Hamiltonian cycles in solid grid graphs

Optimal Covering Tours with Turn Costs

“…The problem is also closely related to the Hamiltonicity problem in grid graphs; the results of [44] suggest that in simple polygons, minimum-length milling may in fact have a polynomial-time algorithm.…”

“…While we tend to believe that Problem 6.1 may have the answer "NP-complete", a polynomial solution would immediately lead to a 1.5-approximation for the orthogonal case, and a (1 + For various optimization problems dealing with geometric regions, there is a notable difference in complexity between a region with holes, and a simple region that does not have any holes. (In particular, it can be decided in polynomial time whether a given grid graph without holes has a Hamiltonian cycle [44], even though the complexity of the TSP on these graphs is still open.) Our NP-hardness proof makes strong use of holes; furthermore, the complexity of the PTAS described above is exponential in the number of holes.…”

An algorithm for computing simple k-factors

“…The idea of computing 2-factors for obtaining subgraphs as close as possible to Hamiltonian cycles has also been used on solid grid graphs [14]. Umans and Lenhart present an algorithm that by merging cycles of a 2-factor produces a Hamiltonian cycle, provided that the graph is Hamiltonian.…”

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AbstractA k-factor of graph G is defined as a k-regular spanning subgraph of G. For instance, a 2-factor of G is a set of cycles that span G. 2-factors have multiple applications in Graph Theory, Computer Graphics, and Computational Geometry [5,4,6,14]. We define a simple 2-factor as a 2-factor without degenerate cycles.

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On the Competitive Complexity of Navigation Tasks

“…There are, however, some results concerning the related Hamiltonian cycle and path problems [14,44] and approximations [2,38].…”