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.
Keywords
- Network design
- Survivable network
- Decision diagram
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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.
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This work was supported by JSPS KAKENHI Grant Number 15H05711.
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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
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