Interval Query Problem on Cube-Free 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 đť’® be a commutative semigroup. For each vertex v in G, we are given an element p(v) in đť’®. 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(logÂ˛ n) time. The required data structure is constructed in O(n logÂł n) time and O(n logÂ˛ 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.
Data Structures
Range Query Problems
Median Graphs
Mathematics of computing~Combinatorial algorithms
18:1-18:14
Regular Paper
https://arxiv.org/abs/2010.05652
We are grateful to our supervisor Prof. Hiroshi Hirai for supporting our work. He gave us a lot of ideas to improve our paper. In particular, he simplified the proofs and helped us improve the introduction and the overall structure of this paper.
Soh
Kumabe
Soh Kumabe
The University of Tokyo, Japan
10.4230/LIPIcs.ISAAC.2021.18
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Soh Kumabe
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