Abstract
Suppose Alice and Bob each start with private randomness and no other input, and they wish to engage in a protocol in which Alice ends up with a set x⊆ [n] and Bob ends up with a set y⊆ [n], such that (x,y) is uniformly distributed over all pairs of disjoint sets. We prove that for some constant β < 1, this requires Ω (n) communication even to get within statistical distance 1− βn of the target distribution. Previously, Ambainis, Schulman, Ta-Shma, Vazirani, and Wigderson (FOCS 1998) proved that Ω (√n) communication is required to get within some constant statistical distance ɛ > 0 of the uniform distribution over all pairs of disjoint sets of size √n.
- Scott Aaronson. 2014. The equivalence of sampling and searching. Theory Comput. Syst. 55, 2 (2014), 281--298. DOI:https://doi.org/10.1007/s00224-013-9527-3Google Scholar
Digital Library
- Scott Aaronson and Andris Ambainis. 2005. Quantum search of spatial regions. Theory Comput. 1, 1 (2005), 47--79. DOI:https://doi.org/10.4086/toc.2005.v001a004Google Scholar
Cross Ref
- Scott Aaronson and Avi Wigderson. 2009. Algebrization: A new barrier in complexity theory. ACM Trans. Comput. Theory 1, 1 (2009), 2:1--2:54. DOI:https://doi.org/10.1145/1490270.1490272Google Scholar
Digital Library
- Amir Abboud, Aviad Rubinstein, and Ryan Williams. 2017. Distributed PCP theorems for hardness of approximation in P. In Proceedings of the 58th Symposium on Foundations of Computer Science (FOCS’17). IEEE, 25--36. DOI:https://doi.org/10.1109/FOCS.2017.12Google Scholar
Cross Ref
- Josh Alman, Joshua Wang, and Huacheng Yu. 2018. Cell-probe lower bounds from online communication complexity. In Proceedings of the 50th Symposium on Theory of Computing (STOC’18). ACM, 1003--1012. DOI:https://doi.org/10.1145/3188745.3188862Google Scholar
Digital Library
- Noga Alon, Yossi Matias, and Mario Szegedy. 1999. The space complexity of approximating the frequency moments. J. Comput. System Sci. 58, 1 (1999), 137--147. DOI:https://doi.org/10.1006/jcss.1997.1545Google Scholar
Digital Library
- Andris Ambainis, Leonard Schulman, Amnon Ta-Shma, Umesh Vazirani, and Avi Wigderson. 2003. The quantum communication complexity of sampling. SIAM J. Comput. 32, 6 (2003), 1570--1585. DOI:https://doi.org/10.1137/S009753979935476Google Scholar
Digital Library
- Sepehr Assadi, Yu Chen, and Sanjeev Khanna. 2019. Polynomial pass lower bounds for graph streaming algorithms. In Proceedings of the 51st Symposium on Theory of Computing (STOC’19). ACM, 265--276. DOI:https://doi.org/10.1145/3313276.3316361Google Scholar
Digital Library
- László Babai, Peter Frankl, and Janos Simon. 1986. Complexity classes in communication complexity theory. In Proceedings of the 27th Symposium on Foundations of Computer Science (FOCS’86). IEEE, 337--347. DOI:https://doi.org/10.1109/SFCS.1986.15Google Scholar
Digital Library
- Ziv Bar-Yossef, T. S. Jayram, Ravi Kumar, and D. Sivakumar. 2004. An information statistics approach to data stream and communication complexity. J. Comput. Syst. Sci. 68, 4 (2004), 702--732. DOI:https://doi.org/10.1016/j.jcss.2003.11.006Google Scholar
Digital Library
- Paul Beame and Dang-Trinh Huynh-Ngoc. 2009. Multiparty communication complexity and threshold circuit size of . In Proceedings of the 50th Symposium on Foundations of Computer Science (FOCS’09). IEEE, 53--62. DOI:https://doi.org/10.1109/FOCS.2009.12Google Scholar
Cross Ref
- Paul Beame, Toniann Pitassi, Nathan Segerlind, and Avi Wigderson. 2006. A strong direct product theorem for corruption and the multiparty communication complexity of disjointness. Comput. Complex. 15, 4 (2006), 391--432. DOI:https://doi.org/10.1007/s00037-007-0220-2Google Scholar
Digital Library
- Christopher Beck, Russell Impagliazzo, and Shachar Lovett. 2012. Large deviation bounds for decision trees and sampling lower bounds for -circuits. In Proceedings of the 53rd Symposium on Foundations of Computer Science (FOCS’12). IEEE, 101--110. DOI:https://doi.org/10.1109/FOCS.2012.82Google Scholar
Digital Library
- Avraham Ben-Aroya, Oded Regev, and Ronald de Wolf. 2008. A hypercontractive inequality for matrix-valued functions with applications to quantum computing and LDCs. In Proceedings of the 49th Symposium on Foundations of Computer Science (FOCS’08). IEEE, 477--486. DOI:https://doi.org/10.1109/FOCS.2008.45Google Scholar
Digital Library
- Itai Benjamini, Gil Cohen, and Igor Shinkar. 2014. Bi-Lipschitz bijection between the Boolean cube and the Hamming ball. In Proceedings of the 55th Symposium on Foundations of Computer Science (FOCS’14). IEEE, 81--89. DOI:https://doi.org/10.1109/FOCS.2014.17Google Scholar
Digital Library
- Lucas Boczkowski, Iordanis Kerenidis, and Frédéric Magniez. 2018. Streaming communication protocols. ACM Trans. Comput. Theory 10, 4 (2018), 19:1--19:21. DOI:https://doi.org/10.1145/3276748Google Scholar
Digital Library
- Ralph Bottesch, Dmitry Gavinsky, and Hartmut Klauck. 2015. Correlation in hard distributions in communication complexity. In Proceedings of the 19th International Workshop on Randomization and Computation (RANDOM’15). Schloss Dagstuhl, 544--572. DOI:https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2015.544Google Scholar
- Mark Braverman, Faith Ellen, Rotem Oshman, Toniann Pitassi, and Vinod Vaikuntanathan. 2013. A tight bound for set disjointness in the message-passing model. In Proceedings of the 54th Symposium on Foundations of Computer Science (FOCS’13). IEEE, 668--677. DOI:https://doi.org/10.1109/FOCS.2013.77Google Scholar
Digital Library
- Mark Braverman, Ankit Garg, Young Kun-Ko, Jieming Mao, and Dave Touchette. 2018. Near-optimal bounds on the bounded-round quantum communication complexity of disjointness. SIAM J. Comput. 47, 6 (2018), 2277--2314. DOI:https://doi.org/10.1137/16M1061400Google Scholar
Cross Ref
- Mark Braverman, Ankit Garg, Denis Pankratov, and Omri Weinstein. 2013. From information to exact communication. In Proceedings of the 45th Symposium on Theory of Computing (STOC’13). ACM, 151--160. DOI:https://doi.org/10.1145/2488608.2488628Google Scholar
Digital Library
- Mark Braverman and Ankur Moitra. 2013. An information complexity approach to extended formulations. In Proceedings of the 45th Symposium on Theory of Computing (STOC’13). ACM, 161--170. DOI:https://doi.org/10.1145/2488608.2488629Google Scholar
Digital Library
- Mark Braverman and Rotem Oshman. 2015. On information complexity in the broadcast model. In Proceedings of the 34th Symposium on Principles of Distributed Computing (PODC’15). ACM, 355--364. DOI:https://doi.org/10.1145/2767386.2767425Google Scholar
Digital Library
- Mark Braverman and Rotem Oshman. 2017. A rounds vs. communication tradeoff for multi-party set disjointness. In Proceedings of the 58th Symposium on Foundations of Computer Science (FOCS’17). IEEE, 144--155. DOI:https://doi.org/10.1109/FOCS.2017.22Google Scholar
Cross Ref
- Joshua Brody, Amit Chakrabarti, Ranganath Kondapally, David Woodruff, and Grigory Yaroslavtsev. 2014. Beyond set disjointness: The communication complexity of finding the intersection. In Proceedings of the 33rd Symposium on Principles of Distributed Computing (PODC’14). ACM, 106--113. DOI:https://doi.org/10.1145/2611462.2611501Google Scholar
Digital Library
- Harry Buhrman, Richard Cleve, and Avi Wigderson. 1998. Quantum vs. classical communication and computation. In Proceedings of the 30th Symposium on Theory of Computing (STOC’98). ACM, 63--68. DOI:https://doi.org/10.1145/276698.276713Google Scholar
Digital Library
- Harry Buhrman, David Garcia-Soriano, Arie Matsliah, and Ronald de Wolf. 2013. The non-adaptive query complexity of testing -parities. Chicago J. Theoret. Comput. Sci. 2013, 6 (2013), 1--11. DOI:https://doi.org/10.4086/cjtcs.2013.006Google Scholar
Cross Ref
- Amit Chakrabarti, Subhash Khot, and Xiaodong Sun. 2003. Near-optimal lower bounds on the multi-party communication complexity of set disjointness. In Proceedings of the 18th Conference on Computational Complexity. IEEE, 107--117. DOI:https://doi.org/10.1109/CCC.2003.1214414Google Scholar
Cross Ref
- Arkadev Chattopadhyay and Anil Ada. 2008. Multiparty Communication Complexity of Disjointness. Technical Report TR08-002. Electronic Colloquium on Computational Complexity (ECCC). Retrieved from https://eccc.weizmann.ac.il//eccc-reports/2008/TR08-002/.Google Scholar
- Lijie Chen. 2018. On the hardness of approximate and exact (bichromatic) maximum inner product. In Proceedings of the 33rd Computational Complexity Conference (CCC’18). Schloss Dagstuhl, 14:1--14:45. DOI:https://doi.org/10.4230/LIPIcs.CCC.2018.14Google Scholar
Digital Library
- Yuval Dagan, Yuval Filmus, Hamed Hatami, and Yaqiao Li. 2018. Trading information complexity for error. Theory Comput. 14, 1 (2018), 1--73. DOI:https://doi.org/10.4086/toc.2018.v014a006Google Scholar
Cross Ref
- Anirban Dasgupta, Ravi Kumar, and D. Sivakumar. 2012. Sparse and lopsided set disjointness via information theory. In Proceedings of the 16th International Workshop on Randomization and Computation (RANDOM’12). Springer, 517--528. DOI:https://doi.org/10.1007/978-3-642-32512-0_44Google Scholar
- Anindya De and Thomas Watson. 2012. Extractors and lower bounds for locally samplable sources. ACM Trans. Comput. Theory 4, 1 (2012), 3:1--3:21. DOI:https://doi.org/10.1145/2141938.2141941Google Scholar
Digital Library
- Yuval Filmus, Hamed Hatami, Yaqiao Li, and Suzin You. 2017. Information complexity of the AND function in the two-party and multi-party settings. In Proceedings of the 23rd International Computing and Combinatorics Conference (COCOON’17). Springer, 200--211. DOI:https://doi.org/10.1007/978-3-319-62389-4_17Google Scholar
Cross Ref
- Dmitry Gavinsky. 2016. Communication Complexity of Inevitable Intersection. Technical Report abs/1611.08842. arXiv.Google Scholar
- Dmitry Gavinsky and Alexander Sherstov. 2010. A separation of NP and coNP in multiparty communication complexity. Theory Comput. 6, 1 (2010), 227--245. DOI:https://doi.org/10.4086/toc.2010.v006a010Google Scholar
Cross Ref
- Oded Goldreich, Shafi Goldwasser, and Asaf Nussboim. 2010. On the implementation of huge random objects. SIAM J. Comput. 39, 7 (2010), 2761--2822. DOI:https://doi.org/10.1137/080722771Google Scholar
Digital Library
- Mika Göös, Shachar Lovett, Raghu Meka, Thomas Watson, and David Zuckerman. 2016. Rectangles are nonnegative juntas. SIAM J. Comput. 45, 5 (2016), 1835--1869. DOI:https://doi.org/10.1137/15M103145XGoogle Scholar
Cross Ref
- Mika Göös, Toniann Pitassi, and Thomas Watson. 2016. Zero-information protocols and unambiguity in Arthur--Merlin communication. Algorithmica 76, 3 (2016), 684--719. DOI:https://doi.org/10.1007/s00453-015-0104-9Google Scholar
Digital Library
- Mika Göös and Thomas Watson. 2016. Communication complexity of set-disjointness for all probabilities. Theory Comput. 12, 9 (2016), 1--23. DOI:https://doi.org/10.4086/toc.2016.v012a009Google Scholar
- Mika Göös and Thomas Watson. 2019. A lower bound for sampling disjoint sets. In Proceedings of the 23rd International Conference on Randomization and Computation (RANDOM’19). Schloss Dagstuhl, 51:1--51:13. DOI:https://doi.org/10.4230/LIPIcs.APPROX-RANDOM.2019.51Google Scholar
- Vince Grolmusz. 1994. The BNS lower bound for multi-party protocols is nearly optimal. Info. Comput. 112, 1 (1994), 51--54. DOI:https://doi.org/10.1006/inco.1994.1051Google Scholar
Digital Library
- André Gronemeier. 2009. Asymptotically optimal lower bounds on the NIH-multi-party information complexity of the AND-function and disjointness. In Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS’09). Schloss Dagstuhl, 505--516. DOI:https://doi.org/10.4230/LIPIcs.STACS.2009.1846Google Scholar
- Johan Håstad and Avi Wigderson. 2007. The randomized communication complexity of set disjointness. Theory Comput. 3, 1 (2007), 211--219. DOI:https://doi.org/10.4086/toc.2007.v003a011Google Scholar
Cross Ref
- Peter Høyer and Ronald de Wolf. 2002. Improved quantum communication complexity bounds for disjointness and equality. In Proceedings of the 19th Symposium on Theoretical Aspects of Computer Science (STACS’02). Springer, 299--310. DOI:https://doi.org/10.1007/3-540-45841-7_24Google Scholar
Digital Library
- Dawei Huang, Seth Pettie, Yixiang Zhang, and Zhijun Zhang. 2020. The communication complexity of set intersection and multiple equality testing. In Proceedings of the 31st Symposium on Discrete Algorithms (SODA’20). ACM--SIAM, 1715--1732. DOI:https://doi.org/10.1137/1.9781611975994.105Google Scholar
Cross Ref
- Rahul Jain and Hartmut Klauck. 2010. The partition bound for classical communication complexity and query complexity. In Proceedings of the 25th Conference on Computational Complexity (CCC’10). IEEE, 247--258. DOI:https://doi.org/10.1109/CCC.2010.31Google Scholar
Digital Library
- Rahul Jain, Hartmut Klauck, and Ashwin Nayak. 2008. Direct product theorems for classical communication complexity via subdistribution bounds. In Proceedings of the 40th Symposium on Theory of Computing (STOC’08). ACM, 599--608. DOI:https://doi.org/10.1145/1374376.1374462Google Scholar
Digital Library
- Rahul Jain, Jaikumar Radhakrishnan, and Pranab Sen. 2003. A lower bound for the bounded round quantum communication complexity of set disjointness. In Proceedings of the 44th Symposium on Foundations of Computer Science (FOCS’03). IEEE, 220--229. DOI:https://doi.org/10.1109/SFCS.2003.1238196Google Scholar
Cross Ref
- Rahul Jain, Yaoyun Shi, Zhaohui Wei, and Shengyu Zhang. 2013. Efficient protocols for generating bipartite classical distributions and quantum states. IEEE Trans. Info. Theory 59, 8 (2013), 5171--5178. DOI:https://doi.org/10.1109/TIT.2013.2258372Google Scholar
Digital Library
- T. S. Jayram. 2009. Hellinger strikes back: A note on the multi-party information complexity of AND. In Proceedings of the 13th International Workshop on Randomization and Computation (RANDOM’09). Springer, 562--573. DOI:https://doi.org/10.1007/978-3-642-03685-9_42Google Scholar
Digital Library
- Bala Kalyanasundaram and Georg Schnitger. 1992. The probabilistic communication complexity of set intersection. SIAM J. Discrete Math. 5, 4 (1992), 545--557. DOI:https://doi.org/10.1137/0405044Google Scholar
Digital Library
- Hartmut Klauck. 2003. Rectangle size bounds and threshold covers in communication complexity. In Proceedings of the 18th Conference on Computational Complexity (CCC’03). IEEE, 118--134. DOI:https://doi.org/10.1109/CCC.2003.1214415Google Scholar
Cross Ref
- Hartmut Klauck. 2010. A strong direct product theorem for disjointness. In Proceedings of the 42nd Symposium on Theory of Computing (STOC’10). ACM, 77--86. DOI:https://doi.org/10.1145/1806689.1806702Google Scholar
Digital Library
- Hartmut Klauck, Ashwin Nayak, Amnon Ta-Shma, and David Zuckerman. 2007. Interaction in quantum communication. IEEE Trans. Info. Theory 53, 6 (2007), 1970--1982. DOI:https://doi.org/10.1109/TIT.2007.896888Google Scholar
Digital Library
- Hartmut Klauck and Supartha Podder. 2014. New bounds for the garden-hose model. In Proceedings of the 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS’14). Schloss Dagstuhl, 481--492. DOI:https://doi.org/10.4230/LIPIcs.FSTTCS.2014.481Google Scholar
- Hartmut Klauck, Robert Spalek, and Ronald de Wolf. 2007. Quantum and classical strong direct product theorems and optimal time-space tradeoffs. SIAM J. Comput. 36, 5 (2007), 1472--1493. DOI:https://doi.org/10.1137/05063235XGoogle Scholar
Digital Library
- Gillat Kol, Shay Moran, Amir Shpilka, and Amir Yehudayoff. 2019. Approximate nonnegative rank is equivalent to the smooth rectangle bound. Comput. Complex. 28, 1 (2019), 1--25. DOI:https://doi.org/10.1007/s00037-018-0176-4Google Scholar
Digital Library
- Eyal Kushilevitz and Enav Weinreb. 2009. The communication complexity of set-disjointness with small sets and 0-1 intersection. In Proceedings of the 50th Symposium on Foundations of Computer Science (FOCS’09). IEEE, 63--72. DOI:https://doi.org/10.1109/FOCS.2009.15Google Scholar
Cross Ref
- Troy Lee and Adi Shraibman. 2009. Disjointness is hard in the multiparty number-on-the-forehead model. Comput. Complex. 18, 2 (2009), 309--336. DOI:https://doi.org/10.1007/s00037-009-0276-2Google Scholar
Cross Ref
- László Lovász and Michael Saks. 1993. Communication complexity and combinatorial lattice theory. J. Comput. Syst. Sci. 47, 2 (1993), 322--349. DOI:https://doi.org/10.1016/0022-0000(93)90035-UGoogle Scholar
Digital Library
- Shachar Lovett and Emanuele Viola. 2012. Bounded-depth circuits cannot sample good codes. Comput. Complex. 21, 2 (2012), 245--266. DOI:https://doi.org/10.1007/s00037-012-0039-3Google Scholar
Digital Library
- Mihai Patrascu. 2011. Unifying the landscape of cell-probe lower bounds. SIAM J. Comput. 40, 3 (2011), 827--847. DOI:https://doi.org/10.1137/09075336XGoogle Scholar
Digital Library
- Vladimir Podolskii and Alexander Sherstov. 2017. Inner Product and Set Disjointness: Beyond Logarithmically Many Parties. Technical Report abs/1711.10661. arXiv.Google Scholar
- Anup Rao and Amir Yehudayoff. 2015. Simplified lower bounds on the multiparty communication complexity of disjointness. In Proceedings of the 30th Computational Complexity Conference (CCC’15). Schloss Dagstuhl, 88--101. DOI:https://doi.org/10.4230/LIPIcs.CCC.2015.88Google Scholar
Digital Library
- Alexander Razborov. 1992. On the distributional complexity of disjointness. Theoret. Comput. Sci. 106, 2 (1992), 385--390. DOI:https://doi.org/10.1016/0304-3975(92)90260-MGoogle Scholar
Digital Library
- Alexander Razborov. 2003. Quantum communication complexity of symmetric predicates. Izvestiya: Math. 67, 1 (2003), 145--159. DOI:https://doi.org/10.1070/IM2003v067n01ABEH000422Google Scholar
- Aviad Rubinstein. 2018. Hardness of approximate nearest neighbor search. In Proceedings of the 50th Symposium on Theory of Computing (STOC’18). ACM, 1260--1268. DOI:https://doi.org/10.1145/3188745.3188916Google Scholar
Digital Library
- Mert Saglam and Gábor Tardos. 2013. On the communication complexity of sparse set disjointness and exists-equal problems. In Proceedings of the 54th Symposium on Foundations of Computer Science (FOCS’13). IEEE, 678--687. DOI:https://doi.org/10.1109/FOCS.2013.78Google Scholar
Digital Library
- Alexander Sherstov. 2011. The pattern matrix method. SIAM J. Comput. 40, 6 (2011), 1969--2000. DOI:https://doi.org/10.1137/080733644Google Scholar
Digital Library
- Alexander Sherstov. 2012. Strong direct product theorems for quantum communication and query complexity. SIAM J. Comput. 41, 5 (2012), 1122--1165. DOI:https://doi.org/10.1137/110842661Google Scholar
Cross Ref
- Alexander Sherstov. 2014. Communication lower bounds using directional derivatives. J. ACM 61, 6 (2014), 1--71. DOI:https://doi.org/10.1145/2629334Google Scholar
Digital Library
- Alexander Sherstov. 2016. The multiparty communication complexity of set disjointness. SIAM J. Comput. 45, 4 (2016), 1450--1489. DOI:https://doi.org/10.1137/120891587Google Scholar
Cross Ref
- Yaoyun Shi and Yufan Zhu. 2009. Quantum communication complexity of block-composed functions. Quant. Info. Comput. 9, 5--6 (2009), 444--460.Google Scholar
- Pascal Tesson. 2003. Computational Complexity Questions Related to Finite Monoids and Semigroups. Ph.D. Dissertation. McGill University.Google Scholar
- Emanuele Viola. 2012. The complexity of distributions. SIAM J. Comput. 41, 1 (2012), 191--218. DOI:https://doi.org/10.1137/100814998Google Scholar
Digital Library
- Emanuele Viola. 2012. Extractors for turing-machine sources. In Proceedings of the 16th International Workshop on Randomization and Computation (RANDOM’12). Springer, 663--671. DOI:https://doi.org/10.1007/978-3-642-32512-0_56Google Scholar
Cross Ref
- Emanuele Viola. 2014. Extractors for circuit sources. SIAM J. Comput. 43, 2 (2014), 655--672. DOI:https://doi.org/10.1137/11085983XGoogle Scholar
Cross Ref
- Emanuele Viola. 2016. Quadratic maps are hard to sample. ACM Trans. Comput. Theory 8, 4 (2016), 18:1--18:4. DOI:https://doi.org/10.1145/2934308Google Scholar
Digital Library
- Emanuele Viola. 2020. Sampling lower bounds: Boolean average-case and permutations. SIAM J. Comput. 49, 1 (2020), 119--137. DOI:https://doi.org/10.1137/18M1198405Google Scholar
Cross Ref
- Thomas Watson. 2014. Time hierarchies for sampling distributions. SIAM J. Comput. 43, 5 (2014), 1709--1727. DOI:https://doi.org/10.1137/120898553Google Scholar
Cross Ref
- Thomas Watson. 2016. Nonnegative rank vs. binary rank. Chicago J. Theoret. Comput. Sci. 2016, 2 (2016), 1--13. DOI:https://doi.org/10.4086/cjtcs.2016.002Google Scholar
Cross Ref
- Thomas Watson. 2018. Communication complexity with small advantage. In Proceedings of the 33rd Computational Complexity Conference (CCC’18). Schloss Dagstuhl, 9:1--9:17. DOI:https://doi.org/10.4230/LIPIcs.CCC.2018.9Google Scholar
Digital Library
- Omri Weinstein and David Woodruff. 2015. The simultaneous communication of disjointness with applications to data streams. In Proceedings of the 42nd International Colloquium on Automata, Languages, and Programming (ICALP’15). Springer, 1082--1093. DOI:https://doi.org/10.1007/978-3-662-47672-7_88Google Scholar
Cross Ref
Index Terms
A Lower Bound for Sampling Disjoint Sets
Recommendations
Inner Product and Set Disjointness: Beyond Logarithmically Many Parties
A major goal in complexity theory is to understand the communication complexity of number-on-the-forehead problems f:({0, 1} n)k → {0, 1} with k > log n parties. We study the problems of inner product and set disjointness and determine their randomized ...
Simplified lower bounds on the multiparty communication complexity of disjointness
CCC '15: Proceedings of the 30th Conference on Computational ComplexityWe show that the deterministic number-on-forehead communication complexity of set disjointness for k parties on a universe of size n is Ω(n/ 4k). This gives the first lower bound that is linear in n, nearly matching Grolmusz's upper bound of O(log2(n) + ...
A Tight Bound for Set Disjointness in the Message-Passing Model
FOCS '13: Proceedings of the 2013 IEEE 54th Annual Symposium on Foundations of Computer ScienceIn a multiparty message-passing model of communication, there are k players. Each player has a private input, and they communicate by sending messages to one another over private channels. While this model has been used extensively in distributed ...






Comments