Efficient on-line topological simplification of network-like data

Abstract

We describe an efficient on-line algorithm to simplify network-like data with the goal of speeding up path queries on these data. Our algorithm is on-line in that it reacts to updates on the data, keeping the simplification up-to-date. The supported updates are insertions of vertices and edges; hence, our algorithm is semi-dynamic. We provide both analytical and empirical evaluations of the efficiency of our approach. Specifically, we prove an 0(log m) upper bound on the amortized time complexity of our maintenance algorithm, with m the number of edges. We also show that the overhead due to maintenance is negligible using real data, and illustrate the improved performance on shortest path queries over the same data.