Partially Polynomial Kernels for Set Cover and Test Cover
نویسندگان
چکیده
منابع مشابه
Partially Polynomial Kernels for Set Cover and Test Cover
In a typical covering problem we are given a universe U of size n, a family S (S could be given implicitly) of sizem and an integer k and the objective is to check whether there exists a subfamily S ′ ⊆ S of size at most k satisfying some desired properties. If S ′ is required to contain all the elements of U then it corresponds to the classical Set Cover problem. On the other hand if we requir...
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The input of the Test Cover problem consists of a set V of vertices, and a collection E = {E1, . . . , Em} of distinct subsets of V , called tests. A test Eq separates a pair vi, vj of vertices if |{vi, vj} ∩ Eq| = 1. A subcollection T ⊆ E is a test cover if each pair vi, vj of distinct vertices is separated by a test in T . The objective is to find a test cover of minimum cardinality, if one e...
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Let X = {x1, ..., xn} be a set, and let P = {P1, ..., Pm} be a set of subsets of X. The goal is to find the smallest sub-collection of sets R ⊆ P whose union covers all of X. More concretely, we can say that each xi, 1 ≤ i ≤ n represents a “skill”, and each Pj, 1 ≤ j ≤ m represents a “person”. In this case, xi ∈ Pj if person Pj has the skill xi. Then, as an employer, the goal is to find the min...
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The first part of this report describes the following result that, logarithmic approximation factor for hard capacitated set cover can be achieved from Wolsey's work [9], using a simpler and more intuitive analysis. We further show in our work, that O(log n) approximation factor can be achieved for the same problem by applying analysis of general set cover to analyze Wolsey's algorithm [5]. Thi...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2016
ISSN: 0895-4801,1095-7146
DOI: 10.1137/15m1039584