A frozen glass phase in the multi-index matching problem

Details A frozen glass phase in the multi-index matching problem A frozen glass phase in the multi-index matching problem

2004-07-23

arxiv.org/abs/cond-mat/0407623v1

Physical Review Letters 93 (2004) 217205

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevLett.93.217205

The multi-index matching is an NP-hard combinatorial optimization problem; for two indices it reduces to the well understood bipartite matching problem that belongs to the polynomial complexity class. We use the cavity method to solve the thermodynamics of the multi-index system with random costs. The phase diagram is much richer than for the case of the bipartite matching problem: it shows a finite temperature phase transition to a completely frozen glass phase, similar to what happens in the random energy model. We derive the critical temperature, the ground state energy density, and properties of the energy landscape, and compare the results to numerical studies based on exact analysis of small systems.

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