On-line maintenance of simplified weighted graphs for efficient distance queries
Faculty of Sciences. Mathematics and Computer Science
S.l. :ACM, 2006
Proceedings of the 14th ACM International Symposium on Geographic Information Systems (ACM-GIS 2006), Arlington, Va, USA, November 10-11, 2006 / By, de, Rolf A. [edit.]; et al.
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.