Phase transition in the assignment problem for random matrices

Details Phase transition in the assignment problem for random matrices Phase transition in the assignment problem for random matrices

2005-11-30

arxiv.org/abs/cs/0511107v1

Computer Science

Computational Complexity

7 pages, 5 figures; accepted for publication in Europhys. Lett. http://www.edpsciences.org/journal/index.cfm?edpsname=epl

Scientific paper

10.1209/epl/i2005-10296-6

We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem (a NP-complete problem). Like other phase transitions found in combinatoric problems (K-satisfiability, number partitioning) this can help to understand the nature of the difficulties in solving NP problems an to find more accurate algorithms for them.

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