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Topic: Set cover

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	Munagala, Kamesh; Babu; Shivnath; Motwani, Rajeev; Widom, Jennifer: The Pipelined Set Cover Problem
		We provide an abstraction of this problem as a generalization of set cover called pipelined set* cover, where the sets* are applied sequentially to the universe and the covered elements are discarded.
		The cost of including a set in pipelined set cover is directly proportional to the number of uncovered elements at the point of applying the set.
		We provide an abstraction of this problem as a generalization of set cover called pipelined set cover, where the sets are applied sequentially to the universe and the covered elements are discarded.
	dbpubs.stanford.edu /pub/2003-65 (579 words)

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	MINIMUM SET COVER
		Collection C of subsets of a finite set S.
		Variation in which the subsets have positive weights and the objective is to minimize the sum of the weights in a set cover is also approximable within
		Variation in which a distance matrix between pairs of elements in S is given and the measure of the solution is not the cardinality of the cover but its diameter (i.e., the maximum distance of any pair of elements in C') is not approximable within any constant in the general case.
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	Approximation Algorithms for Submodular Set Cover with Applications - Fujito (ResearchIndex)
		Given a finite set M and a family N of subsets of M, a subfamily S of N is called a set cover if every element of M appears in some subset in S; in other words, the union of all subsets in S coincides with M.
		Each set in N is associated with a (U"C2T0"'# e) cost, and the cost of a family is the sum of costs of subsets in it.
		74 Approximation algorithms for the set covering and vertex cov..
	citeseer.ist.psu.edu /353903.html (703 words)

	set cover
		Definition: A set of sets whose union has all members of the union of all sets.
		The set cover problem is to find a minimum size set.
		Paul E. Black, "set cover", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
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	1.5.3 Vertex Cover (Site not responding. Last check: 2007-10-24)
		Excerpt from The Algorithm Design Manual: Vertex cover is a special case of the more general set cover problem, which takes as input an arbitrary collection of subsets S = (S_1, \ldots, S_n) of the universal set U = \{1,\ldots,m\}.
		To turn vertex cover into a set cover problem, let U be the complete set of edges, and create $S_i$ to be the set of edges incident on vertex i.
		A set of vertices defines a vertex cover in graph $G$ iff the correspondinag subsets define a set cover in the given instance.
	www.cs.sunysb.edu /~algorith/files/vertex-cover.shtml (222 words)

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	1.7.1 Set Cover (Site not responding. Last check: 2007-10-24)
		Excerpt from The Algorithm Design Manual: Set cover arises when you try to efficiently acquire or represent items that have been packaged in a fixed set of lots.
		An interesting application of set cover is Boolean logic minimization.
		Given a set of feasible ``and'' terms, each of which covers a subset of the vectors we need, we seek to ``or'' together the smallest number of terms that realize the function.
	www.cs.sunysb.edu /~algorith/files/set-cover.shtml (253 words)

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		We note that Red-Blue Set Cover is closely related to several combinatorial optimization problems studied earlier.
		8 Primal-dual RNC approximation algorithms for set covering an..
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