Abstract
We preset a siple epth-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 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 Ω (d 2 m) 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 = Ω(n 2).
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© 1997 Springer-Verlag Berlin Heidelberg
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Kwek, S. (1997). On a simple depth-first search strategy for exploring unknown graphs. In: Dehne, F., Rau-Chaplin, A., Sack, JR., Tamassia, R. (eds) Algorithms and Data Structures. WADS 1997. Lecture Notes in Computer Science, vol 1272. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63307-3_73
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DOI: https://doi.org/10.1007/3-540-63307-3_73
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