DMCA
Average Case Analysis of Fully Dynamic Reachability for Directed Graphs
BibTeX
@MISC{Alimonti_averagecase,
author = {Paola Alimonti and Stefano Leonardi and Alberto Marchetti-spaccamela},
title = {Average Case Analysis of Fully Dynamic Reachability for Directed Graphs},
year = {}
}
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Abstract
We consider the problem of maintaining the transitive closure in a directed graph under edge insertions and deletions from the point of view of average case analysis. Say n the number of nodes and m the number of edges. We present a data structure that supports the report of a path between two nodes in O(n \Delta log n) expected time and O(1) amortized time per update, and reachability queries in O(1) expected time and O(n \Delta log n) expected amortized time per update. If m ? n then reachability queries can be performed in O(1) expected time and O(log n) expected amortized time per update. These bounds compares favorably with the best bounds known using worst case analysis.
