Finding solvable subsets of constraint graphs

  • Christoph M. Hoffmann
  • Andrew Lomonosov
  • Meera Sitharam
Session 7a
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1330)


We present a network flow based, degree of freedom analysis for graphs that arise in geometric constraint systems. For a vertex and edge weighted constraint graph with m edges and n vertices, we give an O(n(m + n)) time max-flow based algorithm to isolate a subgraph that can be solved separately. Such a subgraph is called dense. If the constraint problem is not overconstrained, the subgraph will be minimal.

For certain overconstrained problems, finding minimal dense subgraphs may require up to O(n2 (m + n)) steps. Finding a minimum dense subgraph is NP-hard. The algorithm has been implemented and consistently outperforms a simple but fast, greedy algorithm.


Extremal subgraph dense graph network flow combinatorial optimization constraint solving geometric constraint graph geometric modeling 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Christoph M. Hoffmann
    • 1
  • Andrew Lomonosov
    • 2
  • Meera Sitharam
    • 2
  1. 1.Computer SciencePurdue UniversityWest LafayetteUSA
  2. 2.Mathematics and Computer ScienceKent State UniversityKentUSA

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