Abstract
In this paper, we introduce and investigate the Minimum Eccentricity Shortest Path (MESP) problem in unweighted graphs. It asks for a given graph to find a shortest path with minimum eccentricity. We demonstrate that:
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a minimum eccentricity shortest path plays a crucial role in obtaining the best to date approximation algorithm for a minimum distortion embedding of a graph into the line;
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the MESP-problem is NP-hard on general graphs;
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a 2-approximation, a 3-approximation, and an 8-approximation for the MESP-problem can be computed in \(\mathcal {O}(n^3)\) time, in \(\mathcal {O}(nm)\) time, and in linear time, respectively;
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a shortest path of minimum eccentricity k in general graphs can be computed in \(\mathcal {O}(n^{2k+2}m)\) time;
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the MESP-problem can be solved in linear time for trees.
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Dragan, F.F., Leitert, A. (2015). On the Minimum Eccentricity Shortest Path Problem. In: Dehne, F., Sack, JR., Stege, U. (eds) Algorithms and Data Structures. WADS 2015. Lecture Notes in Computer Science(), vol 9214. Springer, Cham. https://doi.org/10.1007/978-3-319-21840-3_23
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DOI: https://doi.org/10.1007/978-3-319-21840-3_23
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