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