Abstract
Various network systems such as communication networks require survivability that is tolerance of attacks, failures, and accidents. Designing a network with high survivability is formulated as a survivable network design problem (SNDP). The input of the SNDP is a pair of an edge-weighted graph and a requirement of topology and survivability. For an edge subset of the graph, if it satisfies the requirement, we call it a desired edge subset (DES). The output of the SNDP is the minimum weight DES. Although the SNDP is an optimization problem, to simply solve it is not always desired in terms of the practical use: Designers sometimes want to test multiple DESs including non-optimal DESs, because the theoretical optimal DES is not always the practical best.
In this paper, instead of the optimization, we propose a method to enumerate all DESs with a compact data structure, called the zero-suppressed binary decision diagram (ZDD). Obtained ZDDs support practical network design by performing optimization, sampling, and filtering of DESs. The proposed method combines two typical techniques constructing ZDDs, called the frontier-based search (FBS) and the family algebra, and includes a novel operation on ZDDs. We demonstrate that our method works on various real-world instances of practical scales.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Although our approach can handle both directed and undirected graphs, we describe only the undirected version (i.e., \(E \subseteq \{\{u,v\} \mid u,v \in V\}\)) in this paper.
References
Ellison, R., Linger, R., Longstaff, T., Mead, N.: Survivable network system analysis: a case study. IEEE Software 16, 70–77 (1999)
Kerivin, H., Mahjoub, A.R.: Design of survivable networks: a survey. Networks 46(1), 1–21 (2005)
Akgün, I.: New formulations for the hop-constrained minimum spanning tree problem via sherali and driscoll’s tightened miller-tucker-zemlin constraints. Comput. Oper. Res. 38(1), 277–286 (2011)
Diarrassouba, I., Gabrel, V., Ridha Mahjoub, A., Gouveia, L., Pesneau, P.: Integer programming formulations for the k-edge-connected 3-hop-constrained network design problem. Networks 67, 148–169 (2015)
Fortz, B.: Design of survivable networks with bounded rings. In: Network Theory and Applications (2000)
Gouveia, L., Simonetti, L., Uchoa, E.: Modeling hop-constrained and diameter-constrained minimum spanning tree problems as steiner tree problems over layered graphs. Math. Program. 128(1), 123–148 (2011)
Rodriguez-Martin, I., Salazar Gonzlez, J.J., Yaman, H.: The ring/\(\kappa \)-rings network design problem: model and branch-and-cut algorithm. Networks 68, 130–140 (2016)
Penttinen, A.: Chapter 10 - Network planning and dimensioning. Lecture Notes: S-38.145 - Introduction to Teletraffic Theory. Helsinki University of Technology (1999)
Minato, S.: Zero-suppressed BDDS for set manipulation in combinatorial problems. In: DAC, pp. 272–277 (1993)
Knuth, D.E.: The Art of Computer Programming: Bitwise tricks & Techniques. Binary Decision Diagrams, vol. 4, fascicle 1. Addison-Wesley Professional, Boston (2009)
Kawahara, J., Inoue, T., Iwashita, H., Minato, S.: Frontier-based search for enumerating all constrained subgraphs with compressed representation. IEICE Trans. Fundam. E100–A(9), 1773–1784 (2017)
Coudert, O.: Solving graph optimization problems with ZBDDS. In: Proceedings of the 1997 European Conference on Design and Test, EDTC 1997, p. 224 (1997)
Kawahara, J., Horiyama, T., Hotta, K., Minato, S.I.: Generating all patterns of graph partitions within a disparity bound. In: WALCOM: Algorithms and Computation, pp. 119–131 (2017)
Kawahara, J., Saitoh, T., Suzuki, H., Yoshinaka, R.: Solving the longest oneway-ticket problem and enumerating letter graphs by augmenting the two representative approaches with ZDDs. In: Phon-Amnuaisuk, S., Au, T.-W., Omar, S. (eds.) CIIS 2016. AISC, vol. 532, pp. 294–305. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-48517-1_26
Minato, S., Ishiura, N., Yajima, S.: Shared binary decision diagram with attributed edges for efficient boolean function manipulation. In: 27th ACM/IEEE Design Automation Conference, pp. 52–57 (1990)
Amarilli, A., Bourhis, P., Jachiet, L., Mengel, S.: A circuit-based approach to efficient enumeration. In: 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), vol. 80, pp. 111:1–111:15 (2017)
Yoshinaka, R., Kawahara, J., Denzumi, S., Arimura, H., Ichi-Minato, S.: Counterexamples to the long-standing conjecture on the complexity of BDD binary operations. Inf. Process. Lett. 112, 636–640 (2012)
Acknowledgement
This work was supported by JSPS KAKENHI Grant Number 15H05711.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Suzuki, H., Ishihata, M., Minato, Si. (2020). Designing Survivable Networks with Zero-Suppressed Binary Decision Diagrams. In: Rahman, M., Sadakane, K., Sung, WK. (eds) WALCOM: Algorithms and Computation. WALCOM 2020. Lecture Notes in Computer Science(), vol 12049. Springer, Cham. https://doi.org/10.1007/978-3-030-39881-1_23
Download citation
DOI: https://doi.org/10.1007/978-3-030-39881-1_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-39880-4
Online ISBN: 978-3-030-39881-1
eBook Packages: Computer ScienceComputer Science (R0)