Phase transition in the assignment problem for random matrices
<|reference_start|>Phase transition in the assignment problem for random matrices: 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.<|reference_end|>
@article{esteve2005phase,
    title={Phase transition in the assignment problem for random matrices},
    author={J. G. Esteve and F. Falceto},
    journal={arXiv preprint arXiv:cs/0511107},
    year={2005},
    doi={10.1209/epl/i2005-10296-6},
    archivePrefix={arXiv},
    eprint={cs/0511107},
    primaryClass={cs.CC cond-mat.stat-mech}
}