STEINER POINT REMOVAL with DISTORTION /bfitO (log /bfitk ) USING the RELAXED-VORONOI ALGORITHM

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Abstract

In the Steiner point removal problem, we are given a weighted graph G = (V, E) and a set of terminals K \subset V of size k. The objective is to find a minor M of G with only the terminals as its vertex set, such that distances between the terminals will be preserved up to a small multiplicative distortion. Kamma, Krauthgamer, and Nguyen [SIAM J. Comput., 44 (2015), pp. 975-995] devised a ball-growing algorithm with exponential distributions to show that the distortion is at most O(log5 k). Cheung [Proceedings of the 29th Annual ACM/SIAM Symposium on Discrete Algorithms, 2018, pp. 1353-1360] improved the analysis of the same algorithm, bounding the distortion by O(log2 k). We devise a novel and simpler algorithm (called the Relaxed-Voronoi algorithm) which incurs distortion O(log k). This algorithm can be implemented in almost linear time (O(| E| log | V | )).

Original languageEnglish
Pages (from-to)249-278
Number of pages30
JournalSIAM Journal on Computing
Volume48
Issue number2
DOIs
StatePublished - 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics

Keywords

  • Distortion
  • Metric embedding
  • Minor graph
  • Randomized algorithm
  • Steiner point removal (SPR)

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