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Encyclopedia of Algorithms pp 329–331Cite as

Fully Dynamic All Pairs Shortest Paths

2004; Demetrescu, Italiano

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Problem Definition

The problem is concerned with efficiently maintaining information about all-pairs shortest paths in a dynamically changing graph. This problem has been investigated since the 60s [17,18,20], and plays a crucial role in many applications, including network optimization and routing, traffic information systems, databases, compilers, garbage collection, interactive verification systems, robotics, dataflow analysis, and document formatting.     

A dynamic graph algorithm maintains a given property \( \mathcal{P} \) on a graph subject to dynamic changes, such as edge insertions, edge deletions and edge weight updates. A dynamic graph algorithm should process queries on property \( \mathcal{P} \) quickly, and perform update operations faster than recomputing from scratch, as carried out by the fastest static algorithm. An algorithm is said to be fully dynamic if it can handle both edge insertions and edge deletions. A partially dynamicalgorithm can handle either edge...

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Recommended Reading

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Authors and Affiliations

  1. Department of Information and Computer Systems, University of Rome, Rome, Italy

    Giuseppe F. Italiano

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  1. Giuseppe F. Italiano
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Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Italiano, G. (2008). Fully Dynamic All Pairs Shortest Paths. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_151

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