An efficient algorithm for constructing Hamiltonian paths in meshes

Authors:
Shao Dong Chen;Hong Shen;Rodney Topor
Affiliations:
Hutchison Telecommunications Limited, Hunghom, Kowloon, Hong Kong;Graduate School of Information Science, Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa 923-1292, Japan;School of Computing and Information Technology, Griffith University, Nathan QLD 4111, Australia
Venue:
Parallel Computing
Year:
2002

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Abstract

This paper presents an efficient linear-time sequential algorithm for constructing Hamiltonian paths between two given vertices in meshes with horizontal size m and vertical size n. The algorithm first partitions the given mesh into a number of submeshes in constant steps, and then constructs a Hamiltonian cycle or path in each submesh and combines them together to become a complete Hamiltonian path in mn steps. Our algorithm has improved the previous algorithm [6] by reducing the number of partition steps from O(m + n) to only a constant. Moreover, we show that our algorithm can be optimally parallelized to obtain a constant-time parallel algorithm on the weakest parallel machine without need of inter-processor communication, while this cannot be achieved for the previous algorithm.