An Algorithm for the Solution of a Linear system by Δ-Y Transformations

Hiroyuki NAKAHARA  Hiromitsu TAKAHASHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.7   pp.1079-1088
Publication Date: 1996/07/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Graphs and Networks
planar graph,  Δ-Y transformation,  embedding,  minor,  linear system,  

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Let W be a real symmetric matrix associated with a weighted 2-connected planar graph. It is important to study a fast algorithm to solve the linear system Wx = c, since the system has many various applicaions, for example to solve partial defferencial equations numerically. In this paper, a new algorithm for the solution of a linear system of equations by Δ-Y transformations is proposed, and a sufficient condition for using this algorithm is proved. We show that this algorithm solves in O (n3/2) time a linear system associated with a planar graph which is embedded a cylinder graph with n vertices.