Abstract
k-Interval Routing Scheme (k-IRS) is a compact routing method that allows up to k interval labels to be assigned to an arc. A fundamental problem is to characterize the networks that admit k-IRS. Many of the problems related to single-shortest-path k-IRS have already been shown to be NP-complete. For all-shortest-path k-IRS, the characterization problem remains open for k≥ 1. We investigate the time complexity of devising minimal-space all-shortest-path k-IRS and prove that it is NP-complete to decide whether a graph admits an all-shortest-path k-IRS, for every integer k≥ 3, as well as whether a graph admits an all-shortest-path k-strict IRS, for every integer k≥ 4. These are the first NP-completeness results for all-shortest-path k-IRS where k is a constant and the graph is unweighted. Moreover, the NP-completeness holds also for the linear case.
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Wang, R., Lau, F.C.M., Liu, Y.Y. (2004). NP-Completeness Results for All-Shortest-Path Interval Routing. In: Královic̆, R., Sýkora, O. (eds) Structural Information and Communication Complexity. SIROCCO 2004. Lecture Notes in Computer Science, vol 3104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27796-5_24
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DOI: https://doi.org/10.1007/978-3-540-27796-5_24
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