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DOI: 10.4230/LIPIcs.ISAAC.2021.18
URN: urn:nbn:de:0030-drops-154510
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15451/
Kumabe, Soh
Interval Query Problem on Cube-Free Median Graphs
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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 | |
| Seminar: | 32nd International Symposium on Algorithms and Computation (ISAAC 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 30.11.2021 |
