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Fully Dynamic Algorithm for the Vertex Connectivity of Interval Graphs

선분 그래프의 정점 연결성에 대한 완전 동적 알고리즘

Kim, Jae-hoon
김재훈

  • Received : 2015.10.23
  • Accepted : 2015.11.30
  • Published : 2016.02.29

Abstract

A graph G=(V,E) is called an interval graph with a set V of vertices representing intervals on a line such that there is an edge $(i,j){\in}E$ if and only if intervals i and j intersect. In this paper, we are concerned in the vertex connectivity, one of various characteristics of the graph. Specifically, the vertex connectivity of an interval graph is represented by the overlapping of intervals. Also we propose an efficient algorithm to compute the vertex connectivity on the fully dynamic environment in which the vertices or the edges are inserted or deleted. Using a special kind of interval tree, we show how to compute the vertex connectivity and to maintain the tree in O(logn) time when a new interval is added or an existing interval is deleted.

Keywords

interval graph;vertex connectivity;fully dynamic;interval tree;algorithm;interval

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Acknowledgement

Supported by : Busan University of Foreign Studies