Traces

Vivek S. Borkar (), Vladimir Ejov (), Jerzy A. Filar () and Giang T. Nguyen ()
Additional contact information
Vivek S. Borkar: IIT, Powai
Vladimir Ejov: Flinders University
Jerzy A. Filar: Flinders University
Giang T. Nguyen: Université libre de Bruxelles

Chapter Chapter 6 in Hamiltonian Cycle Problem and Markov Chains, 2012, pp 91-109 from Springer

Abstract: 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.

Keywords: Markov Chain; Transient State; Hamiltonian Cycle; Fundamental Matrice; Deviation Matrix (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4614-3232-6_6

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DOI: 10.1007/978-1-4614-3232-6_6

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