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Symbolic Coloured SCC Decomposition

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12652)

Abstract

Problems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale.

We propose a new, symbolic algorithm that 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 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.

Keywords

  • strongly connected components
  • symbolic algorithm
  • edge-coloured digraphs
  • systems biology

Supported by the Czech Science Foundation grant No. 18-00178S.

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Beneš, N., Brim, L., Pastva, S., Šafránek, D. (2021). Symbolic Coloured SCC Decomposition. In: Groote, J.F., Larsen, K.G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2021. Lecture Notes in Computer Science(), vol 12652. Springer, Cham. https://doi.org/10.1007/978-3-030-72013-1_4

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  • DOI: https://doi.org/10.1007/978-3-030-72013-1_4

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