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

J 2022

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

BENEŠ, Nikola, Luboš BRIM, Samuel PASTVA and David ŠAFRÁNEK

Basic information

Original name

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

Authors

BENEŠ, Nikola (203 Czech Republic, belonging to the institution), Luboš BRIM (203 Czech Republic, belonging to the institution), Samuel PASTVA (703 Slovakia, belonging to the institution) and David ŠAFRÁNEK (203 Czech Republic, guarantor, belonging to the institution)

Edition

Logical Methods in Computer Science, Episciences, 2022, 1860-5974

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 0.600

RIV identification code

RIV/00216224:14330/22:00125612

Organization unit

Faculty of Informatics

DOI

http://dx.doi.org/10.46298/LMCS-18(1:38)2022

UT WoS

000769134500001

Keywords in English

strongly connected components; symbolic algorithm; BDD

Abstract

V originále

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 . 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). 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.

Links

MUNI/A/1145/2021, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace XI. (Acronym: SV-FI MAV XI.)

Investor: Masaryk University

Citovat

BENEŠ, Nikola, Luboš BRIM, Samuel PASTVA and David ŠAFRÁNEK. BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs. Logical Methods in Computer Science. Episciences, 2022, vol. 18, No 1, p. 1-27. ISSN 1860-5974. Available from: https://dx.doi.org/10.46298/LMCS-18(1:38)2022.

@article{1845005,
   author = {Beneš, Nikola and Brim, Luboš and Pastva, Samuel and Šafránek, David},
   article_number = {1},
   doi = {http://dx.doi.org/10.46298/LMCS-18(1:38)2022},
   keywords = {strongly connected components; symbolic algorithm; BDD},
   language = {eng},
   issn = {1860-5974},
   journal = {Logical Methods in Computer Science},
   title = {BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs},
   url = {https://lmcs.episciences.org/9198},
   volume = {18},
   year = {2022}
}

TY  - JOUR
ID  - 1845005
AU  - Beneš, Nikola - Brim, Luboš - Pastva, Samuel - Šafránek, David
PY  - 2022
TI  - BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs
JF  - Logical Methods in Computer Science
VL  - 18
IS  - 1
SP  - 1-27
EP  - 1-27
PB  - Episciences
SN  - 18605974
KW  - strongly connected components
KW  - symbolic algorithm
KW  - BDD
UR  - https://lmcs.episciences.org/9198
N2  - 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 . 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). 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.
ER  -

BENEŠ, Nikola, Luboš BRIM, Samuel PASTVA and David ŠAFRÁNEK. BDD-Based Algorithm for SCC Decomposition of Edge-Coloured Graphs. \textit{Logical Methods in Computer Science}. Episciences, 2022, vol.~18, No~1, p.~1-27. ISSN~1860-5974. Available from: https://dx.doi.org/10.46298/LMCS-18(1:38)2022.

Detailed Information on Publication Record