Implementation issues for Feo and Provan's delta-wye-delta reduction algorithm
Date
2001
Authors
Song, Xiaohuan
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Abstract
A graph is planar if it can be drawn on the plane with no crossing edges. A graph that can be efficiently reduced to a single edge by repeatedly using one of the six transformations (loop, pendant, series, parallel, delta-wye and wye-delta) in any order is called a D.Y 6-reducible graph and the corresponding algorithm is called 61'' 6-algorithm. A simple O(n2) 6Y 6 algorithm for reducing a planar graph to a single edge was provided by Feo and Provan m 1993. We diagnosed a problem with the algorithm, then fixed it and proved the correctness of the modified algorithm. We also proved this algorithm is f2(n2) through reducing on a family of graph we have constructed. The final code was tested using a large number of small graphs and the output was used to investigate various conjectures.