Two Efficient Graph Representations for SimpleTwo Efficient Graph Representations for Simple Graphs

• Main Authors: Chia-Yi Chang, 張嘉益
• Other Authors: Yue-Li Wang
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/91938888012934084888

碩士 === 國立臺灣科技大學 === 資訊管理系 === 93 === Representing graphs is a fundamental data-structuring problem. Adjacency matrices and adjacency lists are two well known representations. The operations on an adjacency matrix which contain adjacency test, inserting/deleting an edge can be done in constant time. However, finding all adjacency vertices of a given vertex will take θ(n) time by using an adjacent matrix. On the other hand, to test adjacency on adjacency lists will take O(deg(i)) time, where deg(i) is the degree of vertex i. In this thesis, we propose two efficient representations which not only support adjacency test in constant time, but also support the adjacency test of a given vertex in θ(deg(i)). Our representation will take θ(n2) time to initialize. However, inserting/deleting an edge only takes constant time. The proposed representations will be very efficient for the problems with a lot of inserting/deleting edge operations.