Efficient Spanning Tree Enumeration Using Loop Domain

Abstract

Abstract-Exhaustive enumeration of spanning trees in a graph requires substantial time and computational overheads. The proposed method, using the concept of LOOP DOMAIN, greatly reduces the complexity of enumeration. The initial graph is transformed into a graph in loop domain where the spanning tree enumeration is then carried out. Subsequently spanning trees of initial graph are generated. The proposed method eliminates all the two degree vertices in a graph. This finds application in power system distribution networks, which have substantial number of two degree vertices. The consequent reduction in size of graph and its corresponding trees is highly desirable. The proposed method is demonstrated on a 33 vertex system and reduction incomplexity is evaluated.

Reconfiguration of power networks based on graph-theoretic algorithms

“…The computation complexity can be reduced substantially if the spanning tree generation algorithm is carried on a simplified graph, especially for a distribution system network [55]. For the distribution restoration problem, the output is a sequence of switching operations that correspond to the cyclic interchange operations between different spanning trees.…”