TY - JOUR

T1 - An approximation algorithm for the hamiltonian walk problem on maximal planar graphs

AU - Nishizeki, Takao

AU - Asano, Takao

AU - Watanabe, Takahiro

N1 - Funding Information:
We wish to thank Professor N. Saito for valuabled iscussionsa nd suggestionosn the subjects.T his work was supportedi n part by the Grant in Aid for Scientific Researcho f the Ministry of Eduction, Sciencea nd Culture of Japan under Grant: CooperativeR esearch( A) 435013(1979E)Y, S 475235(1979a)n d EYS 475259(1979).

PY - 1983/2

Y1 - 1983/2

N2 - 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.

AB - 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.

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U2 - 10.1016/0166-218X(83)90042-2

DO - 10.1016/0166-218X(83)90042-2

M3 - Article

AN - SCOPUS:0020707585

SN - 0166-218X

VL - 5

SP - 211

EP - 222

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 2

ER -