A new approach to dynamic all pairs shortest paths. - Demetrescu, Camil
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 real-valued edge weights that supports any sequence of operations in O(n2log3n) 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.
Keywords: Data; Data structures; Graphs and networks; Theory of computation; Analysis of algorithms and problem complexity; Nonnumerical algorithms and problems; Computations and discrete structures; Mathematics of computing; Discrete mathematics; Graph theory; Graph algorithms; Algorithms