A Fully Dynamic Algorithm for Maintaining theTransitive
نویسندگان
چکیده
This paper presents an eecient fully dynamic graph algorithm for maintaining the transitive closure of a directed graph. The algorithm updates the adjacency matrix of the transitive closure with each update to the graph. Hence, each reachability query of the form \Is there a directed path from i to j?" can be answered in O(1) time. The algorithm is randomized; it is correct when answering yes, but has O(1=n c) probability of error when answering no, for any constant c. In acyclic graphs, worst case update time is O(n 2). In general graphs, update time is O(n 2+), where = minf.26, maximum size of a strongly connected componentg. The space complexity of the algorithm is O(n 2).
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