Algorithms for (0, 1,<i>d</i>)-graphs with<i>d</i>constrains

Liu, Yueping; Lou, Dingjun; Lu, Yunting

doi:10.1080/00207160802562523

Cited by 1 publication

(7 citation statements)

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“…The application scenario in [8] is similar with our paper. They determine whether the jobs can be assigned out while one edge (circuit line) is failed.…”

Section: Introduction and Terminologymentioning

confidence: 61%

“…Recently, Li, Lou and Lu [8] investigated the (0, 1, d)-bipartite graphs in graph family F d . The application scenario in [8] is similar with our paper.…”

Section: Introduction and Terminologymentioning

confidence: 99%

“…They determine whether the jobs can be assigned out while one edge (circuit line) is failed. The main result of [8] is the following theorem: H is a (0, 1, d)-graph if and only if H is 1-extendable.…”

Section: Introduction and Terminologymentioning

confidence: 99%

“…Based on this result, an algorithm for determining (0, 1, d)-bipartite graph was presented in [8]. Furthermore, they proposed the algorithm for augmenting one bipartite graph in F d to be a (0, 1, d)-bipartite graph using fewest edges.…”

Section: Introduction and Terminologymentioning

confidence: 99%

“…In the light of these results in [8], we investigate the scenario that whether the jobs can be distributed out if one machine fails. By the definition in Section I, this scenario is modeled by critical bipartite graphs.…”

Section: Introduction and Terminologymentioning

confidence: 99%

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An Algorithm for Determining Critical Bipartite Graphs

Zhang

Liu

2012

2012 International Symposium on Computer, Consumer and Control

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A matching which saturates all the vertices of a graph is called a perfect matching. Let GB = (U, W ) be a bipartite graph with bipartitions U and W , where |U | = |W |−1 and |U | ≥ 1. Bipartite graph GB is called critical bipartite graph if the following property holds: graph GB has a perfect matching after removing any vertex of W . Critical bipartite graph plays an important role in the design of robust job assignment circuit. This paper proposes one sufficient and necessary condition of critical bipartite graph. Based on this result, a determining algorithm is developed which is superior to the best algorithm known by far. The time complexity of our algorithm is linear.

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“…The application scenario in [8] is similar with our paper. They determine whether the jobs can be assigned out while one edge (circuit line) is failed.…”

Section: Introduction and Terminologymentioning

confidence: 61%

“…Recently, Li, Lou and Lu [8] investigated the (0, 1, d)-bipartite graphs in graph family F d . The application scenario in [8] is similar with our paper.…”

Section: Introduction and Terminologymentioning

confidence: 99%

Section: Introduction and Terminologymentioning

confidence: 99%

Section: Introduction and Terminologymentioning

confidence: 99%

Section: Introduction and Terminologymentioning

confidence: 99%

See 3 more Smart Citations