Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees

Authors Markus Chimani, Joachim Spoerhase

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Markus Chimani
Joachim Spoerhase

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Markus Chimani and Joachim Spoerhase. Network Design Problems with Bounded Distances via Shallow-Light Steiner Trees. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 238-248, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


In a directed graph G with non-correlated edge lengths and costs, the network design problem with bounded distances asks for a cost-minimal spanning subgraph subject to a length bound for all node pairs. We give a bi-criteria (2+\varepsilon,O(n^{0.5+\varepsilon}))-approximation for this problem. This improves on the currently best known linear approximation bound, at the cost of violating the distance bound by a factor of at most 2+\varepsilon. In the course of proving this result, the related problem of directed shallow-light Steiner trees arises as a subproblem. In the context of directed graphs, approximations to this problem have been elusive. We present the first non-trivial result by proposing a (1+\varepsilon,O(|R|^{\varepsilon}))-ap\-proximation, where R is the set of terminals. Finally, we show how to apply our results to obtain an (\alpha+\varepsilon,O(n^{0.5+\varepsilon}))-approximation for light-weight directed \alpha-spanners. For this, no non-trivial approximation algorithm has been known before. All running times depends on n and \varepsilon and are polynomial in n for any fixed \varepsilon>0.
  • network design
  • approximation algorithm
  • shallow-light spanning trees
  • spanners


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  1. Ingo Althöfer, Gautam Das, David P. Dobkin, Deborah Joseph, and José Soares. On sparse spanners of weighted graphs. Discrete & Computational Geometry, 9:81-100, 1993. Google Scholar
  2. Piotr Berman, Arnab Bhattacharyya, Konstantin Makarychev, Sofya Raskhodnikova, and Grigory Yaroslavtsev. Approximation algorithms for spanner problems and directed steiner forest. Inf. Comput., 222:93-107, 2013. Google Scholar
  3. Arnab Bhattacharyya, Elena Grigorescu, Kyomin Jung, Sofya Raskhodnikova, and David P. Woodruff. Transitive-closure spanners. SIAM J. Comput., 41(6):1380-1425, 2012. Google Scholar
  4. Moses Charikar, Chandra Chekuri, To-Yat Cheung, Zuo Dai, Ashish Goel, Sudipto Guha, and Ming Li. Approximation algorithms for directed steiner problems. J. Algorithms, 33(1):73-91, 1999. (preliminary version appeared at SODA'98). Google Scholar
  5. Michael Dinitz and Robert Krauthgamer. Directed spanners via flow-based linear programs. In Proceedings of the 43rd ACM Symposium on Theory of Computing (STOC'11), pages 323-332, 2011. Google Scholar
  6. Yevgeniy Dodis and Sanjeev Khanna. Designing networks with bounded pairwise distance. In Proc. 21st Ann. ACM Symposium on Theory of Computing (STOC'99), pages 750-759, 1999. Google Scholar
  7. Funda Ergun, Rakesh Sinha, and Lisa Zhang. An improved FPTAS for restricted shortest path. Information Processing Letters, 83:287-291, 2002. Google Scholar
  8. Moran Feldman, Guy Kortsarz, and Zeev Nutov. Improved approximation algorithms for directed steiner forest. J. Comput. Syst. Sci., 78(1):279-292, 2012. Google Scholar
  9. Refael Hassin. Approximation schemes for the restricted shortest path problem. Mathematics of Operations Research, 17(1):36-42, 1992. Google Scholar
  10. C. S. Helvig, G. Robins, and A. Zelikovsky. An improved approximation scheme for the group steiner problem. Networks, 37(1):8-20, 2001. Google Scholar
  11. Guy Kortsarz and David Peleg. Approximating shallow-light trees. In Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA'97), pages 103-110, 1997. Google Scholar
  12. Joseph Naor and Baruch Schieber. Improved approximations for shallow-light spanning trees. In 38th Annual Symposium on Foundations of Computer Science (FOCS'97), pages 536-541, 1997. Google Scholar
  13. David Peleg and Alejandro A. Schäffer. Graph spanners. Journal of Graph Theory, 13(1):99-116, 1989. Google Scholar
  14. A. Zelikovsky. A series of approximation algorithms for the acyclic directed steiner tree problem. Algorithmica, 18:99-110, 1997. Google Scholar