Determinant Factorization: A New Encoding Scheme for Spanning Trees Applied to the Probabilistic Minimum Spanning Tree Problem

This paper describes a new encoding scheme for the representation of spanning trees This new encoding scheme is based on the factor ization of the determinant of the in degree matrix of the original graph Each factor represents a spanning tree if the determi nant corresponding to that factor is equal to one Our new determinant encoding will be compared to the Pr ufer encoding and to the node and link biased encoding by solv ing an NP complete variation of the mini mum spanning tree problem known as the Probabilistic Minimum Spanning Tree Prob lem Given a connected graph G V E a cost function c E and a probability func tion P V the problem is to nd an a priori spanning tree of minimum expected length Our results show a signi cant im provement in using the new determinant en coding and the node and link biased encod ing compared to Pr ufer s encoding We also show empirically that our new determinant encoding scheme is as good as the node and link biased encoding Our new determinant encoding works very well for restricted span ning trees and for incomplete graphs