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Maintaining Longest Paths Incrementally

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Abstract

Modeling and programming tools for neighborhood search often support invariants, i.e., data structures specified declaratively and automatically maintained incrementally under changes. This paper considers invariants for longest paths in directed acyclic graphs, a fundamental abstraction for many applications. It presents bounded incremental algorithms for arc insertion and deletion which run in O(∥δ∥ + |δ| log|δ|) time and O(∥δ∥) time respectively, where |δ| and ∥δ∥ are measures of the change in the input and output. The paper also shows how to generalize the algorithm to various classes of multiple insertions/deletions encountered in scheduling applications. Preliminary experimental results show that the algorithms behave well in practice.

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Authors and Affiliations

  1. Max-Plank-Institut für Informatik, Saarbrücken, Germany

    Irit Katriel

  2. University of Connecticut, Storrs, CT, 06269-2155, USA

    Laurent Michel

  3. Brown University, Box 1910, Providence, RI, 02912, USA

    Pascal Van Hentenryck

Authors
  1. Irit Katriel
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  2. Laurent Michel
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  3. Pascal Van Hentenryck
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Correspondence to Irit Katriel.

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Katriel, I., Michel, L. & Van Hentenryck, P. Maintaining Longest Paths Incrementally. Constraints 10, 159–183 (2005). https://doi.org/10.1007/s10601-005-0554-9

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