Traces

  • Vivek S. Borkar
  • Vladimir Ejov
  • Jerzy A. Filar
  • Giang T. Nguyen
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 171)

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

Summing 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Vivek S. Borkar
    • 1
  • Vladimir Ejov
    • 2
  • Jerzy A. Filar
    • 2
  • Giang T. Nguyen
    • 3
  1. 1.Department of Electrical EngineeringIIT, PowaiMumbaiIndia
  2. 2.Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and MathematicsFlinders UniversityBedford ParkAustralia
  3. 3.Département d’InformatiqueUniversité libre de BruxellesBrusselsBelgium

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