Computing Critical Nodes in Directed Graphs

Paudel, Nilakantha; Georgiadis, Loukas; Italiano, Giuseppe F.

doi:10.1137/1.9781611974768.4

Cited by 5 publications

(7 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Being a modular framework, it will be expanded to handle weighted networks, in the near future, and directed networks, immediately after. These features, which are shared with some other key-player detection methods and tools [ 28 , 49 , 50 ], are relevant to make Pyntacle fully capable of analyzing all kinds of biological networks. It will also be enriched with new optimization search algorithms and with a new algorithm to compute the set nestedness.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Pyntacle: a parallel computing-enabled framework for large-scale network biology analysis

et al. 2020

View full text Add to dashboard Cite

Background Some natural systems are big in size, complex, and often characterized by convoluted mechanisms of interaction, such as epistasis, pleiotropy, and trophism, which cannot be immediately ascribed to individual natural events or biological entities but that are often derived from group effects. However, the determination of important groups of entities, such as genes or proteins, in complex systems is considered a computationally hard task. Results We present Pyntacle, a high-performance framework designed to exploit parallel computing and graph theory to efficiently identify critical groups in big networks and in scenarios that cannot be tackled with traditional network analysis approaches. Conclusions We showcase potential applications of Pyntacle with transcriptomics and structural biology data, thereby highlighting the outstanding improvement in terms of computational resources over existing tools.

show abstract

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Pyntacle: a parallel computing-enabled framework for large-scale network biology analysis

et al. 2020

View full text Add to dashboard Cite

show abstract

“…By setting , −1 = +, − and f (x) = x(x − 1)/2, we can compute the number of strongly connected pairs in G \ e, for all edges e. Hence, we obtain a linear-time algorithm to compute the most critical edge of a directed graph with respect to strong connectivity, i.e., the edge e of G such that the number of strongly connected pairs of vertices in G \ e is minimized. (See Section 6 for the vertex version of this problem, and [37] for an alternative linear-time algorithm.) By setting , −1 = * , / and f (x) = x, we can compute the product of the sizes of the strongly connected components in G \ e, for all edges e.…”

Section: Counting the Number Of Strongly Connected Components Of G \ Ementioning

confidence: 99%

“…Hence, we obtain a linear-time algorithm to compute the most critical node of a directed graph with respect to strong connectivity, i.e., the vertex u of G such that the number of strongly connected pairs of vertices in G \ u is minimized. Based on our framework, [37] presented and evaluated an alternative linear-time algorithm for computing the most critical node of a digraph that avoids vertex-spitting.…”

Section: Counting the Number Of Strongly Connected Components Of G \ Umentioning

confidence: 99%

“…Our framework provides linear time algorithms for finding the most critical node for a plethora of functions f (G \ x), including all the aforementioned cases. Based on our framework, [37] obtains an alternative linear-time algorithm for the critical node detection problem, where f (G\x) is set to be the number of strongly connected pairs of vertices in G \ x, and shows that repeated applications of the most critical node detection algorithm gives an efficient heuristic for the more general problem where we wish to compute a set S ⊆ V of at most k vertices that minimizes f (G \ S). As noted in [3], the critical node detection problem has, in particular, several applications in the field of social network analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Strong Connectivity in Directed Graphs under Failures, with Applications

Georgiadis¹,

Italiano²,

Parotsidis³

2020

SIAM J. Comput.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…As pointed out in [20,37], this data structure is motivated by applications in many areas, including computational biology [21,34] social network analysis [30,44], network resilience [40] and network immunization [4,7,32].…”

Section: Introductionmentioning

confidence: 99%

Incremental Strong Connectivity and 2-Connectivity in Directed Graphs

Georgiadis

Italiano

Parotsidis

2018

LATIN 2018: Theoretical Informatics

Self Cite

View full text Add to dashboard Cite

In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of those cuts. We give a conditional lower bound that provides evidence that our algorithms may be tight up to a sub-polynomial factors. As an additional result, with our approach we can also maintain dynamically the 2-vertex-connected components of a digraph during any sequence of edge insertions in a total of O(mn) time. This matches the bounds for the incremental maintenance of the 2-edge-connected components of a digraph.

show abstract

Computing Critical Nodes in Directed Graphs

Cited by 5 publications

References 19 publications

Pyntacle: a parallel computing-enabled framework for large-scale network biology analysis

Pyntacle: a parallel computing-enabled framework for large-scale network biology analysis

Strong Connectivity in Directed Graphs under Failures, with Applications

Incremental Strong Connectivity and 2-Connectivity in Directed Graphs

Contact Info

Product

Resources

About