Volume 72, Number 5, December 2005
|Page(s)||691 - 697|
|Published online||26 October 2005|
Phase transition in the assignment problem for random matrices
Departamento de Física Teórica, Universidad de Zaragoza - Zaragoza, Spain and Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza Zaragoza, Spain
Accepted: 30 September 2005
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.
PACS: 02.60.Pn – Numerical optimization / 02.70.Rr – General statistical methods / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems
© EDP Sciences, 2005
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