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Encyclopedia of Algorithms pp 838–841Cite as

Shortest Paths in Planar Graphs with Negative Weight Edges

2001; Fakcharoenphol, Rao

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Keywords and Synonyms

Shortest paths in planar graphs with general arc weights; Shortest paths in planar graphs with arbitrary arc weights      

Problem Definition

This problem is to find shortest paths in planar graphs with general edge weights. It is known that shortest paths exist only in graphs that contain no negative weight cycles. Therefore, algorithms that work in this case must deal with the presence of negative cycles, i. e., they must be able to detect negative cycles.

In general graphs, the best known algorithm, the Bellman‐Ford algorithm, runs in time O(mn) on graphs with n nodes and m edges, while algorithms on graphs with no negative weight edges run much faster. For example, Dijkstra's algorithm implemented with the Fibonacchi heap runs in time \( O(m + n\log n) \), and, in case of integer weights Thorup's algorithm runs in linear time. Goldberg [5] also presented an \( O(m\sqrt{n}\log L) \)-time algorithm where Ldenotes the absolute value of the most negative edge weights....

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Engineering, Kasetsart University, Bangkok, Thailand

    Jittat Fakcharoenphol

  2. Department of Computer Science, University of California at Berkeley, Berkeley, CA, USA

    Satish Rao

Authors
  1. Jittat Fakcharoenphol
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  2. Satish Rao
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Editor information

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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Fakcharoenphol, J., Rao, S. (2008). Shortest Paths in Planar Graphs with Negative Weight Edges. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_372

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