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On a Simple Depth-First Search Strategy for Exploring Unknown Graphs (1997)
| Venue: | In Proceedings of the Workshop on Algorithms and Data Structures |
| Citations: | 9 - 0 self |
BibTeX
@INPROCEEDINGS{Kwek97ona,
author = {Stephen Kwek},
title = {On a Simple Depth-First Search Strategy for Exploring Unknown Graphs},
booktitle = {In Proceedings of the Workshop on Algorithms and Data Structures},
year = {1997},
pages = {345--353},
publisher = {Springer}
}
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Abstract
. We present a simple depth-first search strategy for exploring (constructing) an unknown strongly connected graph G with m edges and n vertices by traversing at most min(mn;dn 2 +m) edges. Here, d is the minimum number of edges needed to add to G to make it Eulerian. This parameter d is known as the deficiency of a graph and was introduced by Kutten [Kut88]. It was conjectured that graphs with low deficiency can be traversed more efficiently than graphs with high deficiency. Deng and Papadimitriou [DP90] provided evidence that the conjecture may be true by exhibiting a family of graphs where the robot can be forced to traverse\Omega \Gamma d 2 m \Delta edges in the worst case. Since then, there has been some interest in determining whether a graph with deficiency d can be explored by traversing O(poly(d)m) edges. Our algorithm achieves such bound when the graph is dense, say m =\Omega (n 2 ). 1 Introduction The Graph Exploration Problem We look at the following classic g...
