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.
online algorithms network graph algorithms topological simplification