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Traces

In: Hamiltonian Cycle Problem and Markov Chains

Author

Listed:
  • Vivek S. Borkar

    (IIT, Powai)

  • Vladimir Ejov

    (Flinders University)

  • Jerzy A. Filar

    (Flinders University)

  • Giang T. Nguyen

    (Université libre de Bruxelles)

Abstract

In this chapter, we present an alternative optimisation model that is equivalent to the Hamiltonian cycle problem. We show that instead of minimising top-left elements of the fundamental matrices like in Chapter 3, or maximising the determinant of the inverse of the fundamental matrices like in Chapter 5, one can minimise the traces of the fundamental matrices to determine the Hamiltonicity of a given graph. While it is unclear whether the trace function offers an algorithmic advantage over the top-left element or the determinant functions, the trace operator is certainly well studied and frequently employed.

Suggested Citation

  • Vivek S. Borkar & Vladimir Ejov & Jerzy A. Filar & Giang T. Nguyen, 2012. "Traces," International Series in Operations Research & Management Science, in: Hamiltonian Cycle Problem and Markov Chains, edition 127, chapter 0, pages 91-109, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-3232-6_6
    DOI: 10.1007/978-1-4614-3232-6_6
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