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28 March 2024
 
  » arxiv » cond-mat/0407623

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A frozen glass phase in the multi-index matching problem
O. C. Martin ; M. Mezard ; O. Rivoire ;
Date 23 Jul 2004
Journal Physical Review Letters 93 (2004) 217205
Subject Disordered Systems and Neural Networks | cond-mat.dis-nn
AbstractThe 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.
Source arXiv, cond-mat/0407623
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