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

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. Categories and Subject Descriptors: E.1: Graphs and networks General Terms: Algorithms.

• Type: Conference
• Year: 2006
• Where: GIS
• Authors: Floris Geerts, Peter Z. Revesz, Jan Van den Bussche
• Keywords: Amortized Time Complexity, Database, Efficient On-line Algorithms, GIS 2006, Maintenance Algorithms