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Distance-Preserving Subgraphs of Interval Graphs

Authors Kshitij Gajjar, Jaikumar Radhakrishnan



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Kshitij Gajjar
Jaikumar Radhakrishnan

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Kshitij Gajjar and Jaikumar Radhakrishnan. Distance-Preserving Subgraphs of Interval Graphs. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 39:1-39:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ESA.2017.39

Abstract

We consider the problem of finding small distance-preserving subgraphs of undirected, unweighted interval graphs that have k terminal vertices. We show that every interval graph admits a distance-preserving subgraph with O(k log k) branching vertices. We also prove a matching lower bound by exhibiting an interval graph based on bit-reversal permutation matrices. In addition, we show that interval graphs admit subgraphs with O(k) branching vertices that approximate distances up to an additive term of +1.
Keywords
  • interval graphs
  • shortest path
  • distance-preserving subgraphs
  • bit-reversal permutation matrix

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