Symbolic Coloured SCC Decomposition

Beneš, Nikola; Brim, Luboš; Pastva, Samuel; Šafránek, David

doi:10.1007/978-3-030-72013-1_4

Cited by 3 publications

(2 citation statements)

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“…This article is an extended version of an article that appeared in the Proceedings of TACAS 2021 [BBPŠ21]. We extend the information provided in the TACAS Proceedings with more in-depth technical details of the algorithm and related proof, including explanation of its key steps.…”

Section: Introductionmentioning

confidence: 99%

BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs

Beneš¹,

Brim²,

Pastva³

et al. 2022

Logical Methods in Computer Science

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Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental problems for edge-coloured graphs is the detection of strongly connected components, or SCCs. The size of edge-coloured graphs appearing in practice can be enormous both in the number of vertices and colours. The large number of vertices prevents us from analysing such graphs using explicit SCC detection algorithms, such as Tarjan's, which motivates the use of a symbolic approach. However, the large number of colours also renders existing symbolic SCC detection algorithms impractical. This paper proposes a novel algorithm that symbolically computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $O(p \cdot n \cdot log~n)$ symbolic steps, where $p$ is the number of colours and $n$ is the number of vertices. We evaluate the algorithm using an experimental implementation based on binary decision diagrams (BDDs). Specifically, we use our implementation to explore the SCCs of a large collection of coloured graphs (up to $2^{48}$) obtained from Boolean networks -- a modelling framework commonly appearing in systems biology.

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Section: Introductionmentioning

confidence: 99%

BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs

Beneš¹,

Brim²,

Pastva³

et al. 2022

Logical Methods in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…A conclusion is provided in the last section. This article is an extended version of an article that appeared in the Proceedings of TACAS 2021 [BBPS21]. We extend the information provided in the TACAS Proceedings with technical details of the algorithm including in-depth explanation of the key steps.…”

Section: Introductionmentioning

confidence: 99%

BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs

Beneš,

Brim,

Pastva

et al. 2021

Preprint

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Edge-coloured directed graphs provide an essential structure for modelling and computing complex problems arising in many scientific disciplines. The size of edge-coloured graphs appearing in practice can be enormous in the number of both vertices and colours. An important fundamental problem that needs to be solved over edge-coloured graphs is detecting strongly connected components. The problem becomes challenging for large graphs with a large number of colours.In this paper, we describe a novel symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs O(p • n • log n) symbolic steps, where p is the number of colours and n is the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to 2 48 ) coloured graphs produced by models appearing in systems biology.

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