Exploring an unknown graph efficiently

Authors:
Rudolf Fleischer;Gerhard Trippen
Affiliations:
Shanghai Key Laboratory of Intelligent Information Processing, Department of Computer Science and Engineering, Fudan University, Shanghai, China;Department of Computer Science, The Hong Kong University of Science and Technology, Hong Kong
Venue:
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Year:
2005

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Abstract

We study the problem of exploring an unknown, strongly connected directed graph. Starting at some node of the graph, we must visit every edge and every node at least once. The goal is to minimize the number of edge traversals. It is known that the competitive ratio of online algorithms for this problem depends on the deficiency d of the graph, which is the minimum number of edges that must be added to make the graph Eulerian. We present the first deterministic online exploration algorithm whose competitive ratio is polynomial in d (it is O(d8)).