Doubly Stochastic Matrices & The Hamiltonian Cycle Problem
(J Filar with VS Borkar and W Murray)
Funding
ARC (2006 – 2010), “Doubly Stochastic Matrices & The Hamiltonian Cycle
Problem”.
Leading CI: Prof JA Filar
Collaborators: Overseas Investigators: Prof VS Borkar (Tata Inst. Of Fundamental Research, Mumbai, India, Prof W Murray (Stanford, USA)
Note: Includes funding for a prestigious Australian Professorial Fellowship for Professor Jerzy Filar
Publications
V. Borkar, V. Ejov, and J. A. Filar. On the Hamiltonicity gap and doubly
stochastic matrices, to appear in Random Structures and Algorithms, (2009).
V. Ejov, J. Filar, W. Murray and G. T. Nguyen, "Determinants and longest
cycles of graphs", SIAM J. Discrete Math., 22:3 (2008), pp. 1215-1225.
J. A. Filar. Controlled Markov chains, graphs, and Hamiltonicity.
Foundations and Trends in Stochastic Systems, 1:2 (2007), pp. 77-162.
V. Ejov, J. Filar, S. Lucas and P. Zograf, Clustering of spectra and
fractals of regular graphs, Journal of Mathematical Analysis and
Application, 333 (2007), pp. 236-246.
V. Ejov, J. Filar, J. Nelson, and S. Lucas, Solving the Hamiltonian Cycle
problem using symbolic determinants, Taiwanese Journal of Mathematics, 10:2
(2006), pp. 327-338.
V. Borkar, V. Ejov and J. Filar, Directed graphs, Hamiltonicity and doubly
stochastic matrices, Random Structures and Algorithms, 25 (2005), pp.
376-395.
J. A. Filar, A. Gupta, and S. K. Lucas. Connected co-spectral graphs are not
necessarily both Hamiltonian. The Australian Mathematical Society Gazette,
32:3 (2005), 193.
V. Ejov, J. Filar and J. Gondzio, An Interior Point Heuristic for the
Hamiltonian Cycle Problem via Markov Decision Processes, Journal of Global
Optimization, 29 (2004), pp. 315-334.
V. Ejov, J. Filar and M. Nguyen, Hamiltonian Cycles and Singularly Perturbed
Markov Chains, Mathematics of Operations Research, v. 29:1 (2004), pp.
114-131.
V. Ejov, J. Filar and J. Thredgold, Geometric interpretation of Hamiltonian
Cycles problem via singularly perturbed Markov decision processes,
Optimization, 52 (2003), pp. 441-458.
J. A. Filar and J-B Lasserre. A non-standard branch and bound method for the
Hamiltonian cycle problem. ANZIAM Journal, 42(E) (2000), pp. 556-577.
J. A. Filar and K. Liu. Hamiltonian cycle problem and singularly perturbed
decision process. IMS Lecture Notes-Monograph Series, Statistics,
probability and game theory: Papers in honour of David Blackwell (1996) pp.
44-63.