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Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching

Authors Michael Crouch, Daniel M. Stubbs

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Michael Crouch
Daniel M. Stubbs

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Michael Crouch and Daniel M. Stubbs. Improved Streaming Algorithms for Weighted Matching, via Unweighted Matching. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 96-104, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)
https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2014.96

Abstract

We present a (4 + epsilon) approximation algorithm for weighted graph matching which applies in the semistreaming, sliding window, and MapReduce models; this single algorithm improves the previous best algorithm in each model. The algorithm operates by reducing the maximum-weight matching problem to a polylog number of copies of the maximum-cardinality matching problem. The algorithm also extends to provide approximation guarantees for the more general problem of finding weighted independent sets in p-systems (which include intersections of p matroids and p-bounded hypergraph matching).
Keywords
  • Streaming Algorithms
  • Graph Matching
  • Weighted Graph Matching
  • MapReduce
  • Independence Systems

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References

  1. Alexandr Andoni, Robert Krauthgamer, and Krzysztof Onak. Streaming algorithms via precision sampling. FOCS, 2011. Google Scholar
  2. B.V. Ashwinkumar. Buyback problem - approximate matroid intersection with cancellation costs. In ICALP, pages 379-390, 2011. Google Scholar
  3. Ajesh Babu, Nutan Limaye, J Radhakrishnan, and Girish Varma. Streaming algorithms for language recognition problems. Theoretical Computer Science, 494:13-23, 2013. Google Scholar
  4. Ziv Bar-Yossef, Ravi Kumar, and D Sivakumar. Reductions in streaming algorithms, with an application to counting triangles in graphs. In SODA, pages 623-632, January 2002. Google Scholar
  5. Amit Chakrabarti and Sagar Kale. Submodular maximization meets streaming: Matchings, matroids, and more. IPCO, 2014. To appear. Google Scholar
  6. Michael Crouch, Andrew McGregor, and Daniel Stubbs. Dynamic graphs in the sliding-window model. ESA, 2013. Google Scholar
  7. Mayur Datar, Aristides Gionis, Piotr Indyk, and Rajeev Motwani. Maintaining stream statistics over sliding windows. SIAM Journal on Computing, 31(6):1794, 2002. Google Scholar
  8. Leah Epstein, Asaf Levin, Julián Mestre, and Danny Segev. Improved approximation guarantees for weighted matching in the semi-streaming model. SIAM Journal on Discrete Mathematics, 25(3):1251-1265, January 2011. Google Scholar
  9. Joan Feigenbaum, Sampath Kannan, Andrew McGregor, Siddharth Suri, and Jian Zhang. On graph problems in a semi-streaming model. Theoretical Computer Science, 348(2-3):207-216, December 2005. Google Scholar
  10. Piotr Indyk and David P Woodruff. Optimal approximations of the frequency moments of data streams. In STOC, pages 202-208. ACM, 2005. Google Scholar
  11. Thomas A Jenkyns. The efficacy of the “greedy” algorithm. Proceedings of the 7th Southeastern Conference on Combinatorics, Graph Theory and Computing, pages 341-350, 1976. Google Scholar
  12. Howard J. Karloff, Siddharth Suri, and Sergei Vassilvitskii. A model of computation for MapReduce. In SODA, pages 938-948, 2010. Google Scholar
  13. Silvio Lattanzi, Benjamin Moseley, Siddharth Suri, and Sergei Vassilvitskii. Filtering: a method for solving graph problems in MapReduce. In SPAA, New York, New York, USA, 2011. ACM Press. Google Scholar
  14. Frédéric Magniez, Claire Mathieu, and Ashwin Nayak. Recognizing well-parenthesized expressions in the streaming model. In STOC, pages 261-270. ACM, 2010. Google Scholar
  15. Andrew McGregor. Finding graph matchings in data streams. APPROX-RANDOM, 2005. Google Scholar
  16. Silvio Micali and Vijay V. Vazirani. An O(sqrt(|V|) |E|) algorithm for finding maximum matching in general graphs. In FOCS, pages 17-27, 1980. Google Scholar
  17. Mariano Zelke. Weighted matching in the semi-streaming model. Algorithmica, pages 669-680, 2012. Google Scholar
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