883 research outputs found
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
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
- …