Abstract
The Interconnection Graph Problem (IGP) is to compute for a given hypergraph H = (V, R) a graph G = (V, E) with the minimum number of edges |E| such that for all hyperedges N ∈ R the subgraph of G induced by N is connected. Computing feasible interconnection graphs is basically motivated by the design of reconfigurable interconnection networks. This paper proves that IGP is NP-complete and hard to approximate even when all hyperedges of H have at most three vertices. Afterwards it presents a search tree based parameterized algorithm showing that the problem is fixed-parameter tractable when the hyperedge size of H is bounded. Moreover, the paper gives a reduction based greedy algorithm and closes with its experimental justification.
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References
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Macmillan Press, London (1976)
Betz, V., Rose, J., Marquardt, A.: Architecture and CAD for Deep-Submicron FPGAs. Kluwer-Academic Publisher, Boston (1999)
Lemieux, G., Lewis, D.: Design of Interconnection Networks for Programmable Logic. Kluwer-Academic Publisher, Boston (2003)
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1998)
Ellis, J., Fan, H., Fellows, M.: The Dominating Set Problem is Fixed Parameter Tractable for Graphs of Bounded Genus. Journal of Algorithms 52(2), 152–168 (2004)
Du, D.-Z., Ko, K.-I.: Theory of Computational Complexity. John Wiley & Sons, Chichester (2000)
Monien, B., Speckenmeyer, E.: Ramsey numbers and an approximation algorithm for the vertex cover problem. Acta Inf. 22, 115–123 (1985)
Papadimitriou, C.H., Yannakakis, M.: Optimization, approximation, and complexity classes. J. Comput. System Sci. 43, 425–440 (1991)
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Fan, H., Hundt, C., Wu, YL., Ernst, J. (2008). Algorithms and Implementation for Interconnection Graph Problem. In: Yang, B., Du, DZ., Wang, C.A. (eds) Combinatorial Optimization and Applications. COCOA 2008. Lecture Notes in Computer Science, vol 5165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85097-7_19
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DOI: https://doi.org/10.1007/978-3-540-85097-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85096-0
Online ISBN: 978-3-540-85097-7
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