Efficient Algorithms for Petersen's Matching Theorem

Biedl, Thérèse; Bose, Prosenjit; Demaine, Erik D.; Lubiw, Anna

doi:10.1006/jagm.2000.1132

Cited by 56 publications

(60 citation statements)

References 32 publications

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“…Mitchell [60] came up with a rule R1 for which (B2) holds. He proved the existence of such initial labeling scheme (so-called compatible initial labeling), and Biedl, Bose, Demaine, and Lubiw [11] gave an optimal O(N) algorithm to find a compatible initial labeling for a triangulation with N elements. In summary, in two dimensions, newest vertex bisection with compatible initial labeling is a bisection method which satisfies (B1) and (B2).…”

Section: For a Sequence Of Bisectionsmentioning

confidence: 99%

Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids

Chen

Nochetto

2009

Multiscale, Nonlinear and Adaptive Approximation

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We give an overview of multilevel methods, such as V-cycle multigrid and BPX preconditioner, for solving various partial differential equations (including H(grad), H(curl) and H(div) systems) on quasi-uniform meshes and extend them to graded meshes and completely unstructured grids. We first discuss the classical multigrid theory on the basis of the method of subspace correction of Xu and a key identity of Xu and Zikatanov. We next extend the classical multilevel methods in H(grad) to graded bisection grids upon employing the decomposition of bisection grids of Chen, Nochetto, and Xu. We finally discuss a class of multilevel preconditioners developed by Hiptmair and Xu for problems discretized on unstructured grids and extend them to H(curl) and H(div) systems over graded bisection grids.

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Section: For a Sequence Of Bisectionsmentioning

confidence: 99%

Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids

Chen

Nochetto

2009

Multiscale, Nonlinear and Adaptive Approximation

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“…Therefore, Petersen's Theorem (see [2]) does not apply and our algorithm is less efficient than Gopi and Eppstein's algorithm [6]: theirs is O(n log 3 n log log n) while ours is O(n 1.5 ).…”

Section: Analysis Of the Algorithmmentioning

confidence: 87%

“…Klein et al [7] propose an O(n 4/3 log n) algorithm for perfect matching in planar bipartite graphs. Biedl et al [2] present an algorithm for perfect matching in 3-regular bridgeless graphs that runs in O(n(log n) 4 ) and O(n) if the graph is also planar. The first of these two algorithms can be improved to O(n log 3 n log log n) using Thorup's data structure [13].…”

Section: Preliminariesmentioning

confidence: 99%

An algorithm for computing simple k-factors

Meijer

Núòez-Rodríguez

Rappaport

2009

Information Processing Letters

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A k-factor of graph G is defined as a k-regular spanning subgraph of G. For instance, a 2-factor of G is a set of cycles that span G. 2-factors have multiple applications in Graph Theory, Computer Graphics, and Computational Geometry [5,4,6,14]. We define a simple 2-factor as a 2-factor without degenerate cycles. In general, simple k-factors are defined as k-regular spanning subgraphs where no edge is used more than once. We propose a new algorithm for computing simple k-factors for all values of k ≥ 2.

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“…Mitchell [37] came up with a rule R1 for which (B2) holds. He proved the existence of such initial labeling scheme (so-called compatible initial labeling), and Biedl, Bose, Demaine, and Lubiw [9] gave an optimal O(N ) algorithm to find a compatible initial labeling for a triangulation with N elements. In summary, for d = 2, newest vertex bisection with compatible initial labeling is a bisection method which satisfies (B1) and (B2).…”

Section: Bisection Rulesmentioning

confidence: 99%

Optimal multilevel methods for graded bisection grids

Chen

Nochetto

2011

Numer. Math.

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Abstract. We design and analyze optimal additive and multiplicative multilevel methods for solving H 1 problems on graded grids obtained by bisection. We deal with economical local smoothers: after a global smoothing in the finest mesh, local smoothing for each added node during the refinement needs to be performed only for three vertices -the new vertex and its two parent vertices. We show that our methods lead to optimal complexity for any dimensions and polynomial degree. The theory hinges on a new decomposition of bisection grids in any dimension, which is of independent interest and yields a corresponding decomposition of spaces. We use the latter to bridge the gap between graded and quasi-uniform grids, for which the multilevel theory is well-established.

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Efficient Algorithms for Petersen's Matching Theorem

Cited by 56 publications

References 32 publications

Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids

Optimal multilevel methods for H(grad), H(curl), and H(div) systems on graded and unstructured grids

An algorithm for computing simple k-factors

Optimal multilevel methods for graded bisection grids

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