Abstract: "We state a new sampling lemma and use it to improve the running time of dynamic graph algorithms. For the dynamic connectivity problem the previously best randomized algorithm takes expected time O(log³ n) per update, amortized over [omega](m) updates. Using the new sampling lemma, w...

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Henzinger, Monika R. (VerfasserIn), Thorup, Mikkel 1973- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	København 1995
Schriftenreihe:	Datalogisk Institut <København>: DIKU-Rapport 1995,26
Schlagworte:	Algorithms Machine theory Sampling (Statistics)
Zusammenfassung:	Abstract: "We state a new sampling lemma and use it to improve the running time of dynamic graph algorithms. For the dynamic connectivity problem the previously best randomized algorithm takes expected time O(log³ n) per update, amortized over [omega](m) updates. Using the new sampling lemma, we improve its running time to O(log² n) on a RAM and O(log² n (1 + [epsilon][superscript log*n] / [epsilon]³ = O(log[superscript 2 + o(1)]n) on a pointer machine, where 0 <[epsilon] [<or =] 1. There exists a lower bound in the cell probe model for the time per operation of [omega](log n/ log log n) for this problem. Improved running times are achieved for the following dynamic problems: (1) O(log³ n) to maintain the bridges in a graph (the 2-edge connectivity problem); (2) O(k log² n) to maintain a minimum spanning tree in a graph with k different weights (the k-weight minimum spanning tree problem); (3) O(log² n log U/[epsilon]') to maintain a spanning tree whose weight is a (1 + [epsilon]')-approximation of the weight of the minimum spanning tree, where U is the maximum weight in the graph (the (1 + [epsilon]')-approximate minimum spanning tree problem); and (4) O(log² n) to test if the graph is bipartite (the bipartiteness-testing problem)."
Beschreibung:	9 S.