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(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.
A new approach to dynamic all pairs shortest paths / C., Demetrescu; Italiano, Giuseppe Francesco. - In: JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY. - ISSN 0004-5411. - 51:6(2004), pp. 968-992. [10.1145/1039488.1039492]
A new approach to dynamic all pairs shortest paths
ITALIANO G
2004
Abstract
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(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.File | Dimensione | Formato | |
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