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Finding Short Right-Hand-on-the-Wall Walks in Graphs

  • Conference paper
Structural Information and Communication Complexity (SIROCCO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3499))

Abstract

We consider the problem of perpetual traversal by a single agent in an anonymous undirected graph G. Our requirements are: (1) deterministic algorithm, (2) each node is visited within O(n) moves, (3) the agent uses no memory, it can use only the label of the link via which it arrived to the current node, (4) no marking of the underlying graph is allowed and (5) no additional information is stored in the graph (e.g. routing tables, spanning tree) except the ability to distinguish between the incident edges (called Local Orientation).

This problem is unsolvable, as has been proven in [9,28] even for much less restrictive setting. Our approach is to somewhat relax the requirement (5). We fix the following traversal algorithm: “Start by taking the edge with the smallest labelx. Afterwards, whenever you come to a node, continue by taking the successor edge (in the local orientation) to the edge via which you arrived” and ask whether it is for every undirected graph possible to assign the local orientations in such a way that the resulting perpetual traversal visits every node in O(n) moves.

We give a positive answer to this question, by showing how to construct such local orientations. This leads to an extremely simple, memoryless, yet efficient traversal algorithm.

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Author information

Authors and Affiliations

  1. SITE, University of Ottawa, Canada

    Stefan Dobrev

  2. Department of Computer Science and Information Systems, The University of Hong Kong, Hong Kong

    Jesper Jansson

  3. School of Computing, National University of Singapore,  

    Wing-Kin Sung

  4. Department of Computer Science and Communication Engineering, Kyushu University, Japan

    Kunihiko Sadakane

Authors
  1. Stefan Dobrev
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  2. Jesper Jansson
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  3. Kunihiko Sadakane
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  4. Wing-Kin Sung
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Editor information

Editors and Affiliations

  1. Département d’informatique, Université du Québec en Outaouais, J8X 3X7, Gatineau, Québec, Canada

    Andrzej Pelc

  2. IRISA, Université de Rennes, France

    Michel Raynal

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© 2005 Springer-Verlag Berlin Heidelberg

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Dobrev, S., Jansson, J., Sadakane, K., Sung, WK. (2005). Finding Short Right-Hand-on-the-Wall Walks in Graphs. In: Pelc, A., Raynal, M. (eds) Structural Information and Communication Complexity. SIROCCO 2005. Lecture Notes in Computer Science, vol 3499. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11429647_12

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  • DOI: https://doi.org/10.1007/11429647_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26052-3

  • Online ISBN: 978-3-540-32073-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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