Computing 2-Connected Components and Maximal 2-Connected Subgraphs in Directed Graphs: An Experimental Study

Georgiadis, Loukas; Italiano, Giuseppe F.; Karanasiou, Aikaterini; Parotsidis, Nikos; Paudel, Nilakantha

doi:10.1137/1.9781611975055.15

Cited by 6 publications

(5 citation statements)

References 20 publications

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Section: Discussionmentioning

confidence: 99%

“…Thus, our data structures are able to improve one order of magnitude over previously known bounds. Furthermore, our approach is able to provide alternative linear-time algorithms for computing the 2-edge-connected and 2vertex-connected components of a digraph, which are much simpler than the algorithms presented in [19,20], and thus are likely to be more amenable to practical implementations [18]. Finally, we show how to obtain in linear time, a strongly connected spanning subgraph of G with O(n) edges that maintains: (i) the 1-connectivity cuts of G (i.e., 1-edge cuts given by strong bridges, and 1-vertex cuts given by strong articulation points) and the decompositions induced by those cuts, and (ii) the 2-edge-connected and 2-vertex-connected components of G.…”

Section: Introductionmentioning

confidence: 99%

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Strong Connectivity in Directed Graphs under Failures, with Applications

Georgiadis¹,

Italiano²,

Parotsidis³

2020

SIAM J. Comput.

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In this paper, we investigate some basic connectivity problems in directed graphs (digraphs). Let G be a digraph with m edges and n vertices, and let G \ e (resp., G \ v) be the digraph obtained after deleting edge e (resp., vertex v) from G. As a first result, we show how to compute in O(m + n) worst-case time: • The total number of strongly connected components in G \ e (resp., G \ v), for all edges e (resp., for all vertices v) in G. • The size of the largest and of the smallest strongly connected components in G \ e (resp., G \ v), for all edges e (resp., for all vertices v) in G. Let G be strongly connected. We say that edge e (resp., vertex v) separates two vertices x and y, if x and y are no longer strongly connected in G \ e (resp., G \ v). As a second set of results, we show how to build in O(m + n) time O(n)-space data structures that can answer in optimal time the following basic connectivity queries on digraphs: • Report in O(n) worst-case time all the strongly connected components of G \ e (resp., G \ v), for a query edge e (resp., vertex v). • Test whether an edge or a vertex separates two query vertices in O(1) worst-case time. • Report all edges (resp., vertices) that separate two query vertices in optimal worst-case time, i.e., in time O(k), where k is the number of separating edges (resp., separating vertices). (For k = 0, the time is O(1)). All our bounds are tight and are obtained with a common algorithmic framework, based on a novel compact representation of the decompositions induced by the 1-connectivity (i.e., 1-edge and 1-vertex) cuts in digraphs, which might be of independent interest. With the help of our data structures we can design efficient algorithms for several other connectivity problems on digraphs and we can also obtain in linear time a strongly connected spanning subgraph of G with O(n) edges that maintains the 1-connectivity cuts of G and the decompositions induced by those cuts.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Strong Connectivity in Directed Graphs under Failures, with Applications

Georgiadis¹,

Italiano²,

Parotsidis³

2020

SIAM J. Comput.

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“…Finally, we note that our approach is also able to provide alternative linear-time algorithms for computing the 2-edge-connected and 2-vertex-connected components of a digraph, which appear to be simpler than previous algorithms, and therefore likely to perform better in practice. We refer to [18] for an experimental evaluation of such algorithms. Matúš Mihalák, Przemys law Uznański and Pencho Yordanov for useful discussions on the practical applications of this problem and for pointing out references [24,35].…”

Section: Discussionmentioning

confidence: 99%

Strong Connectivity in Directed Graphs under Failures, with Applications

Georgiadis¹,

Italiano²,

Parotsidis³

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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Let G be a directed graph (digraph) with m edges and n vertices, and let G \ e (resp., G \ v) be the digraph obtained after deleting edge e (resp., vertex v) from G. We show how to compute in O(m + n) worst-case time:• The total number of strongly connected components in G \ e (resp., G \ v), for all edges e (resp., for all vertices v) in G.• The size of the largest and of the smallest strongly connected components in G \ e (resp., G \ v), for all edges e (resp., for all vertices v) in G. Let G be strongly connected. We say that edge e (resp., vertex v) separates two vertices x and y, if x and y are no longer strongly connected in G \ e (resp., G \ v). We also show how to build in O(m+n) time O(n)-space data structures that can answer in optimal time the following basic connectivity queries on digraphs:• Report in O(n) worst-case time all the strongly connected components of G \ e (resp., G \ v), for a query edge e (resp., vertex v).• Test whether an edge or a vertex separates two query vertices in O(1) worst-case time.• Report all edges (resp., vertices) that separate two query vertices in optimal worst-case time, i.e., in time O(k), where k is the number of separating edges (resp., separating vertices). (For k = 0, the time is O(1)). All our bounds are tight and are obtained with a common algorithmic framework, based on a novel compact representation of the decompositions induced by 1-edge and 1-vertex cuts in digraphs, which might be of independent interest. With the help of our data structures we can design efficient algorithms for several other connectivity problems on digraphs and we can also obtain in linear time a strongly connected spanning subgraph of G with O(n) edges that maintains the 1-connectivity cuts of G and the decompositions induced by those cuts.

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“…Two vertices u, v ∈ V are said to be 2-edge-connected (resp., 2-vertexconnected ), and we denote this relation by u ←→ 2e v (resp., u ←→ 2v v), if there are two edge-disjoint (resp., two internally vertex-disjoint) directed paths from u to v and two edge-disjoint (resp., two internally vertex-disjoint) directed paths from v to u (note that a path from u to v and a path from v to u need not be edge-disjoint or vertex-disjoint). A 2-edge-connected component (resp., 2-vertex-connected component)o fad i g r a p hG = (V, E) is defined as a maximal subset B ⊆ V such that v ←→ 2e w (resp., v ←→ 2v w) for all v, w ∈ B [10]. A visualisation of these definitions can be seen in Figure 1.…”

Section: Methodsmentioning

confidence: 99%

Sustainability of online communities of open-source projects

Perekhodko,

Welles

2024

Preprint

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Open source software projects rely on groups of volunteer contributors who collaborate to produce code and documentation. Their work is often coordinated and supported by online communities, which are essential to sustain open source projects. In this paper we analyze the structure of the underlying social networks of online communities of practice. We analyze the emergent structure of five online communities associated with highly successful open source projects in order to identify the structural correlates of successful projects, as well as moments of vulnerability in community structure that could be monitored and proactively addressed. Specifically, we consider the structure of the core of five established online open source communities. Our findings demonstrate that the core of the largest strongly connected component these communities is the most sustainable part, and the rest of the largest strongly connected component is more vulnerable to the loss of contributors and collaborators. Moreover, we analyze the evolution of the community structure over time and demonstrate that the period just prior to the emergence of the largest 2 edge connected component inside the core of the communities is the most vulnerable point in the life cycle of online open source communities. PACS: 0000, 1111 2000 MSC: 0000, 1111

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Computing 2-Connected Components and Maximal 2-Connected Subgraphs in Directed Graphs: An Experimental Study

Cited by 6 publications

References 20 publications

Strong Connectivity in Directed Graphs under Failures, with Applications

Strong Connectivity in Directed Graphs under Failures, with Applications

Strong Connectivity in Directed Graphs under Failures, with Applications

Sustainability of online communities of open-source projects

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