Incremental FO( +, < ) Maintenance of All-Pairs Shortest Paths for Undirected Graphs after Insertions and Deletions
We give incremental algorithms, which support both edge insertions and deletions, for the all-pairs shortest-distance problem (APSD) in weighted undirected graphs. Our algorithms use first-order queries, + (addition) and < (less-than); they store O(n 2) number of tuples, where n is the number of vertices, and have AC 0 data complexity for integer weights. Since FO(+,<) is supported by almost all current database systems, our maintenance algorithms are more appropriate for database applications than non-database query type of maintenance algorithms. Our algorithms can also be extended to duplicate semantics.
KeywordsShort Path Undirected Graph Transitive Closure Incremental Algorithm Edge Deletion
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