Effective and Efficient Data Reduction for the Subset Interconnection Design Problem
The NP-hard Subset Interconnection Design problem is motivated by applications in designing vacuum systems and scalable overlay networks. It has as input a set V and a collection of subsets V1, V2, …, Vm, and asks for a minimum-cardinality edge set E such that for the graph G = (V,E) all induced subgraphs G[V1], G[V2], …, G[Vm] are connected. It has also been studied under the name Minimum Topic-Connected Overlay. We study Subset Interconnection Design in the context of polynomial-time data reduction rules that preserve optimality. Our contribution is threefold: First, we point out flaws in earlier polynomial-time data reduction rules. Second, we provide a fixed-parameter tractability result for small subset sizes and tree-like output graphs. Third, we show linear-time solvability in case of a constant number m of subsets, implying fixed-parameter tractability for the parameter m. To achieve our results, we elaborate on polynomial-time data reduction rules (partly “repairing” previous flawed ones) which also may be of practical use in solving Subset Interconnection Design.
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- 1.Angluin, D., Aspnes, J., Reyzin, L.: Inferring social networks from outbreaks. In: Hutter, M., Stephan, F., Vovk, V., Zeugmann, T. (eds.) ALT 2010. LNCS (LNAI), vol. 6331, pp. 104–118. Springer, Heidelberg (2010)Google Scholar
- 2.Chockler, G., Melamed, R., Tock, Y., Vitenberg, R.: Constructing scalable overlays for pub-sub with many topics. In: Proc. 26th PODC, pp. 109–118. ACM (2007)Google Scholar
- 3.Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer (1999)Google Scholar
- 7.Fan, H., Wu, Y.-L.: Interconnection graph problem. In: Proc. FCS 2008, pp. 51–55. CSREA Press (2008)Google Scholar
- 9.Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer (2006)Google Scholar
- 13.Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
- 15.Tang, T.-Z.: An optimality condition for minimum feasible graphs. Applied Mathematics - A Journal of Chinese Universities, 24–21 (1989) (in Chinese)Google Scholar