Abstract
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(n 2 (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.
Supported in part by NSF Grants CDA 92-23502 and CCR 95-05745, and by ONR Contract N00014-96-1-0635.
Supported in part by NSF Grant CCR 94-09809.
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Hoffmann, C.M., Lomonosov, A., Sitharam, M. (1997). Finding solvable subsets of constraint graphs. In: Smolka, G. (eds) Principles and Practice of Constraint Programming-CP97. CP 1997. Lecture Notes in Computer Science, vol 1330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017460
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DOI: https://doi.org/10.1007/BFb0017460
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