Abstract
We examine existing parallel algorithms for detection of strongly connected components and discuss their applicability to the case when the graph to be decomposed is given implicitly. In particular, we list individual techniques that parallel algorithms for SCC detection are assembled from and show how to assemble a new more efficient algorithm for solving the problem. In the paper we also report on a preliminary experimental study we did to evaluate the new algorithm.
This work has been partially supported by the Grant Agency of Czech Republic grant No. 201/06/1338.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Amato, N.: Improved processor bounds for parallel algorithms for weighted directed graphs. Inf. Process. Lett. 45(3), 147–152 (1993)
Barnat, J., Brim, L., Černá, I., Moravec, P., Ročkai, P., Šimeček, P.: Divine – a tool for distributed verification. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, Springer, Heidelberg (2006)
Barnat, J., Brim, L., Chaloupka, J.: Parallel Breadth-First Search LTL Model-Checking. In: 18th IEEE International Conference on Automated Software Engineering (ASE’03), Oct. 2003, pp. 106–115. IEEE Computer Society Press, Los Alamitos (2003)
Behrmann, G.: A performance study of distributed timed automata reachability analysis. In: Proc. Workshop on Parallel and Distributed Model Checking. Electronic Notes in Theoretical Computer Science, vol. 68, Elsevier Science Publishers, Amsterdam (2002)
Brim, L., Černá, I., Moravec, P., Šimša, J.: Accepting Predecessors are Better than Back Edges in Distributed LTL Model-Checking. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 352–366. Springer, Heidelberg (2004)
Caselli, S., Conte, G., Marenzoni, P.: Parallel state space exploration for GSPN models. In: DeMichelis, G., Díaz, M. (eds.) Application and Theory of Petri Nets 1995. LNCS, vol. 935, pp. 181–200. Springer, Heidelberg (1995)
Ciardo, G., Gluckman, J., Nicol, D.M.: Distributed State Space Generation of Discrete-State Stochastic Models. INFORMS Journal of Computing (1997)
Ciesinski, F., Baier, C.: LiQuor: A tool for Qualitative and Quantitative Linear Time analysis of Reactive Systems (2006)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (1999)
Cole, R., Vishkin, U.: Faster optimal parallel prefix sums and list ranking. Inf. Comput. 81(3), 334–352 (1989)
Fisler, K., Fraer, R., Kamhi, G., Vardi, M.Y., Yang, Z.: Is there a best symbolic cycle-detection algorithm? In: Margaria, T., Yi, W. (eds.) ETAPS 2001 and TACAS 2001. LNCS, vol. 2031, pp. 420–434. Springer, Heidelberg (2001)
Fleischer, L.K., Hendrickson, B., Pinar, A.: On identifying strongly connected components in parallel. In: Rolim, J.D.P. (ed.) Parallel and Distributed Processing. LNCS, vol. 1800, pp. 505–511. Springer, Heidelberg (2000)
Garavel, H., Mateescu, R., Smarandache, I.M.: Parallel State Space Construction for Model-Checking. In: Dwyer, M.B. (ed.) Model Checking Software. LNCS, vol. 2057, pp. 200–216. Springer, Heidelberg (2001)
Gazit, H., Miller, G.L.: An improved parallel algorithm that computes the bfs numbering of a directed graph. Inf. Process. Lett. 28(2), 61–65 (1988)
McLendon III., W., Hendrickson, B., Plimpton, S.J., Rauchwerger, L.: Finding strongly connected components in distributed graphs. J. Parallel Distrib. Comput. 65(8), 901–910 (2005)
Lerda, F., Sisto, R.: Distributed-memory model checking with SPIN. In: Dams, D.R., Gerth, R., Leue, S., Massink, M. (eds.) Theoretical and Practical Aspects of SPIN Model Checking. LNCS, vol. 1680, Springer, Heidelberg (1999)
Orzan, S.: On Distributed Verification and Verified Distribution. PhD thesis, Free University of Amsterdam (2004)
Orzan, S.M., van de Pol, J.C.: Detecting strongly connected components in large distributed state spaces. Technical Report SEN-E0501, CWI (2005)
Reif, J.H.: Depth-first search is inherently sequential. Information Processing Letters 20(5), 229–234 (1985)
Tarjan, R.: Depth first search and linear graph algorithms. SIAM Journal on computing, 146–160 (1972)
Stern, U., Dill, D.L.: Parallelizing the murϕ verifier. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 256–267. Springer, Heidelberg (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Barnat, J., Moravec, P. (2007). Parallel Algorithms for Finding SCCs in Implicitly Given Graphs . In: Brim, L., Haverkort, B., Leucker, M., van de Pol, J. (eds) Formal Methods: Applications and Technology. PDMC 2006. Lecture Notes in Computer Science, vol 4346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70952-7_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-70952-7_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70951-0
Online ISBN: 978-3-540-70952-7
eBook Packages: Computer ScienceComputer Science (R0)