An approximation algorithm for the hamiltonian walk problem on maximal planar graphs

Takao Nishizeki, Takao Asano, Takahiro Watanabe

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

A hamiltonian walk of a graph is a shortest closed walk that passes through every vertex at least once, and the length is the total number of traversed edges. The hamiltonian walk problem in which one would like to find a hamiltonian walk of a given graph is NP-complete. The problem is a generalized hamiltonian cycle problem and is a special case of the traveling salesman problem. Employing the techniques of divide-and-conquer and augmentation, we present an approximation algorithm for the problem on maximal planar graphs. The algorithm finds, in O(p2) time, a closed spanning walk of a given arbitrary maximal planar graph, and the length of the obtained walk is at most 3 2(p - 3) if the graph has p (≥ 9) vertices. Hence the worst-case bound is 3 2.

Original languageEnglish
Pages (from-to)211-222
Number of pages12
JournalDiscrete Applied Mathematics
Volume5
Issue number2
DOIs
Publication statusPublished - 1983
Externally publishedYes

Fingerprint

Hamiltonians
Approximation algorithms
Walk
Planar graph
Approximation Algorithms
Traveling salesman problem
Graph in graph theory
Closed
Divide and conquer
Hamiltonian circuit
Augmentation
Travelling salesman problems
NP-complete problem
Arbitrary
Vertex of a graph

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics
  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

An approximation algorithm for the hamiltonian walk problem on maximal planar graphs. / Nishizeki, Takao; Asano, Takao; Watanabe, Takahiro.

In: Discrete Applied Mathematics, Vol. 5, No. 2, 1983, p. 211-222.

Research output: Contribution to journalArticle

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