2022-12-09T07:43:53Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:002065102020-08-24T15:00:00Z01164:02592:10084:10299
Interval Query Problem on Cube-free Median GraphsInterval Query Problem on Cube-free Median Graphsenghttp://id.nii.ac.jp/1001/00206410/Technical Reporthttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=206510&item_no=1&attribute_id=1&file_no=1Copyright (c) 2020 by the Information Processing Society of JapanThe University of TokyoSoh, KumabeIn 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 stairs decomposition, to decompose an interval of cube-free median graphs into simpler substructures.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 stairs decomposition, to decompose an interval of cube-free median graphs into simpler substructures.AN1009593X研究報告アルゴリズム（AL）2020-AL-1792182020-08-252188-85662020-08-20