Abstract
In this paper, we introduce the problem of computing a minimum edge ranking spanning tree (MERST); i.e., find a spanning tree of a given graph G whose edge ranking is minimum. Although the minimum edge ranking of a given tree can be computed in polynomial time, we show that problem MERST is NP-hard. Furthermore, we present an approximation algorithm for MERST, which realizes its worst case performance ratio \( \frac{{\min \{ (\Delta ^* - 1)\log n/\Delta ^* ,\Delta ^* - 1\} }} {{\log (\Delta ^* + 1) - 1}} \), where n is the number of vertices in G and Δ* is the maximum degree of a spanning tree whose maximum degree is minimum. Although the approximation algorithm is a combination of two existing algorithms for the restricted spanning tree problem and for the minimum edge ranking problem of trees, the analysis is based on novel properties of the edge ranking of trees.
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© 1999 Springer-Verlag Berlin Heidelberg
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Makino, K., Uno, Y., Ibaraki, T. (1999). On Minimum Edge Ranking Spanning Trees. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_36
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DOI: https://doi.org/10.1007/3-540-48340-3_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66408-6
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