A new approach to dynamic all pairs shortest paths

We study novel combinatorial properties of graphs that allow us to devise a completely new approach to dynamic all pairs shortest paths problems. Our approach yields a fully dynamic algorithm for general directed graphs with non-negative realvalued edge weights that supports any sequence of operations in O(n2 log3 n) amortized time per update and unit worst-case time per distance query, where n is the number of vertices. We can also report shortest paths in optimal worst-case time. These bounds improve substantially over previous results and solve a long-standing open problem. Our algorithm is deterministic, uses simple data structures, and appears to be very fast in practice.

• Type: Conference
• Year: 2003
• Where: STOC
• Authors: Camil Demetrescu, Giuseppe F. Italiano
• Keywords: Algorithms, Long-standing Open Problem, Non-negative Realvalued Edge, STOC 2003, Uses Simple Data