Phase transition in the assignment problem for random matrices
Abstract
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.
- Publication:
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EPL (Europhysics Letters)
- Pub Date:
- December 2005
- DOI:
- 10.1209/epl/i2005-10296-6
- arXiv:
- arXiv:cs/0511107
- Bibcode:
- 2005EL.....72..691E
- Keywords:
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- Computer Science - Computational Complexity;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 7 pages, 5 figures