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Locating phase transitions in computationally hard problems

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Abstract

We discuss how phase-transitions may be detected in computationally hard problems in the context of anytime algorithms. Treating the computational time, value and utility functions involved in the search results in analogy with quantities in statistical physics, we indicate how the onset of a computationally hard regime can be detected and the transit to higher quality solutions be quantified by an appropriate response function. The existence of a dynamical critical exponent is shown, enabling one to predict the onset of critical slowing down, rather than finding it after the event, in the specific case of a travelling salesman problem (TSP). This can be used as a means of improving efficiency and speed in searches, and avoiding needless computations.

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Author notes

  1. T. K. Patra

    Present address: Department of Chemical Engineering, Indian Institute of Technology, Kanpur, 208 016, India

Authors and Affiliations

  1. Advanced Centre of Research in High Energy Materials, University of Hyderabad, Central University P.O., Gachi Bowli, Hyderabad, 500 046, India

    B. Ashok

  2. School of Physics, University of Hyderabad, Central University P.O., Gachi Bowli, Hyderabad, 500 046, India

    T. K. Patra

Authors
  1. B. Ashok
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  2. T. K. Patra
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Correspondence to B. Ashok.

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Ashok, B., Patra, T.K. Locating phase transitions in computationally hard problems. Pramana - J Phys 75, 549–563 (2010). https://doi.org/10.1007/s12043-010-0138-0

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  • DOI: https://doi.org/10.1007/s12043-010-0138-0

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