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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 52, 2003 - Issue 4-5
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Original Articles

Geometric interpretation of Hamiltonian cycles problem via singularly perturbed Markov decision processes

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Pages 441-458 | Received 09 Jan 2003, Accepted 23 Jul 2003, Published online: 13 May 2010

References

  • Andramonov M. Filar J.A. Rubinov A. Pardalos P. 2000 Hamiltonian cycle problem via Markov chains and min-type approaches In: P.M. Pardalos (Ed.) Approximation and Complexity in Numerical Optimization: Continuous and Discrete Problems pp. 31–47 Kluwer Academic Publishers Dordrecht The Netherlands
  • Filar J. Gondzio J. Ejov V. 2003 An interior point heuristic for the Hamiltonian cycle problem via Markov decision processes Journal of Global Optimization (to appear)
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  • Filar , J.A. and Lasserre , J-B. 2000 . A non-standard branch and bound method for the Hamiltonian cycle problem . ANZIAM J. , 42 ( E ) : C556 – C577 .
  • Filar J. Vrieze K. 1996 Competitive Markov Decision Processes Springer New York
  • Kallenberg L.C.M 1983 Linear programming and finite Markovian control problems Mathematical Centre Tract  148 Mathematisch Centrum Amsterdam
  • Karp , R. 1977 . Probabilistic analysis of partitioning algorithms for the travelling-salesman problem in the plane . Mathematics of Operations Research , 2 ( 3 ) : 209 – 224 .
  • Murray W. Ng K.-M. 2003 An algorithm for nonlinear optimization problems with discrete variables Submitted to Mathematical Programming
  • Parberry , I. 1997 . An efficient algorithm for the Knight's tour problem . Discrete Applied Mathematics , 73 : 251 – 260 .
  • Robinson , R. and Wormald , N. 1994 . Almost all regular graphs are Hamiltonian . Random Structures and Algorithms , 5 ( 2 ) : 363 – 374 .
  • Wilson R.J. 1996 Introduction to Graph Theory Longman Harlow

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