Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Shortest Paths in Planar Graphs with Negative Weight Edges

2001; Fakcharoenphol, Rao
  • Jittat Fakcharoenphol
  • Satish Rao
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_372
How to cite

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 \( O(m + n\log n) \)

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Jittat Fakcharoenphol
    • 1
  • Satish Rao
    • 2
  1. 1.Department of Computer EngineeringKasetsart UniversityBangkokThailand
  2. 2.Department of Computer ScienceUniversity of California at BerkeleyBerkeleyUSA