The bridge-connectivity augmentation problem with a partition constraint

Chen, Yen-Chiu; Wei, Hsin-Wen; Huang, Pei-Chi; Shih, Wei-Kuan; Hsu, Tsan-sheng

doi:10.1016/j.tcs.2010.04.019

Cited by 5 publications

(4 citation statements)

References 22 publications

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“…Due to its planarity structure, it finds applications in VLSI design and computer networks [14], and it has been an active graph class in the literature, see [15,16,17] for recent works on Halin graphs. Although combinatorial problems such as planarity testing [18], bipartiteness testing [19], chordality testing [20], connectivity augmentation [21,22,23], etc., have received attention in parallel algorithmics, enumeration of sets satisfying some structural property have not received much attention in the past.…”

Section: Introductionmentioning

confidence: 99%

Listing all spanning trees in Halin graphs — sequential and Parallel view

Reddy

Renjith

Sadagopan

2018

Discrete Math. Algorithm. Appl.

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Abstract. For a connected labelled graph G, a spanning tree T is a connected and an acyclic subgraph that spans all vertices of G. In this paper, we consider a classical combinatorial problem which is to list all spanning trees of G. A Halin graph is a graph obtained from a tree with no degree two vertices and by joining all leaves with a cycle. We present a sequential and parallel algorithm to enumerate all spanning trees in Halin graphs. Our approach enumerates without repetitions and we make use of O( (2pd) p ) processors for parallel algorithmics, where d and p are the depth, the number of leaves, respectively, of the Halin graph. We also prove that the number of spanning trees in Halin graphs is O( (2pd) p ).

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Section: Introductionmentioning

confidence: 99%

Listing all spanning trees in Halin graphs — sequential and Parallel view

Reddy

Renjith

Sadagopan

2018

Discrete Math. Algorithm. Appl.

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“…Let M-kECAMP denote kECAMP in which G is an r-paritite graph, where "M-" means a multipartite graph. Recently, [2] proposed a linear time algorithm for 2ECAMP, and an O(log |V|) parallel time algorithm on an EREW PRAM with a linear number of processors.…”

Section: Introductionmentioning

confidence: 99%

A Fast Algorithm for Augmenting Edge-Connectivity by One with Bipartition Constraints

Oki

Taoka

Mashima

et al. 2012

IEICE Trans. Inf. & Syst.

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SUMMARYThe k-edge-connectivity augmentation problem with bipartition constraints (kECABP, for short) is defined by "Given an undirected graph G = (V, E) and a bipartition π = {V B , V W } of V with V B ∩V W = ∅, find an edge set E f of minimum cardinality, consisting of edges that connect V B and V W , such that G = (V, E ∪ E f ) is k-edge-connected." The problem has applications for security of statistical data stored in a cross tabulated table, and so on. In this paper we propose a fast algorithm for finding an optimal solution to (σ + 1)ECABP in O(|V||E| + |V 2 | log |V|) time when G is σ-edge-connected (σ > 0), and show that the problem can be solved in linear time if σ ∈ {1, 2}.

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“…The proposed algorithm is done in O(log |V|) parallel time on an EREW PRAM using a linear number of processors. Very recently, [2] proposed a sequential linear time algorithm for 2ECAM, and a parallel algorithm on an EREW PRAM using a linear number of processors. However, our approach is different from one of [2].…”

Section: Introductionmentioning

confidence: 99%

“…Very recently, [2] proposed a sequential linear time algorithm for 2ECAM, and a parallel algorithm on an EREW PRAM using a linear number of processors. However, our approach is different from one of [2]. The paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

A Parallel Algorithm for 2-Edge-Connectivity Augmentation of a Connected Graph with Multipartition Constraints

Oki

Taoka

Watanabe

2010

2010 First International Conference on Networking and Computing

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The k-edge-connectivity augmentation problem with multipartition constraints (kECAM for short) is defined by "Given an undirected graph G = (V, E) and a multipartitionfind an edge set E of minimum cardinality, consisting of edges that connect distinct members of π, such that G = (V, E ∪ E ) is kedge-connected." In this paper, we propose a parallel algorithm, running on an EREW PRAM, for finding a solution to 2ECAM when G is connected. The main idea is to reduce 2ECAM to the bipartition case, that is, 2ECAM with r = 2.

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The bridge-connectivity augmentation problem with a partition constraint

Cited by 5 publications

References 22 publications

Listing all spanning trees in Halin graphs — sequential and Parallel view

Listing all spanning trees in Halin graphs — sequential and Parallel view

A Fast Algorithm for Augmenting Edge-Connectivity by One with Bipartition Constraints

A Parallel Algorithm for 2-Edge-Connectivity Augmentation of a Connected Graph with Multipartition Constraints

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