Years and Authors of Summarized Original Work
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2009; Bernstein
Problem Definition
A dynamic graph algorithm maintains information about a graph that is changing over time. Given a property \(\mathcal{P}\) of the graph (e.g., maximum matching), the algorithm must support an online sequence of query and update operations, where an update operation changes the underlying graph, while a query operation asks for the state of \(\mathcal{P}\) in the current graph. In the typical model studied, each update affects a single edge, in which case the most general setting is the fully dynamic one, where an update can either insert an edge, delete an edge, or change the weight of an edge. Common restrictions of this include the decremental setting, where an update can only delete an edge or increase a weight, and the incremental setting where an update can insert an edge or decrease a weight.
This entry addresses the problem of maintaining α-approximate all-pairs shortest paths (APSP) in the fully...
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Baswana S, Sen S (2006) Approximate distance oracles for unweighted graphs in expected o(n2) time. ACM Trans Algorithms 2(4):557–577
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Bernstein A (2009) Fully dynamic approximate all-pairs shortest paths with query and close to linear update time. In: Proceedings of the 50th FOCS, Atlanta, pp 50–60
Bernstein A (2012) Near linear time (1 +ε)-approximation for restricted shortest paths in undirected graphs. In: Proceedings of the 23rd SODA, San Francisco, pp 189–201
Bernstein A (2013) Maintaining shortest paths under deletions in weighted directed graphs: [extended abstract]. In: STOC, Palo Alto, pp 725–734
Demetrescu C, Italiano GF (2004) A new approach to dynamic all pairs shortest paths. J ACM 51(6):968–992. doi:http://doi.acm.org/10.1145/1039488.1039492
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Bernstein, A. (2016). Dynamic Approximate-APSP. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_563
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