Annals of Operations Research

, Volume 180, Issue 1, pp 233–263 | Cite as

Discovering implied constraints in precedence graphs with alternatives



During automated problem solving it may happen that some knowledge that is known at the user level is lost in the formal model. As this knowledge might be important for efficient problem solving, it seems useful to re-discover it in order to improve the efficiency of the solving procedure. This paper compares three methods for discovering certain implied constraints in the constraint models describing manufacturing (and other) processes with serial, parallel, and alternative operations. In particular, we focus on identifying equivalent nodes in the precedence graph with parallel and alternative branches. Equivalent nodes correspond to operations that either must be all simultaneously present or none of them can be present in the schedule. Such information is frequently known at the user level, but it is lost in the formal model. The paper shows that identifying equivalent nodes is an NP-hard problem in general, but it is tractable if the graph has a nested structure. As the nested structure is typical for real-life processes and workflows, we use the nested graphs to experimentally compare the proposed methods.


Constraint satisfaction Modelling Implied constraints Temporal networks 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPrague 1Czech Republic
  2. 2.Institute of Finance and AdministrationPrague 10Czech Republic

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