873 research outputs found
A physicist's approach to number partitioning
The statistical physics approach to the number partioning problem, a
classical NP-hard problem, is both simple and rewarding. Very basic notions and
methods from statistical mechanics are enough to obtain analytical results for
the phase boundary that separates the ``easy-to-solve'' from the
``hard-to-solve'' phase of the NPP as well as for the probability distributions
of the optimal and sub-optimal solutions. In addition, it can be shown that
solving a number partioning problem of size to some extent corresponds to
locating the minimum in an unsorted list of \bigo{2^N} numbers. Considering
this correspondence it is not surprising that known heuristics for the
partitioning problem are not significantly better than simple random search.Comment: 35 pages, to appear in J. Theor. Comp. Science, typo corrected in
eq.1
Computational Complexity for Physicists
These lecture notes are an informal introduction to the theory of
computational complexity and its links to quantum computing and statistical
mechanics.Comment: references updated, reprint available from
http://itp.nat.uni-magdeburg.de/~mertens/papers/complexity.shtm
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