Abstract
We present a solution to the fully-dynamic all pairs shortest path problem for a directed graph with arbitrary weights allowing negative cycles. We support each vertex update in \(O(n^2({\rm log} n + {\rm log^2}(\overline{m}/n)))\) amortized time. Here, n is the number vertices, m the number of edges and \(\overline{m} = n + m\). A vertex update inserts or deletes a vertex with all incident edges, and we update a complete distance matrix accordingly. The algorithm runs on a comparison-addition based pointer-machine.
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Thorup, M. (2004). Fully-Dynamic All-Pairs Shortest Paths: Faster and Allowing Negative Cycles. In: Hagerup, T., Katajainen, J. (eds) Algorithm Theory - SWAT 2004. SWAT 2004. Lecture Notes in Computer Science, vol 3111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27810-8_33
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DOI: https://doi.org/10.1007/978-3-540-27810-8_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22339-9
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