2026-07-31T00:38:37Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:15451 2024-03-06T10:55:19Z ddc:004 open_access

Interval Query Problem on Cube-Free Median Graphs Kumabe, Soh Data Structures Range Query Problems Median Graphs 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Soh Kumabe 2021 Is Part Of LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2021.18 urn:nbn:de:0030-drops-154510 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.18 eng https://creativecommons.org/licenses/by/4.0/legalcode