Data structures for on-line updating of minimum spanning trees

Abstract

Data structures are presented for the problem of maintaining a minimum spanning tree on-line under the operation of updating the cost of some edge in the graph. For the case of a general graph, maintaining the data structure and updating the tree are shown to take O((@@@@)m) time, where m is the number of edges in the graph. For the case of a planar graph, a data structure is presented which supports an update time of O ((log m)2).