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 travelingsalesman problem (a NPcomplete problem). Like other phase transitions found in combinatoric problems (Ksatisfiability, 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:

EPL (Europhysics Letters)
 Pub Date:
 December 2005
 DOI:
 10.1209/epl/i2005102966
 arXiv:
 arXiv:cs/0511107
 Bibcode:
 2005EL.....72..691E
 Keywords:

 Computer Science  Computational Complexity;
 Condensed Matter  Statistical Mechanics
 EPrint:
 7 pages, 5 figures