Abstract
In this paper we consider the problem of maintaining the transitive closure in a directed graph under both 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 · log n) expected time and O(1) amortized time per update, and connectivity queries in a dense graph in O(1) expected time and O(n · log n) expected amortized time per update. If m > n4/3 then connectivity queries can be performed in O(1) expected time and O(log3 n) expected amortized time per update. These bounds compares favorably with the best bounds known using worst case analysis. Moreover we consider an intermediate model beetween worst case analysis and average case analysis, the semi-random adversary introduced in [2].
This work was partly supported by the ESPRIT Basic Research Action No. 7141 (AL-COM II) and by the italian projects “Algoritmi, Modelli di Calcolo e Strutture Informative”, Ministero dell'Università e della Ricerca Scientifica e Tecnologica, and “Progetto Finalizzato Trasporti II”, Consiglio Nazionale delle Ricerche.
Supported by a grant from Consiglio Nazionale delle Ricerche, Italia.
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Alimonti, P., Leonardi, S., Marchetti-Spacccamela, A., Messeguer, X. (1994). Average case analysis of fully dynamic connectivity for directed graphs. In: van Leeuwen, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 1993. Lecture Notes in Computer Science, vol 790. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57899-4_43
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DOI: https://doi.org/10.1007/3-540-57899-4_43
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