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Dynamic Approximate-APSP

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 42 Accesses

Years and Authors of Summarized Original Work

  • 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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Recommended Reading

  1. 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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  4. 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

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  5. Bernstein A (2013) Maintaining shortest paths under deletions in weighted directed graphs: [extended abstract]. In: STOC, Palo Alto, pp 725–734

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Author information

Authors and Affiliations

  1. Department of Computer Science, Columbia University, New York, NY, USA

    Aaron Bernstein

Authors
  1. Aaron Bernstein
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Corresponding author

Correspondence to Aaron Bernstein .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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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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