\({\cal O}(n \log n)\) Overload Checking for the Cumulative Constraint and Its Application

  • Armin Wolf
  • Gunnar Schrader
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4369)


Overload checking is an important method for unary as well as for cumulative resource constraints in constraint-based scheduling, as it tests for a sufficient inconsistency property. While an algorithm with time complexity \({\cal O}(n \log n)\) exists that is known for unary resource constraints, to our knowledge no such algorithms have been established to date for overload checking in cumulative constraints on n tasks. In this paper, an \({\cal O}(n \log n)\) overload checking algorithm is presented as well as its application to a more specific problem domain: the non-overlapping placement of n rectangles in a two-dimensional area. There, the runtime complexity of overload checking is \({\cal O}(n^3 \log n)\).


Schedule Problem Constraint Program Runtime Complexity Early Start Time Balance Binary Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Armin Wolf
    • 1
  • Gunnar Schrader
    • 1
  1. 1.Fraunhofer FIRSTBerlinGermany

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