Hadas Shachnai ; Lisa Zhang - The master ring problem

dmtcs:3383 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms - https://doi.org/10.46298/dmtcs.3383
The master ring problemArticle

Authors: Hadas Shachnai 1; Lisa Zhang 2

  • 1 Department of Computer Science [Haifa]
  • 2 Alcatel-Lucent Bell Labs

We consider the $\textit{master ring problem (MRP)}$ which often arises in optical network design. Given a network which consists of a collection of interconnected rings $R_1, \ldots, R_K$, with $n_1, \ldots, n_K$ distinct nodes, respectively, we need to find an ordering of the nodes in the network that respects the ordering of every individual ring, if one exists. Our main result is an exact algorithm for MRP whose running time approaches $Q \cdot \prod_{k=1}^K (n_k/ \sqrt{2})$ for some polynomial $Q$, as the $n_k$ values become large. For the $\textit{ring clearance problem}$, a special case of practical interest, our algorithm achieves this running time for rings of $\textit{any}$ size $n_k \geq 2$. This yields the first nontrivial improvement, by factor of $(2 \sqrt{2})^K \approx (2.82)^K$, over the running time of the naive algorithm, which exhaustively enumerates all $\prod_{k=1}^K (2n_k)$ possible solutions.

Volume: DMTCS Proceedings vol. AD, International Conference on Analysis of Algorithms
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: Master ring,shortest common supersequence,optical networks,exact algorithms,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]

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