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| HAL: hal-00374071, version 1 |
| DOI: 10.1007/978-3-642-02930-1_34 |
| Detailed view |  Export this paper |
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| ICALP 2009, Greece (2009) |
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| Derandomizing Random Walks in Undirected Graphs Using Locally Fair Exploration Strategies |
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| Colin Cooper 1David Ilcinkas 2, 3 |
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| (2009-07) |
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| We consider the problem of exploring an anonymous undirected graph using an oblivious robot. The studied exploration strategies are designed so that the next edge in the robot's walk is chosen using only local information, and so that some local equity (fairness) criterion is satisfied for the adjacent undirected edges. Such strategies can be seen as an attempt to derandomize random walks, and are natural undirected counterparts of the rotor-router model for symmetric directed graphs. The first of the studied strategies, known as Oldest-First (OF), always chooses the neighboring edge for which the most time has elapsed since its last traversal. Unlike in the case of symmetric directed graphs, we show that such a strategy in some cases leads to exponential cover time. We then consider another strategy called Least-Used-First (LUF) which always uses adjacent edges which have been traversed the smallest number of times. We show that any Least-Used-First exploration covers a graph G=(V,E) of diameter diam within time O(diam|E|), and in the long run traverses all edges of G with the same frequency. |
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| 1: | Department of Computer Science (DCS) |
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King's College London |
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| 2: | Laboratoire Bordelais de Recherche en Informatique (LaBRI) |
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CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – Ecole Nationale Supérieure d'Electronique, Informatique et Radiocommunications de Bordeaux – Université Victor Segalen - Bordeaux II |
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| 3: | CEPAGE (INRIA Bordeaux - Sud-Ouest) |
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INRIA – CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – ENSEIRB |
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| 4: | Department of Algorithms and System Modeling [Gdansk] |
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Gdansk University of Technology |
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| Combinatoire et Algorithmique |
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| Subject | : | Computer Science/Distributed, Parallel, and Cluster Computing Computer Science/Data Structures and Algorithms |
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| graph exploration : Propp machine |
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| Attached file list to this document: | |||||
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| hal-00374071, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00374071 | |
| oai:hal.archives-ouvertes.fr:hal-00374071 | |
| From: Ralf Klasing | |
| Submitted on: Tuesday, 16 June 2009 17:28:21 | |
| Updated on: Thursday, 1 December 2011 20:39:46 | |
