Minimum paired-dominating set in chordal bipartite graphs and perfect elimination bipartite graphs

Panda, B. S.; Pradhan, D.

doi:10.1007/s10878-012-9483-x

Cited by 21 publications

(9 citation statements)

References 18 publications

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“…More recently, Chen et al [7] demonstrated that the problem is also NP-complete in bipartite graphs, chordal graphs, and split graphs. Panda and Pradhan [22] strengthened the above results by showing that the problem is NP-complete for perfect elimination bipartite graphs. In addition, McCoy and Henning [21] investigated variants of the paired-domination problem in graphs.…”

Section: Introductionmentioning

confidence: 76%

“…To improve the results in [8], Lappas et al [18] introduced an O(n)-time algorithm. In addition, Hung [16] described an O(n)-time algorithm for convex bipartite graphs; Panda and Pradhan [22] proposed an O(m + n)-time algorithm for chordal bipartite graphs; Chen et al [7] introduced O(m + n)-time algorithms for block graphs and interval graphs; and Cheng et al [9] designed an O(m + n)-time algorithm for interval graphs and an O(m(m + n))-time algorithm for circular-arc graphs. In this paper, given an intersection model of interval graph G with sorted endpoints, we improve the above results with time complexity O(n) for interval graphs and circular-arc graphs.…”

Section: Introductionmentioning

confidence: 99%

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A linear-time algorithm for paired-domination on circular-arc graphs

Lin

2015

Theoretical Computer Science

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In a graph G, a vertex subset S ⊆ V (G) is said to be a dominating set of G if every vertex not in S is adjacent to a vertex in S. A dominating set S of a graph G is called a paired-dominating set if the induced subgraph G[S] contains a perfect matching. The paired-domination problem involves finding a smallest paired-dominating set of G. Given an intersection model of an interval graph G with sorted endpoints, Cheng et al. [9] designed an O(m + n)-time algorithm for interval graphs and an O(m(m + n))time algorithm for circular-arc graphs. In this paper, to solve the paired-domination problem in interval graphs, we propose an O(n)-time algorithm that searches for a minimum paired-dominating set of G incrementally in a greedy manner. Then, we extend the results to design an algorithm for circular-arc graphs that also runs in O(n) time.

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Section: Introductionmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

A linear-time algorithm for paired-domination on circular-arc graphs

Lin

2015

Theoretical Computer Science

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“…Bipartite graph matching has been widely studied and has applications in various fields of science (Panda and Pradhan, 2013), (Fishkel et al, 2006). It is particularly suitable for a two-class matching problem.…”

Section: Search Of Mutual Best Match In a Bipartite Graphmentioning

confidence: 99%

Matching CAD Model and Image Features for Robot Navigation and Inspection of an Aircraft

Jovanźeviź

Viana

Orteu

et al. 2016

Proceedings of the 5th International Conference on Pattern Recognition Applications and Methods

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Abstract:This paper focuses on the navigation of a moving robot equipped with cameras, moving around an aircraft to perform inspection of different types of items (probes, doors, etc.). Matching CAD model and image features is useful to provide meaningful features for localization and inspection tasks. In our approach two primitive sets are matched using a similarity function. The similarity scores are injected in the edges of a bipartite graph. A best-match search procedure in bipartite graph guarantees the uniqueness of the match solution. The method provides good matching results even when the location of the robot with respect to the aircraft is badly estimated. Inspection approaches on static ports and air inlet vent are presented.

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“…Graph Bipartite graph matching has been widely studied and has applications in various fields of science, such as data mining, 40 mathematics, 37 computer vision, and image analysis. 20,21,41 By its definition, it is obvious that it is particularly suitable for a two-class matching problem.…”

Section: Search Of Mutual Best Match In a Bipartitementioning

confidence: 99%

Inspection of aeronautical mechanical parts with a pan-tilt-zoom camera: an approach guided by the computer-aided design model

Viana

Orteu

Cornille³

et al. 2015

J. Electron. Imaging

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International audienceWe focus on quality control of mechanical parts in aeronautical context using a single pan-tilt-zoom (PTZ) camera and a computer-aided design (CAD) model of the mechanical part. We use the CAD model to create a theoretical image of the element to be checked, which is further matched with the sensed image of the element to be inspected, using a graph theory–based approach. The matching is carried out in two stages. First, the two images are used to create two attributed graphs representing the primitives (ellipses and line segments) in the images. In the second stage, the graphs are matched using a similarity function built from the primitive parameters. The similarity scores of the matching are injected in the edges of a bipartite graph. A best-match-search procedure in the bipartite graph guarantees the uniqueness of the match solution. The method achieves promising performance in tests with synthetic data including missing elements, displaced elements, size changes, and combinations of these cases. The results open good prospects for using the method with realistic data

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Minimum paired-dominating set in chordal bipartite graphs and perfect elimination bipartite graphs

Cited by 21 publications

References 18 publications

A linear-time algorithm for paired-domination on circular-arc graphs

A linear-time algorithm for paired-domination on circular-arc graphs

Matching CAD Model and Image Features for Robot Navigation and Inspection of an Aircraft

Inspection of aeronautical mechanical parts with a pan-tilt-zoom camera: an approach guided by the computer-aided design model

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