Document Open Access Logo

Weighted Matching in the Random-Order Streaming and Robust Communication Models

Authors Diba Hashemi , Weronika Wrzos-Kaminska

PDF

File

Thumbnail PDF
PDF
LIPIcs.APPROX-RANDOM.2024.16.pdf
  • Filesize: 0.95 MB
  • 26 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Maximum Weight Matching
  • Streaming
  • Random-Order Streaming
  • Robust Communication Complexity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

We study the maximum weight matching problem in the random-order semi-streaming model and in the robust communication model. Unlike many other sublinear models, in these two frameworks, there is a large gap between the guarantees of the best known algorithms for the unweighted and weighted versions of the problem. 
In the random-order semi-streaming setting, the edges of an n-vertex graph arrive in a stream in a random order. The goal is to compute an approximate maximum weight matching with a single pass over the stream using O(npolylog n) space. Our main result is a (2/3-ε)-approximation algorithm for maximum weight matching in random-order streams, using space O(n log n log R), where R is the ratio between the heaviest and the lightest edge in the graph. Our result nearly matches the best known unweighted (2/3+ε₀)-approximation (where ε₀ ∼ 10^{-14} is a small constant) achieved by Assadi and Behnezhad [Assadi and Behnezhad, 2021], and significantly improves upon previous weighted results. Our techniques also extend to the related robust communication model, in which the edges of a graph are partitioned randomly between Alice and Bob. Alice sends a single message of size O(npolylog n) to Bob, who must compute an approximate maximum weight matching. We achieve a (5/6-ε)-approximation using O(n log n log R) words of communication, matching the results of Azarmehr and Behnezhad [Azarmehr and Behnezhad, 2023] for unweighted graphs.

Cite As Get BibTex

Diba Hashemi and Weronika Wrzos-Kaminska. Weighted Matching in the Random-Order Streaming and Robust Communication Models. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 16:1-16:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.16

Author Details

Diba Hashemi
  • EPFL, Lausanne, Switzerland
Weronika Wrzos-Kaminska
  • EPFL, Lausanne, Switzerland

Acknowledgements

We thank Ola Svensson and Michael Kapralov for helpful discussions. We additionally thank Michael Kapralov for useful comments on the manuscript.

References

  1. Kook Jin Ahn and Sudipto Guha. Linear programming in the semi-streaming model with application to the maximum matching problem. Inf. Comput., 222:59-79, 2013. Google Scholar
  2. Kook Jin Ahn and Sudipto Guha. Access to data and number of iterations: Dual primal algorithms for maximum matching under resource constraints. ACM Trans. Parallel Comput., 4(4):17:1-17:40, 2018. Google Scholar
  3. Sepehr Assadi. A two-pass (conditional) lower bound for semi-streaming maximum matching. In Proceedings of the 2022 ACM-SIAM Symposium on Discrete Algorithms, SODA 2022, Virtual Conference / Alexandria, VA, USA, January 9 - 12, 2022, pages 708-742. SIAM, 2022. Google Scholar
  4. Sepehr Assadi. A simple (1 - ε)-approximation semi-streaming algorithm for maximum (weighted) matching. In 2024 Symposium on Simplicity in Algorithms, SOSA 2024, Alexandria, VA, USA, January 8-10, 2024, pages 337-354. SIAM, 2024. Google Scholar
  5. Sepehr Assadi, MohammadHossein Bateni, Aaron Bernstein, Vahab S. Mirrokni, and Cliff Stein. Coresets meet EDCS: algorithms for matching and vertex cover on massive graphs. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, CA, USA, January 6-9, 2019, pages 1616-1635, 2019. Google Scholar
  6. Sepehr Assadi and Soheil Behnezhad. Beating Two-Thirds For Random-Order Streaming Matching. In 48th International Colloquium on Automata, Languages, and Programming, ICALP 2021, July 12-16, 2021, Glasgow, Scotland (Virtual Conference), volume 198 of LIPIcs, pages 19:1-19:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. Google Scholar
  7. Sepehr Assadi and Soheil Behnezhad. On the Robust Communication Complexity of Bipartite Matching. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021, August 16-18, 2021, University of Washington, Seattle, Washington, USA (Virtual Conference), volume 207 of LIPIcs, pages 48:1-48:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. Google Scholar
  8. Sepehr Assadi, Soheil Behnezhad, Sanjeev Khanna, and Huan Li. On regularity lemma and barriers in streaming and dynamic matching. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, STOC 2023, Orlando, FL, USA, June 20-23, 2023, pages 131-144. ACM, 2023. Google Scholar
  9. Sepehr Assadi and Aaron Bernstein. Towards a unified theory of sparsification for matching problems. In 2nd Symposium on Simplicity in Algorithms, SOSA 2019, January 8-9, 2019, San Diego, CA, USA, pages 11:1-11:20, 2019. Google Scholar
  10. Sepehr Assadi, Arun Jambulapati, Yujia Jin, Aaron Sidford, and Kevin Tian. Semi-streaming bipartite matching in fewer passes and optimal space. In Proceedings of the 2022 ACM-SIAM Symposium on Discrete Algorithms, SODA 2022, Virtual Conference / Alexandria, VA, USA, January 9 - 12, 2022, pages 627-669. SIAM, 2022. Google Scholar
  11. Sepehr Assadi, Sanjeev Khanna, and Yang Li. On estimating maximum matching size in graph streams. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, Hotel Porta Fira, January 16-19, pages 1723-1742. SIAM, 2017. Google Scholar
  12. Sepehr Assadi, Sanjeev Khanna, Yang Li, and Grigory Yaroslavtsev. Maximum matchings in dynamic graph streams and the simultaneous communication model. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, Arlington, VA, USA, January 10-12, 2016, pages 1345-1364. SIAM, 2016. Google Scholar
  13. Sepehr Assadi, Gillat Kol, Raghuvansh R. Saxena, and Huacheng Yu. Multi-pass graph streaming lower bounds for cycle counting, max-cut, matching size, and other problems. In 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020, Durham, NC, USA, November 16-19, 2020, pages 354-364. IEEE, 2020. Google Scholar
  14. Sepehr Assadi, S. Cliff Liu, and Robert E. Tarjan. An auction algorithm for bipartite matching in streaming and massively parallel computation models. In 4th Symposium on Simplicity in Algorithms, SOSA 2021, Virtual Conference, January 11-12, 2021, pages 165-171. SIAM, 2021. Google Scholar
  15. Sepehr Assadi and Vishvajeet N. Graph streaming lower bounds for parameter estimation and property testing via a streaming XOR lemma. In STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21-25, 2021, pages 612-625. ACM, 2021. Google Scholar
  16. Sepehr Assadi and Ran Raz. Near-quadratic lower bounds for two-pass graph streaming algorithms. In 61st IEEE Annual Symposium on Foundations of Computer Science, FOCS 2020, Durham, NC, USA, November 16-19, 2020, pages 342-353. IEEE, 2020. Google Scholar
  17. Sepehr Assadi and Vihan Shah. An asymptotically optimal algorithm for maximum matching in dynamic streams. In 13th Innovations in Theoretical Computer Science Conference, ITCS 2022, January 31 - February 3, 2022, Berkeley, CA, USA, volume 215 of LIPIcs, pages 9:1-9:23. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  18. Sepehr Assadi and Janani Sundaresan. Hidden permutations to the rescue: Multi-pass streaming lower bounds for approximate matchings. In 64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023, Santa Cruz, CA, USA, November 6-9, 2023, pages 909-932. IEEE, 2023. Google Scholar
  19. Sepehr Assadi and Janani Sundaresan. (Noisy) gap cycle counting strikes back: Random order streaming lower bounds for connected components and beyond. In Proceedings of the 55th Annual ACM Symposium on Theory of Computing, STOC 2023, Orlando, FL, USA, June 20-23, 2023, pages 183-195. ACM, 2023. Google Scholar
  20. Amir Azarmehr and Soheil Behnezhad. Robust communication complexity of matching: EDCS achieves 5/6 approximation. In 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023, July 10-14, 2023, Paderborn, Germany, volume 261 of LIPIcs, pages 14:1-14:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. Google Scholar
  21. Soheil Behnezhad, Alireza Farhadi, MohammadTaghi Hajiaghayi, and Nima Reyhani. Stochastic matching with few queries: New algorithms and tools. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2019, San Diego, CA, USA, January 6-9, 2019, pages 2855-2874. SIAM, 2019. Google Scholar
  22. Aaron Bernstein. Improved bounds for matching in random-order streams. In 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference), volume 168 of LIPIcs, pages 12:1-12:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. Google Scholar
  23. Aaron Bernstein, Aditi Dudeja, and Zachary Langley. A framework for dynamic matching in weighted graphs. In STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21-25, 2021, pages 668-681. ACM, 2021. Google Scholar
  24. Aaron Bernstein and Cliff Stein. Fully Dynamic Matching in Bipartite Graphs. In Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part I, volume 9134 of Lecture Notes in Computer Science, pages 167-179. Springer, 2015. Google Scholar
  25. Aaron Bernstein and Cliff Stein. Faster fully dynamic matchings with small approximation ratios. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, Arlington, VA, USA, January 10-12, 2016, pages 692-711. SIAM, 2016. Google Scholar
  26. Stéphane Boucheron, Gábor Lugosi, and Pacal Massart. On concentration of self-bounding functions. Electronic Journal of Probability, 14:1884-1899, 2009. Google Scholar
  27. Marc Bury, Elena Grigorescu, Andrew McGregor, Morteza Monemizadeh, Chris Schwiegelshohn, Sofya Vorotnikova, and Samson Zhou. Structural results on matching estimation with applications to streaming. Algorithmica, 81(1):367-392, 2019. Google Scholar
  28. Marc Bury and Chris Schwiegelshohn. Sublinear estimation of weighted matchings in dynamic data streams. In Algorithms - ESA 2015 - 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings, volume 9294 of Lecture Notes in Computer Science, pages 263-274. Springer, 2015. Google Scholar
  29. Amit Chakrabarti, Graham Cormode, and Andrew McGregor. Robust lower bounds for communication and stream computation. In Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, May 17-20, 2008, STOC '08, pages 641-650. ACM, 2008. Google Scholar
  30. Lijie Chen, Gillat Kol, Dmitry Paramonov, Raghuvansh R. Saxena, Zhao Song, and Huacheng Yu. Almost optimal super-constant-pass streaming lower bounds for reachability. In STOC '21: 53rd Annual ACM SIGACT Symposium on Theory of Computing, Virtual Event, Italy, June 21-25, 2021, pages 570-583. ACM, 2021. Google Scholar
  31. Ashish Chiplunkar, John Kallaugher, Michael Kapralov, and Eric Price. Factorial lower bounds for (almost) random order streams. In 63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022, Denver, CO, USA, October 31 - November 3, 2022, pages 486-497. IEEE, 2022. Google Scholar
  32. Rajesh Chitnis, Graham Cormode, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Andrew McGregor, Morteza Monemizadeh, and Sofya Vorotnikova. Kernelization via sampling with applications to finding matchings and related problems in dynamic graph streams. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, Arlington, VA, USA, January 10-12, 2016, pages 1326-1344. SIAM, 2016. Google Scholar
  33. Rajesh Hemant Chitnis, Graham Cormode, MohammadTaghi Hajiaghayi, and Morteza Monemizadeh. Parameterized streaming: Maximal matching and vertex cover. In Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, January 4-6, 2015, pages 1234-1251. SIAM, 2015. Google Scholar
  34. Graham Cormode, Hossein Jowhari, Morteza Monemizadeh, and S. Muthukrishnan. The sparse awakens: Streaming algorithms for matching size estimation in sparse graphs. In 25th Annual European Symposium on Algorithms, ESA 2017, September 4-6, 2017, Vienna, Austria, volume 87 of LIPIcs, pages 29:1-29:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. Google Scholar
  35. Michael S. 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, September 4-6, 2014, Barcelona, Spain, volume 28 of LIPIcs, pages 96-104. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014. Google Scholar
  36. Jacques Dark and Christian Konrad. Optimal lower bounds for matching and vertex cover in dynamic graph streams. In 35th Computational Complexity Conference, CCC 2020, July 28-31, 2020, Saarbrücken, Germany (Virtual Conference), volume 169 of LIPIcs, pages 30:1-30:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. Google Scholar
  37. Sebastian Eggert, Lasse Kliemann, Peter Munstermann, and Anand Srivastav. Bipartite matching in the semi-streaming model. Algorithmica, 63(1-2):490-508, 2012. Google Scholar
  38. Leah Epstein, Asaf Levin, Julián Mestre, and Danny Segev. Improved approximation guarantees for weighted matching in the semi-streaming model. SIAM J. Discret. Math., 25(3):1251-1265, 2011. Google Scholar
  39. Hossein Esfandiari, MohammadTaghi Hajiaghayi, Vahid Liaghat, Morteza Monemizadeh, and Krzysztof Onak. Streaming algorithms for estimating the matching size in planar graphs and beyond. ACM Trans. Algorithms, 14(4):48:1-48:23, 2018. Google Scholar
  40. Hossein Esfandiari, MohammadTaghi Hajiaghayi, and Morteza Monemizadeh. Finding large matchings in semi-streaming. In IEEE International Conference on Data Mining Workshops, ICDM Workshops 2016, December 12-15, 2016, Barcelona, Spain, pages 608-614. IEEE Computer Society, 2016. Google Scholar
  41. Alireza Farhadi, MohammadTaghi Hajiaghayi, Tung Mah, Anup Rao, and Ryan A. Rossi. Approximate maximum matching in random streams. In Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, UT, USA, January 5-8, 2020, pages 1773-1785. SIAM, 2020. Google Scholar
  42. 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, 2005. Google Scholar
  43. Moran Feldman and Ariel Szarf. Maximum matching sans maximal matching: A new approach for finding maximum matchings in the data stream model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2022, September 19-21, 2022, University of Illinois, Urbana-Champaign, USA (Virtual Conference), volume 245 of LIPIcs, pages 33:1-33:24. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  44. Manuela Fischer, Slobodan Mitrovic, and Jara Uitto. Deterministic (1+ε)-approximate maximum matching with poly(1/ε) passes in the semi-streaming model and beyond. In STOC '22: 54th Annual ACM SIGACT Symposium on Theory of Computing, Rome, Italy, June 20 - 24, 2022, pages 248-260. ACM, 2022. Google Scholar
  45. Buddhima Gamlath, Sagar Kale, Slobodan Mitrovic, and Ola Svensson. Weighted matchings via unweighted augmentations. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, PODC 2019, Toronto, ON, Canada, July 29 - August 2, 2019, pages 491-500. ACM, 2019. Google Scholar
  46. Paritosh Garg, Sagar Kale, Lars Rohwedder, and Ola Svensson. Robust Algorithms Under Adversarial Injections. In 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020, July 8-11, 2020, Saarbrücken, Germany (Virtual Conference), volume 168 of LIPIcs, pages 56:1-56:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. Google Scholar
  47. Mohsen Ghaffari and David Wajc. Simplified and Space-Optimal Semi-Streaming (2+ε)-Approximate Matching. In 2nd Symposium on Simplicity in Algorithms, SOSA 2019, January 8-9, 2019, San Diego, CA, USA, volume 69 of OASIcs, pages 13:1-13:8. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. Google Scholar
  48. Ashish Goel, Michael Kapralov, and Sanjeev Khanna. On the communication and streaming complexity of maximum bipartite matching. In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012, Kyoto, Japan, January 17-19, 2012, pages 468-485. SIAM, 2012. Google Scholar
  49. Sudipto Guha and Andrew McGregor. Approximate quantiles and the order of the stream. In Proceedings of the Twenty-Fifth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, June 26-28, 2006, Chicago, Illinois, USA, pages 273-279. ACM, 2006. Google Scholar
  50. Sudipto Guha and Andrew McGregor. Lower bounds for quantile estimation in random-order and multi-pass streaming. In Automata, Languages and Programming, 34th International Colloquium, ICALP 2007, Wroclaw, Poland, July 9-13, 2007, Proceedings, volume 4596 of Lecture Notes in Computer Science, pages 704-715. Springer, 2007. Google Scholar
  51. Sudipto Guha and Andrew McGregor. Stream order and order statistics: Quantile estimation in random-order streams. SIAM J. Comput., 38(5):2044-2059, 2009. Google Scholar
  52. Manoj Gupta and Richard Peng. Fully dynamic (1+ ε)-approximate matchings. In 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013, 26-29 October, 2013, Berkeley, CA, USA, pages 548-557. IEEE Computer Society, October 2013. Google Scholar
  53. Venkatesan Guruswami and Krzysztof Onak. Superlinear lower bounds for multipass graph processing. Algorithmica, 76(3):654-683, 2016. Google Scholar
  54. Chien-Chung Huang and François Sellier. Maximum Weight b-Matchings in Random-Order Streams. In 30th Annual European Symposium on Algorithms, ESA 2022, September 5-9, 2022, Berlin/Potsdam, Germany, volume 244 of LIPIcs, pages 68:1-68:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. Google Scholar
  55. Shang-En Huang and Hsin-Hao Su. (1-ε)-approximate maximum weighted matching in poly(1/ε, log n) time in the distributed and parallel settings. In Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing, PODC 2023, Orlando, FL, USA, June 19-23, 2023, pages 44-54. ACM, 2023. Google Scholar
  56. Sagar Kale and Sumedh Tirodkar. Maximum matching in two, three, and a few more passes over graph streams. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2017, August 16-18, 2017, Berkeley, CA, USA, volume 81 of LIPIcs, pages 15:1-15:21. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. Google Scholar
  57. Ming-Yang Kao, Tak-Wah Lam, Wing-Kin Sung, and Hing-Fung Ting. A decomposition theorem for maximum weight bipartite matchings. SIAM Journal on Computing, 31(1):18-26, 2001. Google Scholar
  58. Michael Kapralov. Better bounds for matchings in the streaming model. In Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013, New Orleans, Louisiana, USA, January 6-8, 2013, pages 1679-1697. SIAM, 2013. Google Scholar
  59. Michael Kapralov. Space lower bounds for approximating maximum matching in the edge arrival model. In Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, Virtual Conference, January 10 - 13, 2021, pages 1874-1893. SIAM, 2021. Google Scholar
  60. Michael Kapralov, Sanjeev Khanna, and Madhu Sudan. Approximating matching size from random streams. In Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014, Portland, Oregon, USA, January 5-7, 2014, pages 734-751. SIAM, 2014. Google Scholar
  61. Michael Kapralov, Slobodan Mitrovic, Ashkan Norouzi-Fard, and Jakab Tardos. Space efficient approximation to maximum matching size from uniform edge samples. In Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, UT, USA, January 5-8, 2020, pages 1753-1772. SIAM, 2020. Google Scholar
  62. Christian Konrad. Maximum matching in turnstile streams. In Algorithms - ESA 2015 - 23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings, volume 9294 of Lecture Notes in Computer Science, pages 840-852. Springer, 2015. Google Scholar
  63. Christian Konrad. A Simple Augmentation Method for Matchings with Applications to Streaming Algorithms. In 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, August 27-31, 2018, Liverpool, UK, volume 117 of LIPIcs, pages 74:1-74:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. Google Scholar
  64. Christian Konrad, Frédéric Magniez, and Claire Mathieu. Maximum matching in semi-streaming with few passes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 15th International Workshop, APPROX 2012, and 16th International Workshop, RANDOM 2012, Cambridge, MA, USA, August 15-17, 2012. Proceedings, volume 7408 of Lecture Notes in Computer Science, pages 231-242. Springer, 2012. Google Scholar
  65. Christian Konrad and Kheeran K. Naidu. On two-pass streaming algorithms for maximum bipartite matching. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021, August 16-18, 2021, University of Washington, Seattle, Washington, USA (Virtual Conference), volume 207 of LIPIcs, pages 19:1-19:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. Google Scholar
  66. Christian Konrad and Kheeran K. Naidu. An unconditional lower bound for two-pass streaming algorithms for maximum matching approximation. In Proceedings of the 2024 ACM-SIAM Symposium on Discrete Algorithms, SODA 2024, Alexandria, VA, USA, January 7-10, 2024, pages 2881-2899. SIAM, 2024. Google Scholar
  67. Christian Konrad, Kheeran K. Naidu, and Arun Steward. Maximum matching via maximal matching queries. In 40th International Symposium on Theoretical Aspects of Computer Science, STACS 2023, March 7-9, 2023, Hamburg, Germany, volume 254 of LIPIcs, pages 41:1-41:22. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. Google Scholar
  68. Harry Lang. Online facility location on semi-random streams. CoRR, abs/1711.09384, 2017. URL: https://arxiv.org/abs/1711.09384.
  69. Andrew McGregor. Finding graph matchings in data streams. In Approximation, Randomization and Combinatorial Optimization, Algorithms and Techniques, 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2005 and 9th InternationalWorkshop on Randomization and Computation, RANDOM 2005, Berkeley, CA, USA, August 22-24, 2005, Proceedings, volume 3624 of Lecture Notes in Computer Science, pages 170-181. Springer, 2005. Google Scholar
  70. Andrew McGregor and Sofya Vorotnikova. Planar matching in streams revisited. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2016, September 7-9, 2016, Paris, France, volume 60 of LIPIcs, pages 17:1-17:12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. Google Scholar
  71. Andrew McGregor and Sofya Vorotnikova. A simple, space-efficient, streaming algorithm for matchings in low arboricity graphs. In 1st Symposium on Simplicity in Algorithms, SOSA 2018, January 7-10, 2018, New Orleans, LA, USA, volume 61 of OASIcs, pages 14:1-14:4. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. Google Scholar
  72. Morteza Monemizadeh, S. Muthukrishnan, Pan Peng, and Christian Sohler. Testable bounded degree graph properties are random order streamable. In 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, volume 80 of LIPIcs, pages 131:1-131:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. Google Scholar
  73. Ami Paz and Gregory Schwartzman. A (2 + ε)-approximation for maximum weight matching in the semi-streaming model. In Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, Barcelona, Spain, January 16-19, pages 2153-2161. SIAM, 2017. Google Scholar
  74. Alexander Schrijver. Combinatorial optimization: polyhedra and efficiency, volume 24. Springer, 2003. Google Scholar
  75. Sumedh Tirodkar. Deterministic algorithms for maximum matching on general graphs in the semi-streaming model. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2018, December 11-13, 2018, Ahmedabad, India, volume 122 of LIPIcs, pages 39:1-39:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. Google Scholar
  76. David Wajc. Negative association-definition, properties, and applications, 2017. Google Scholar
  77. Andrew Chi-Chih Yao. Some complexity questions related to distributive computing (preliminary report). In Proceedings of the 11h Annual ACM Symposium on Theory of Computing, April 30 - May 2, 1979, Atlanta, Georgia, USA, pages 209-213. ACM, 1979. Google Scholar
  78. Mariano Zelke. Weighted matching in the semi-streaming model. Algorithmica, 62(1-2):1-20, 2012. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact