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Lower Bounds for Number-in-Hand Multiparty Communication Complexity, Made Easy [article]

Jeff M. Phillips and Elad Verbin and Qin Zhang
2015 arXiv   pre-print
In this paper we prove lower bounds on randomized multiparty communication complexity, both in the blackboard model (where each message is written on a blackboard for all players to see) and (mainly) in  ...  All of our lower bounds allow randomized communication protocols with two-sided error. We also use the symmetrization technique to prove several direct-sum-like results for multiparty communication.  ...  Acknowledgements We would like to thank Andrew McGregor for helpful discussions, and for suggesting to study the connectivity problem. We also thank David Woodruff for some insightful comments.  ... 
arXiv:1107.2559v2 fatcat:6bg5yqjppjfl5fo3344vbde2f4

Lower Bounds for Number-in-Hand Multiparty Communication Complexity, Made Easy [chapter]

Jeff M. Phillips, Elad Verbin, Qin Zhang
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
In this paper we prove lower bounds on randomized multiparty communication complexity, both in the blackboard model (where each message is written on a blackboard for all players to see) and (mainly) in  ...  communication complexity O(C/k) and error bound ε + 4k/n.  ...  Acknowledgements We would like to thank Andrew McGregor for helpful discussions, and for suggesting to study the connectivity problem. We also thank David Woodruff for some insightful comments.  ... 
doi:10.1137/1.9781611973099.42 dblp:conf/soda/PhillipsVZ12 fatcat:pj7dpjv3pbdefpwmwij6e6nwyi

Lower Bounds for Number-in-Hand Multiparty Communication Complexity, Made Easy

Jeff M. Phillips, Elad Verbin, Qin Zhang
2016 SIAM journal on computing (Print)  
In this paper we prove lower bounds on randomized multiparty communication complexity, both in the blackboard model (where each message is written on a blackboard for all players to see) and (mainly) in  ...  communication complexity O(C/k) and error bound ε + 4k/n.  ...  Acknowledgements We would like to thank Andrew McGregor for helpful discussions, and for suggesting to study the connectivity problem. We also thank David Woodruff for some insightful comments.  ... 
doi:10.1137/15m1007525 fatcat:i5tvpt5gmbf7hn6gwnyaneydeq

Quantum multiparty communication complexity and circuit lower bounds

IORDANIS KERENIDIS
2009 Mathematical Structures in Computer Science  
In this paper, we propose a new technique for proving multiparty communication complexity lower bounds and hence, circuit lower bounds.  ...  However, all known techniques for proving multiparty communication lower bounds fail when the number of players becomes k = log n.  ...  Multiparty Communication Complexity and Circuit Lower Bounds Multiparty communication complexity was introduced as a tool for the study of boolean circuits, however the known techniques for proving lower  ... 
doi:10.1017/s0960129508007263 fatcat:huqvq52cvjhepd22n43a66mvuq

Quantum multiparty communication complexity and circuit lower bounds [article]

Iordanis Kerenidis
2005 arXiv   pre-print
We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models.  ...  Finding such an f would allow us to prove strong classical lower bounds for (k>log n) players and hence resolve a main open question about symmetric circuits.  ...  lower bounds up to Ω( n 2 k ) for the k-party communication complexity of functions and explicitly shown such a bound for GIP (X 1 , . . . , X k ).  ... 
arXiv:quant-ph/0504087v1 fatcat:znmjwdyl4fg7zgszvh2fuowd2m

The NOF Multiparty Communication Complexity of Composed Functions

Anil Ada, Arkadev Chattopadhyay, Omar Fawzi, Phuong Nguyen
2014 Computational Complexity  
We study the k-party 'number on the forehead' communication com  ...  Although communication complexity bounds have been proven using Ramsey theory, no bounds on Ramsey numbers have been proven via communication complexity bounds before. .  ...  In a very recent paper, Sherstov [33] significantly improves on the bounds of [21] , [10] and [6] on the multiparty bounded error communication complexity of disjointness: R .  ... 
doi:10.1007/s00037-013-0078-4 fatcat:z5lolz6qmzeuldku7rq2bwbzm4

The NOF Multiparty Communication Complexity of Composed Functions [chapter]

Anil Ada, Arkadev Chattopadhyay, Omar Fawzi, Phuong Nguyen
2012 Lecture Notes in Computer Science  
We study the k-party 'number on the forehead' communication com  ...  Although communication complexity bounds have been proven using Ramsey theory, no bounds on Ramsey numbers have been proven via communication complexity bounds before. .  ...  In a very recent paper, Sherstov [33] significantly improves on the bounds of [21] , [10] and [6] on the multiparty bounded error communication complexity of disjointness: R .  ... 
doi:10.1007/978-3-642-31594-7_2 fatcat:ryvwk55djjhahmpwh3tmv6q4tu

Tensor Rank and Strong Quantum Nondeterminism in Multiparty Communication

Marcos VILLAGRA, Masaki NAKANISHI, Shigeru YAMASHITA, Yasuhiko NAKASHIMA
2013 IEICE transactions on information and systems  
In this work we relate strong quantum nondeterministic multiparty communication complexity to the rank of the communication tensor in the Number-On-Forehead and Number-In-Hand models.  ...  , 1) in the Number-On-Forehead model, the cost is upper-bounded by the logarithm of nrank(f); 2) in the Number-In-Hand model, the cost is lower-bounded by the logarithm of nrank(f).  ...  Acknowledgements The authors thank the anonymous reviewers from TAMC'12 for initial reviews of this paper. The first author thanks the NEC C&C Foundation for partially supporting this research.  ... 
doi:10.1587/transinf.e96.d.1 fatcat:423gi4vljjfchpm5v5cajmmvtq

On the Hardness of Information-Theoretic Multiparty Computation [chapter]

Yuval Ishai, Eyal Kushilevitz
2004 Lecture Notes in Computer Science  
Can this be done using a constant number of communication rounds?  ...  We revisit the following open problem in information-theoretic cryptography: Does the communication complexity of unconditionally secure computation depend on the computational complexity of the function  ...  We thanks Amos Beimel and Dieter van Melkebeek for helpful related discussions.  ... 
doi:10.1007/978-3-540-24676-3_26 fatcat:26mpmsczv5gfvkp46l7b7ugj2i

Position-Based Cryptography and Multiparty Communication Complexity [chapter]

Joshua Brody, Stefan Dziembowski, Sebastian Faust, Krzysztof Pietrzak
2017 Lecture Notes in Computer Science  
This is yet another intriguing example where negative results in one area (in our case: lower bounds in multiparty communication complexity) can be used to construct secure cryptographic schemes.  ...  On a more positive side: we also show some implications in the other direction, i.e.: we prove that lower bounds on the communication complexity of certain multiparty problems imply existence of PBC primitives  ...  Secure positioning implies lower bounds for SM complexity We now show that existence of a one-round protocol for secure positioning implies lower bounds for the multiparty communication complexity.  ... 
doi:10.1007/978-3-319-70500-2_3 fatcat:wj6pm5zah5chrcrcicdgx4w6fm

Pseudorandom Bits for Constant‐Depth Circuits with Few Arbitrary Symmetric Gates

Emanuele Viola
2007 SIAM journal on computing (Print)  
communication complexity lower bound by Babai, Nisan and Szegedy (STOC '89).  ...  In particular, we conclude that every function computable by uniform poly(n)size probabilistic constant depth circuits with O(log n) arbitrary symmetric gates is in TIME 2 n o(1) .  ...  Acknowledgments We thank Salil Vadhan for his helpful reading of this paper. We thank Chattopadhyay and Hansen for sending us their paper [CH], and the anonymous referees for helpful comments.  ... 
doi:10.1137/050640941 fatcat:lli7mntqevaerenhvo4exxllqa

The story of set disjointness

Arkadev Chattopadhyay, Toniann Pitassi
2010 ACM SIGACT News  
Acknowledgements We wish to thank the following people for very helpful comments: Scott Aaronson, Joshua Brody, Amit Chakrabarti, Jeff Edmonds, Faith Ellen, Brendan Lucier, Noam Nisan, Michel Schapira,  ...  Lower bounds for multiparty complexity in the number-on-forehead model are connected to major open problems in complexity theory: it has been established that (log n) ω(1) communication complexity lower  ...  It is easy to see that this problem lies in NP cc k for all k. For k = 2 it is complete; moreover it is complete in the number-in-hand model for every k.  ... 
doi:10.1145/1855118.1855133 fatcat:d3zqnoptm5eoxefjpxlaoag44q

Norms, XOR Lemmas, and Lower Bounds for GF(2) Polynomials and Multiparty Protocols

Emanuele Viola, Avi Wigderson
2007 Proceedings - IEEE Conference on Computational Complexity  
This paper presents a unified and simple treatment of basic questions concerning two computational models: multiparty communication complexity and GF (2) polynomials.  ...  The key is the use of (known) norms on Boolean functions, which capture their approximability in each of these models. The main contributions are new XOR lemmas.  ...  We thank Paul Beame, Ronen Shaltiel, Vladimir Trifonov, and the anonymous CCC referees for helpful comments.  ... 
doi:10.1109/ccc.2007.15 dblp:conf/coco/ViolaW07 fatcat:q4byldvmarderbxwsw7xpmtf4u

Exponential Quantum-Classical Gaps in Multiparty Nondeterministic Communication Complexity [article]

Xiaoming Sun, Marcos Villagra
2013 arXiv   pre-print
We argue that there exists a total function that is hard for -communication and easy for -communication.  ...  In this paper we show that multiparty -communication can be exponentially stronger than -communication.  ...  For any k ≥ 2, Theorem 1 immediately implies the same lower bound for de Wolf's function in NPcommunication, BPP-communication, BQP-communication, and QCMA-communication 1 complexities in the Number-On-Forehead  ... 
arXiv:1308.2450v2 fatcat:rcgdspii6jcwbkisrkisem7ini

What We Have Learned About Teaching Multiparty Negotiation

Lawrence Susskind, Robert Mnookin, Lukasz Rozdeiczer, Boyd Fuller
2005 Negotiation journal  
The main question underlying the course is: "How can experts in two-party negotiations make themselves effective multiparty negotiators?"  ...  This article grows out of our experience teaching an advanced course on multiparty negotiation.  ...  ' BATNAs) on top of two-party negotiation theory made a sound foundation for analyzing and acting in multiparty negotiations.  ... 
doi:10.1111/j.1571-9979.2005.00071.x fatcat:v22e327ovjayppf6jzna6auk24
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