eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2021-11-30
18:1
18:14
10.4230/LIPIcs.ISAAC.2021.18
article
Interval Query Problem on Cube-Free Median Graphs
Kumabe, Soh
1
The University of Tokyo, Japan
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol212-isaac2021/LIPIcs.ISAAC.2021.18/LIPIcs.ISAAC.2021.18.pdf
Data Structures
Range Query Problems
Median Graphs