An efficient algorithm for constructing Hamiltonian paths in meshes

Chen, Shao Dong; Shen, Hong; Topor, Rodney W.

doi:10.1016/s0167-8191(02)00135-7

Cited by 33 publications

(1 citation statement)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Zamfirescu et al [13] provided sufficient conditions for a grid graph to have a Hamiltonian cycle and showed that all grid graphs of positive width have Hamiltonian line graphs. Chen et al [14] improved the Hamiltonian path algorithm for rectangular grid graphs and presented a parallel algorithm for the Hamiltonian path problem with two given end vertices. Lenhart and Umans [15] showed that the Hamiltonian cycle problem on solid grid graphs can be solved in polynomial time.…”

Section: Introductionmentioning

confidence: 99%

The Longest (s, t)-Path Problem on O-Shaped Supergrid Graphs

Keshavarz-Kohjerdi

Hung

2023

Mathematics

View full text Add to dashboard Cite

The longest (s,t)-path problem on supergrid graphs is known to be NP-complete. However, the complexity of this problem on supergrid graphs with or without holes is still unknown.In the past, we presented linear-time algorithms for solving the longest (s,t)-path problem on L-shaped and C-shaped supergrid graphs, which form subclasses of supergrid graphs without holes. In this paper, we will determine the complexity of the longest (s,t)-path problem on O-shaped supergrid graphs, which form a subclass of supergrid graphs with holes. These graphs are rectangular supergrid graphs with rectangular holes. It is worth noting that O-shaped supergrid graphs contain L-shaped and C-shaped supergrid graphs as subgraphs, but there is no inclusion relationship between them. We will propose a linear-time algorithm to solve the longest (s,t)-path problem on O-shaped supergrid graphs. The longest (s,t)-paths of O-shaped supergrid graphs have applications in calculating the minimum trace when printing hollow objects using computer embroidery machines and 3D printers.

show abstract

Section: Introductionmentioning

confidence: 99%