On Partial Vertex Cover and Budgeted Maximum Coverage Problems in Bipartite Graphs

Caskurlu, Bugra; Mkrtchyan, Vahan; Parekh, Ojas; Subramani, K.

doi:10.1007/978-3-662-44602-7_2

Cited by 26 publications

(29 citation statements)

References 26 publications

(33 reference statements)

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“…e maximum vertex coverage problem is a special case of this problem in which the universe corresponds to the edges of a given graph and there is a set corresponding to each node of the graph that contains the edges that are incident to that node. For this problem, algorithms based on linear programming achieve a 3/4 approximation for general graphs [1] and a 8/9 approximation for bipartite graphs [17]. Assuming P N P, there does not exist a polynomial-time approximation scheme.…”

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confidence: 99%

Better Streaming Algorithms for the Maximum Coverage Problem

McGregor

2018

Theory Comput Syst

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We study the classic NP-Hard problem of nding the maximum k-set coverage in the data stream model: given a set system of m sets that are subsets of a universe {1, . . . , n}, nd the k sets that cover the most number of distinct elements. e problem can be approximated up to a factor 1 − 1/e in polynomial time. In the streaming-set model, the sets and their elements are revealed online. e main goal of our work is to design algorithms, with approximation guarantees as close as possible to 1 − 1/e, that use sublinear space o(mn). Our main results are:• Two (1 − 1/e − ) approximation algorithms: One uses O( −1 ) passes andÕ( −2 k) space whereas the other uses only a single pass butÕ( −2 m) space.Õ(·) suppresses polylog factors.

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confidence: 99%

Better Streaming Algorithms for the Maximum Coverage Problem

McGregor

2018

Theory Comput Syst

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“…Partial VC Dimension belongs to the category of partial versions of common decision problems, in which, instead of satisfying the problem's constraint task for all elements (here, all 2 k equivalence classes), we ask whether we can satisfy a certain number, ℓ, of these constraints. See for example the papers [21,34,41] that study some partial versions of standard decision problems, such as Set Cover, Vertex Cover or Dominating Set.…”

Section: Partial Vc Dimensionmentioning

confidence: 99%

Parameterized and approximation complexity of Partial VC Dimension

Bazgan

Foucaud

Sikora

2019

Theoretical Computer Science

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We introduce the problem Partial VC Dimension that asks, given a hypergraph H = (X, E) and integers k and ℓ, whether one can select a set C ⊆ X of k vertices of H such that the set {e ∩ C, e ∈ E} of distinct hyperedge-intersections with C has size at least ℓ. The sets e ∩ C define equivalence classes over E. Partial VC Dimension is a generalization of VC Dimension, which corresponds to the case ℓ = 2 k , and of Distinguishing Transversal, which corresponds to the case ℓ = |E| (the latter is also known as Test Cover in the dual hypergraph). We also introduce the associated fixed-cardinality maximization problem Max Partial VC Dimension that aims at maximizing the number of equivalence classes induced by a solution set of k vertices. We study the algorithmic complexity of Partial VC Dimension and Max Partial VC Dimension both on general hypergraphs and on more restricted instances, in particular, neighborhood hypergraphs of graphs.⋆ A preliminary version of this work containing the approximation complexity results appeared in [8].

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“…Because of this autonomous management, EO-1 can save more than one million dollars every year and the events discovered annually worth more than 1.8 million dollars [7]. EO-1 uses SVM [4] to classify land, ice, cloud, etc. The software system on EO-1 is called ASE [24], and uses a scheduling method called CASPER.…”

Section: Introductionmentioning

confidence: 99%