Graph Property Update Algorithms and Their Appligation to Distance Matrices

AbstractAlgorithms are considered to update graph properties after small changes have been made to a graph. Such update algorithms can use the approach either of directly determining the properties from the new graph or of actually updating the properties of the previous graph. Unfortunately, the execution times for the update algorithms developed by these two approaches often have the same worst-case order. One approach to comparing algorithms with equal worst-case orders is to count the frequency of execuuon for key operations, called active operations. For a class of algorithms that includes most update algorithms this technique can be extended to couniiiig the frequency of execution for active blocks of code. The approaches to the development of update algorithms and the use of active blocksin comparisons will be illustrated by the problem of updating ihe distance matrix of an undirected graph after an edge or vertex has been added or deleted.