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Where the REALLY Hard Problems Are (1991)
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| Venue: | IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI-91),VOLUME 1 |
| Citations: | 683 - 1 self |
BibTeX
@INPROCEEDINGS{Cheeseman91wherethe,
author = {Peter Cheeseman and Bob Kanefsky and William M. Taylor},
title = {Where the REALLY Hard Problems Are},
booktitle = {IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI-91),VOLUME 1},
year = {1991},
pages = {331--337},
publisher = {Morgan Kauffman}
}
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Abstract
It is well known that for many NP-complete problems, such as K-Sat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NP-complete problems can be summarized by at least one "order parameter", and that the hard problems occur at a critical value of such a parameter. This critical value separates two regions of characteristically different properties. For example, for K-colorability, the critical value separates overconstrained from underconstrained random graphs, and it marks the value at which the probability of a solution changes abruptly from near 0 to near 1. It is the high density of well-separated almost solutions (local minima) at this boundary that cause search algorithms to "thrash". This boundary is a type of phase transition and we show that it is preserved under mappings between problems. We show that for some P problems either there is no phase transition or it occurs for bounded N (and so bound...
