Simpler and Stronger Approaches for Non-Uniform Hypergraph Matching and the Füredi, Kahn, and Seymour Conjecture

Anegg, Georg; Angelidakis, Haris; Zenklusen, Rico

doi:10.1137/1.9781611976472.22

Cited by 1 publication

(5 citation statements)

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“…Thanks to Rico Zenklusen for some helpful explanations about their paper [1]. Thanks to the journal reviewers for useful suggestions and revisions.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…To better situate the FKS conjecture, let us note a more general result for independent sets in graphs, based on constructions in [1,4]. Theorem 1.4.…”

Section: Corollary 13 ([1]mentioning

confidence: 99%

“…Clearly, if x takes on integral values, then it corresponds to a matching. We say that x is a basic fractional matching if it is an extreme point of the fractional matching polytope given by the constraints (1). Given a non-negative weight function w ∶ E → R ≥0 on the edges, we define the weight of a fractional matching x by w(x) = ∑ e∈E w(e)x(e).…”

Section: Introductionmentioning

confidence: 99%

“…The original version was stated in the primal form below. As shown in [1], the dual version is equivalent to the primal version, both algorithmically and combinatorially.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the FKS conjecture is closely related to approximation algorithms for matchings. A number of recent papers [1,3] have shown weakened versions of Conjecture 1.1; most recently, [1] showed the following:…”

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confidence: 99%

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Some remarks on hypergraph matching and the Füredi–Kahn–Seymour conjecture

Bansal

Harris

2022

Random Struct Algorithms

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A classic conjecture of Füredi, Kahn, and Seymour (1993) states that any hypergraph with non-negative edge weights w(e) has a matching M such that ∑ e∈M (|e| − 1 + 1∕|e|) w(e) ≥ w * , where w * is the value of an optimum fractional matching. We show the conjecture is true for rank-3 hypergraphs and is achieved by a natural iterated rounding algorithm. While the general conjecture remains open, we give several new improved bounds. In particular, we show that the iterated rounding algorithm gives ∑ e∈M (|e| − 𝛿(e)) w(e) ≥ w * , where 𝛿(e) = |e|∕(|e| 2 + |e| − 1), improving upon the baseline guarantee of ∑ e∈M |e| w(e) ≥ w * .

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“…Thanks to Rico Zenklusen for some helpful explanations about their paper [1]. Thanks to the journal reviewers for useful suggestions and revisions.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…To better situate the FKS conjecture, let us note a more general result for independent sets in graphs, based on constructions in [1,4]. Theorem 1.4.…”

Section: Corollary 13 ([1]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The original version was stated in the primal form below. As shown in [1], the dual version is equivalent to the primal version, both algorithmically and combinatorially.…”

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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