Abstract
We consider the problem of removing fill edges from a filled graph G ′ to get a minimal chordal supergraph M of the original graph G; thus G \(\subseteq\) M \(\subseteq\) G ′. We show that a greedy strategy can be applied if fill edges are processed for removal in the reverse order of their introduction. For a filled graph with f fill edges and e original edges, we give a simple O(f(e + f)) algorithm which solves the problem and computes a corresponding minimal elimination ordering. We believe that in practice the runtime of our algorithm is usually better than the worst-case bound of O(f(e+f)).
This research was supported in part by the Norwegian Research Council and was conducted while the first author was visiting the University of Bergen, Norway.
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© 1996 Springer-Verlag Berlin Heidelberg
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Blair, J.R.S., Heggernes, P., Telle, J.A. (1996). Making an arbitrary filled graph minimal by removing fill edges. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_130
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DOI: https://doi.org/10.1007/3-540-61422-2_130
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