A Simple 3-Edge-Connected Component Algorithm

Tsin, Yung H.

doi:10.1007/s00224-005-1269-4

Cited by 25 publications

(25 citation statements)

References 5 publications

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“…2. Let a 3-edge-connected component be an equivalence class of nodes that are 3-edge-connected; these components can be computed in linear time (we use the algorithm given by Tsin [2007]). The graph G 2 contains a node for each 3-edge-connected component in G 1 .…”

Section: Adjacency Graphsmentioning

confidence: 99%

Cactus: Algorithms for genome multiple sequence alignment

Paten¹,

Earl²,

Nguyen³

et al. 2011

Genome Res.

263

290

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Much attention has been given to the problem of creating reliable multiple sequence alignments in a model incorporating substitutions, insertions, and deletions. Far less attention has been paid to the problem of optimizing alignments in the presence of more general rearrangement and copy number variation. Using Cactus graphs, recently introduced for representing sequence alignments, we describe two complementary algorithms for creating genomic alignments. We have implemented these algorithms in the new “Cactus” alignment program. We test Cactus using the Evolver genome evolution simulator, a comprehensive new tool for simulation, and show using these and existing simulations that Cactus significantly outperforms all of its peers. Finally, we make an empirical assessment of Cactus's ability to properly align genes and find interesting cases of intra-gene duplication within the primates.

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Section: Adjacency Graphsmentioning

confidence: 99%

Cactus: Algorithms for genome multiple sequence alignment

Paten¹,

Earl²,

Nguyen³

et al. 2011

Genome Res.

263

290

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“…The random circulation approach yields new linear-time algorithms to compute all cut edges and cut pairs of the Las Vegas type. As far as we are aware, our linear-time cut pair algorithm is the first one that does not rely on either DFS (e.g., see references in Tsin [37]) or open ear decomposition (e.g., see references in Fussell et al [10]). …”

Section: Our Contributionsmentioning

confidence: 99%

Fast computation of small cuts via cycle space sampling

Pritchard

Thurimella

2011

ACM Trans. Algorithms

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We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the cycle space identifies the cuts of a graph. This leads to simple new linear-time sequential algorithms for finding all cut edges and cut pairs (a set of 2 edges that form a cut) of a graph.In the model of distributed computing in a graph G = (V, E) with O(log |V |)-bit messages, our approach yields faster algorithms for several problems. The diameter of G is denoted by D, and the maximum degree by ∆.We obtain simple O(D)-time distributed algorithms to find all cut edges, 2-edge-connected components, and cut pairs, matching or improving upon previous time bounds. Under natural conditions these new algorithms are universally optimal -i.e. a Ω(D)-time lower bound holds on every graph. We obtain a O(D + ∆/ log |V |)-time distributed algorithm for finding cut vertices; this is faster than the best previous algorithm when ∆, D = O( |V |). A simple extension of our work yields the first distributed algorithm with sub-linear time for 3-edge-connected components. The basic distributed algorithms are Monte Carlo, but they can be made Las Vegas without increasing the asymptotic complexity.In the model of parallel computing on the EREW PRAM our approach yields a simple algorithm with optimal time complexity O(log V ) for finding cut pairs and 3-edge-connected components.

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“…Bridges, 2-edge connected components, articulation nodes and biconnected components are computed according to the algorithms in [9,10]. Cut-pairs and 3-edge connected components are computed by the algorithm in [12]. All of them can be done in linear time O(|E|+|V|), where |E| and |V| are the numbers of edges and the number of nodes in the conflict graph G=(E,V) respectively.…”

Section: Flow Of Graph Divisionmentioning

confidence: 99%

An efficient layout decomposition approach for triple patterning lithography

Kuang

Young

2013

Proceedings of the 50th Annual Design Automation Conference

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Triple Patterning Lithography (TPL) is widely recognized as a promising solution for 14/10nm technology node. In this paper, we propose an efficient layout decomposition approach for TPL, with the objective to minimize the number of conflicts and stitches. Based on our analysis of actual benchmarks, we found that the whole layout can be reduced into several types of small feature clusters, by some simplification methods, and the small clusters can be solved very efficiently. We also present a new stitch finding algorithm to find all possible legal stitch positions in TPL. Experimental results show that the proposed approach is very effective in practice, which can achieve significant reduction of manufacturing cost, compared to the previous work.

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A Simple 3-Edge-Connected Component Algorithm

Cited by 25 publications

References 5 publications

Cactus: Algorithms for genome multiple sequence alignment

Cactus: Algorithms for genome multiple sequence alignment

Fast computation of small cuts via cycle space sampling

An efficient layout decomposition approach for triple patterning lithography

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