License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2021.18
URN: urn:nbn:de:0030-drops-154510
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15451/
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Kumabe, Soh

Interval Query Problem on Cube-Free Median Graphs

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LIPIcs-ISAAC-2021-18.pdf (0.7 MB)


Abstract

In this paper, we introduce the interval query problem on cube-free median graphs. Let G be a cube-free median graph and 𝒮 be a commutative semigroup. For each vertex v in G, we are given an element p(v) in 𝒮. For each query, we are given two vertices u,v in G and asked to calculate the sum of p(z) over all vertices z belonging to a u-v shortest path. This is a common generalization of range query problems on trees and grids. In this paper, we provide an algorithm to answer each interval query in O(log² n) time. The required data structure is constructed in O(n log³ n) time and O(n log² n) space. To obtain our algorithm, we introduce a new technique, named the staircases decomposition, to decompose an interval of cube-free median graphs into simpler substructures.

BibTeX - Entry

@InProceedings{kumabe:LIPIcs.ISAAC.2021.18,
  author =	{Kumabe, Soh},
  title =	{{Interval Query Problem on Cube-Free Median Graphs}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/15451},
  URN =		{urn:nbn:de:0030-drops-154510},
  doi =		{10.4230/LIPIcs.ISAAC.2021.18},
  annote =	{Keywords: Data Structures, Range Query Problems, Median Graphs}
}

Keywords: Data Structures, Range Query Problems, Median Graphs
Collection: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue Date: 2021
Date of publication: 30.11.2021


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