# Symbolic Coloured SCC Decomposition

Ontology type: schema:Chapter      Open Access: True

### Chapter Info

DATE

2021-03-23

AUTHORS 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·n·logn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(p\cdot n\cdot \log n)$$\end{document} 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 248\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{48}$$\end{document}) coloured graphs produced by models appearing in systems biology. More... »

PAGES

64-83

### Book

TITLE

Tools and Algorithms for the Construction and Analysis of Systems

ISBN

978-3-030-72012-4
978-3-030-72013-1

### Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-030-72013-1_4

DOI

http://dx.doi.org/10.1007/978-3-030-72013-1_4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1136573975

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