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Is there a polynomial algorithm to solve TSP (or Ham Cycle) on an m by n solid grid graph whose points are at unit distance apart? I've heard about Umans and Lenhart research paper but reading such paper is beyond my capability.

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    $\begingroup$ What problem do you want to solve on solid grid graphs ? Hamiltonian Cycle ? $\endgroup$ – Shiva Kintali Mar 30 '12 at 10:30
  • $\begingroup$ @Shiva, Yes, Hamiltonian Cycle, Travelling Salesman. $\endgroup$ – user8925 Mar 30 '12 at 11:29
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    $\begingroup$ Could you please edit the question (and the title)? $\endgroup$ – Jeffε Mar 30 '12 at 11:47
  • $\begingroup$ What is “m by n solid grid graph”? If it means the m×n grid graph with mn vertices, then it is straightforward to see that the Hamiltonian Cycle problem on such graphs is in P. $\endgroup$ – Tsuyoshi Ito Mar 30 '12 at 16:28
  • $\begingroup$ even if it's beyond you to read the paper, doesn't the abstract answer your question? computer.org/portal/web/csdl/doi/10.1109/SFCS.1997.646138 $\endgroup$ – Sasho Nikolov Mar 30 '12 at 20:00
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This paper is more general than what you're asking for, but should lead you to some answers. It's pretty accessible too:

http://research.cs.queensu.ca/home/yurai/Publications/Hamilt%20of%20thin%20solid%20and%20hard%20grids.pdf

(Though looking at it now the primary reference I'd have suggested out of that would be the Umans and Lenhart paper...)

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