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The purpose of the online graph exploration problem is to visit all the nodes of a given graph and come back to the starting node with the minimum total traverse cost. However, unlike the classical Traveling Salesperson Problem, information of the graph is given online. When an online algorithm (called a searcher) visits a node *v*, then it learns information on nodes and edges adjacent to *v*. The searcher must decide which node to visit next depending on partial and incomplete information of the graph that it has gained in its searching process. The goodness of the algorithm is evaluated by the *competitive analysis*. If input graphs to be explored are restricted to trees, the depth-first search always returns an optimal tour. However, if graphs have cycles, the problem is non-trivial. In this paper we consider two simple cases. First, we treat the problem on simple cycles. Recently, Asahiro et al. proved that there is a 1.5-competitive online algorithm, while no online algorithm can be (1.25-ε)-competitive for any positive constant ε. In this paper, we give an optimal online algorithm for this problem; namely, we give a

- Publication
- IEICE TRANSACTIONS on Information Vol.E92-D No.9 pp.1620-1627

- Publication Date
- 2009/09/01

- Publicized

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.E92.D.1620

- Type of Manuscript
- PAPER

- Category
- Algorithm Theory

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Shuichi MIYAZAKI, Naoyuki MORIMOTO, Yasuo OKABE, "The Online Graph Exploration Problem on Restricted Graphs" in IEICE TRANSACTIONS on Information,
vol. E92-D, no. 9, pp. 1620-1627, September 2009, doi: 10.1587/transinf.E92.D.1620.

Abstract: The purpose of the online graph exploration problem is to visit all the nodes of a given graph and come back to the starting node with the minimum total traverse cost. However, unlike the classical Traveling Salesperson Problem, information of the graph is given online. When an online algorithm (called a searcher) visits a node *v*, then it learns information on nodes and edges adjacent to *v*. The searcher must decide which node to visit next depending on partial and incomplete information of the graph that it has gained in its searching process. The goodness of the algorithm is evaluated by the *competitive analysis*. If input graphs to be explored are restricted to trees, the depth-first search always returns an optimal tour. However, if graphs have cycles, the problem is non-trivial. In this paper we consider two simple cases. First, we treat the problem on simple cycles. Recently, Asahiro et al. proved that there is a 1.5-competitive online algorithm, while no online algorithm can be (1.25-ε)-competitive for any positive constant ε. In this paper, we give an optimal online algorithm for this problem; namely, we give a

URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E92.D.1620/_p

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@ARTICLE{e92-d_9_1620,

author={Shuichi MIYAZAKI, Naoyuki MORIMOTO, Yasuo OKABE, },

journal={IEICE TRANSACTIONS on Information},

title={The Online Graph Exploration Problem on Restricted Graphs},

year={2009},

volume={E92-D},

number={9},

pages={1620-1627},

abstract={The purpose of the online graph exploration problem is to visit all the nodes of a given graph and come back to the starting node with the minimum total traverse cost. However, unlike the classical Traveling Salesperson Problem, information of the graph is given online. When an online algorithm (called a searcher) visits a node *v*, then it learns information on nodes and edges adjacent to *v*. The searcher must decide which node to visit next depending on partial and incomplete information of the graph that it has gained in its searching process. The goodness of the algorithm is evaluated by the *competitive analysis*. If input graphs to be explored are restricted to trees, the depth-first search always returns an optimal tour. However, if graphs have cycles, the problem is non-trivial. In this paper we consider two simple cases. First, we treat the problem on simple cycles. Recently, Asahiro et al. proved that there is a 1.5-competitive online algorithm, while no online algorithm can be (1.25-ε)-competitive for any positive constant ε. In this paper, we give an optimal online algorithm for this problem; namely, we give a

keywords={},

doi={10.1587/transinf.E92.D.1620},

ISSN={1745-1361},

month={September},}

Copy

TY - JOUR

TI - The Online Graph Exploration Problem on Restricted Graphs

T2 - IEICE TRANSACTIONS on Information

SP - 1620

EP - 1627

AU - Shuichi MIYAZAKI

AU - Naoyuki MORIMOTO

AU - Yasuo OKABE

PY - 2009

DO - 10.1587/transinf.E92.D.1620

JO - IEICE TRANSACTIONS on Information

SN - 1745-1361

VL - E92-D

IS - 9

JA - IEICE TRANSACTIONS on Information

Y1 - September 2009

AB - The purpose of the online graph exploration problem is to visit all the nodes of a given graph and come back to the starting node with the minimum total traverse cost. However, unlike the classical Traveling Salesperson Problem, information of the graph is given online. When an online algorithm (called a searcher) visits a node *v*, then it learns information on nodes and edges adjacent to *v*. The searcher must decide which node to visit next depending on partial and incomplete information of the graph that it has gained in its searching process. The goodness of the algorithm is evaluated by the *competitive analysis*. If input graphs to be explored are restricted to trees, the depth-first search always returns an optimal tour. However, if graphs have cycles, the problem is non-trivial. In this paper we consider two simple cases. First, we treat the problem on simple cycles. Recently, Asahiro et al. proved that there is a 1.5-competitive online algorithm, while no online algorithm can be (1.25-ε)-competitive for any positive constant ε. In this paper, we give an optimal online algorithm for this problem; namely, we give a

ER -