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Maintaining Longest Paths in Cyclic Graphs

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 3709)

Abstract

This paper reconsiders the problem of maintaining longest paths in directed graphs, which is at the core of many scheduling applications. It presents bounded incremental algorithms for arc insertion and deletion running in time O(||δ|| + |δ|log|δ|) on Cyclic<0 graphs (i.e., graphs whose cycles have strictly negative lengths), where |δ| and ||δ|| are measures of the change in the input and output. For Cyclic≤0 graphs, maintaining longest paths is unbounded under reasonable computational models; when only arc insertions are allowed, it is shown that the problem can be solved in O(||δ|| + |δ|log|δ|) time even in the presence of zero-length cycles. The algorithms directly apply to shortest paths (by negating the lengths), leading to simpler algorithms than previously known and reducing the worst-case complexity of an operation from Õ(n m) to O(n + m) for Cyclic>0 graphs with n vertices and m arcs.

Keywords

  • Short Path
  • Jobshop Schedule
  • Longe Path
  • Priority Queue
  • Correctness Proof

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Katriel, I., Van Hentenryck, P. (2005). Maintaining Longest Paths in Cyclic Graphs. In: van Beek, P. (eds) Principles and Practice of Constraint Programming - CP 2005. CP 2005. Lecture Notes in Computer Science, vol 3709. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11564751_28

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  • DOI: https://doi.org/10.1007/11564751_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29238-8

  • Online ISBN: 978-3-540-32050-0

  • eBook Packages: Computer ScienceComputer Science (R0)