Phase transition in the assignment problem for random matrices
Jérôme Estève, Fernando Falceto · Europhysics Letters (EPL) · 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.