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