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A generic greedy algorithm, partially-ordered graphs and NP-completeness.

Puricella, A. and Stewart, I. A. (2001) 'A generic greedy algorithm, partially-ordered graphs and NP-completeness.', in Graph-theoretic concepts in computer science : 27th International Workshop, WG 2001, 14-16 June 2001, Boltenhagen, Germany ; proceedings. Berlin: Springer, pp. 306-316. Lecture notes in computer science. (2204).


Let π be any fixed polynomial-time testable, non-trivial, hereditary property of graphs. Suppose that the vertices of a graph G are not necessarily linearly ordered but partially ordered, where we think of this partial order as a collection of (possibly exponentially many) linear orders in the natural way. We prove that the problem of deciding whether a lexicographically first maximal subgraph of G satisfying π, with respect to one of these linear orders, contains a specified vertex is NP-complete.

Item Type:Book chapter
Keywords:Greedy algorithms, NP-completeness, Hereditary properties.
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Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:25 August 2009
Date of first online publication:January 2001
Date first made open access:No date available

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