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Decremental Approximate-APSP in Directed Graphs

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 191 Accesses

Years and Authors of Summarized Original Work

  • 2013; 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., minimum spanning tree), 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 only affects a single edge. In a fully dynamic setting, an update can insert or delete an edge or change the weight of an existing edge; in a decremental setting an update can only delete an edge or increase a weight; in an incremental setting an update can insert an edge or decrease a weight.

This entry addresses the decremental (1 +ε)-approximate all-pairs shortest path problem (APSP) in weighted directed graphs. The goal is to maintain a directed graph Gwith real-valued nonnegative...

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Recommended Reading

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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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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). Decremental Approximate-APSP in Directed Graphs. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_564

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