On-line maintenance of simplified weighted graphs for efficient distance queries

Authors:
Floris Geerts;Peter Revesz;Jan Van den Bussche
Affiliations:
University of Edinburgh and Hasselt University;University of Nebraska-Lincoln and Max Planck Inst. für Informatik;Hasselt University and Transnational Univ. of Limburg
Venue:
GIS '06 Proceedings of the 14th annual ACM international symposium on Advances in geographic information systems
Year:
2006

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Abstract

We give two efficient on-line algorithms to simplify weighted graphs by eliminating degree-two vertices. Our algorithms are on-line---they react to updates on the data, keeping the simplification up-to-date. We provide both analytical and empirical evaluations of the efficiency of our algorithms. We prove an O(log n) upper bound on the amortized time complexity of our maintenance algorithms, with n the number of insertions. One of our algorithms can handle in logarithmic time the deletions of vertices and edges as well.