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 language | English |
|---|---|
| Pages (from-to) | 211-222 |
| Number of pages | 12 |
| Journal | Discrete Applied Mathematics |
| Volume | 5 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1983 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - An approximation algorithm for the hamiltonian walk problem on maximal planar graphs
AU - Nishizeki, Takao
AU - Asano, Takao
AU - Watanabe, Takahiro
PY - 1983
Y1 - 1983
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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UR - http://www.scopus.com/inward/citedby.url?scp=0020707585&partnerID=8YFLogxK
U2 - 10.1016/0166-218X(83)90042-2
DO - 10.1016/0166-218X(83)90042-2
M3 - Article
VL - 5
SP - 211
EP - 222
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
IS - 2
ER -