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Multiparty quantum communication complexity

Harry Buhrman, Wim van Dam, Peter Høyer, Alain Tapp
1999 Physical Review A. Atomic, Molecular, and Optical Physics  
We show that if the parties share prior quantum entanglement, then the communication complexity of F is exactly k.  ...  We also show that if no entangled particles are provided, then the communication complexity of F is roughly k*log(k).  ...  A good method to prove lower bounds for the communication complexity of functions comes from a combinatorial view on the protocol for the communication.  ... 
doi:10.1103/physreva.60.2737 fatcat:uorjwgljrfchvey6fufkowa2u4

Multiparty Communication Complexity of Disjointness [article]

Arkadev Chattopadhyay, Anil Ada
2008 arXiv   pre-print
We obtain a lower bound of n^Omega(1) on the k-party randomized communication complexity of the Disjointness function in the 'Number on the Forehead' model of multiparty communication when k is a constant  ...  Our bound separates the communication complexity classes NP^CC_k and BPP^CC_k for k=o(loglog n).  ...  Preliminaries Multiparty Communication Model In the multiparty communication model introduced by [7] , k players P 1 , . . . , P k wish to collaborate to compute a function f : {0, 1} n → {−1, 1}.  ... 
arXiv:0801.3624v3 fatcat:vq4ay7ntqfgwhddwqybt42cjoi

Partition arguments in multiparty communication complexity

Jan Draisma, Eyal Kushilevitz, Enav Weinreb
2011 Theoretical Computer Science  
We conclude with two results on the multiparty "fooling set technique", another method for obtaining communication complexity lower bounds.  ...  Consider the "Number in Hand" multiparty communication complexity model, where k players holding inputs x 1 , . . . , x k ∈ {0, 1} n communicate to compute the value f (x 1 , . . . , x k ) of a function  ...  In Section 3.2, we use multilinear algebra to show that under a generalized version of the well known log-rank conjecture, partition arguments are universal for multiparty communication complexity.  ... 
doi:10.1016/j.tcs.2010.01.018 fatcat:ctic7v4wznco7hxtfi6mxmozw4

Partition Arguments in Multiparty Communication Complexity [article]

Jan Draisma and Eyal Kushilevitz and Enav Weinreb
2009 arXiv   pre-print
Consider the "Number in Hand" multiparty communication complexity model, where k players holding inputs x_1,...,x_k in 0,1^n communicate to compute the value f(x_1,...  ...  We conclude with two results on the multiparty "fooling set technique", another method for obtaining communication complexity lower bounds.  ...  Related work: Multiparty communication complexity was studied in other models as well.  ... 
arXiv:0909.5684v1 fatcat:d2l6qqvghva3laylfahsc2gtki

Partition Arguments in Multiparty Communication Complexity [chapter]

Jan Draisma, Eyal Kushilevitz, Enav Weinreb
2009 Lecture Notes in Computer Science  
We conclude with two results on the multiparty "fooling set technique", another method for obtaining communication complexity lower bounds.  ...  Consider the "Number in Hand" multiparty communication complexity model, where k players holding inputs x 1 , . . . , x k ∈ {0, 1} n communicate to compute the value f (x 1 , . . . , x k ) of a function  ...  In Section 3.2, we use multilinear algebra to show that under a generalized version of the well known log-rank conjecture, partition arguments are universal for multiparty communication complexity.  ... 
doi:10.1007/978-3-642-02927-1_33 fatcat:i2igbsjri5bpvk2ihf6xjysiwe

Multiparty Communication Complexity: Very Hard Functions [chapter]

Ján Maňuch
1999 Lecture Notes in Computer Science  
We consider the multiparty communication model de ned in DF89] using the formalism from Hr97].  ...  ., functions such that those as well as their complements have the worst possible nondeterministic communication complexity.  ...  ., minimizing the communication complexity.  ... 
doi:10.1007/3-540-48340-3_15 fatcat:zunntbvlyfdnzoalscg32k27m4

Simultaneous Multiparty Communication Complexity of Composed Functions [article]

Yassine Hamoudi
2017 arXiv   pre-print
In the Number On the Forehead (NOF) multiparty communication model, k players want to evaluate a function F : X_1 ×...× X_k→ Y on some input (x_1,...  ...  This has important applications in circuit complexity, as it could help to separate ACC^0 from other complexity classes. One of the candidates belongs to the family of composed functions.  ...  Introduction Number On the Forehead and Simultaneous models The Number On the Forehead (NOF) model is a multiparty communication model introduced by Chandra, Furst and Lipton [CFL83] that generalizes  ... 
arXiv:1710.01969v1 fatcat:jjxa7xzkhrfejgayg6yyh6iq2m

Multiparty communication complexity and very hard functions

Pavol Ďuriš
2004 Information and Computation  
However, we first state an optimal upper bound on the nondeterministic multiparty communication complexity. Claims 1.  ...  C(f) is called the nondeterministic communication complexity of f .  ...  Let c denote the communication vector described by the sequence (u 1 , v 1 ), . . . , (uˆi −1 , vˆi −1 ).  ... 
doi:10.1016/j.ic.2004.03.002 fatcat:yoj3rcrrcjbrphk442xj6rcnmm

Lower Bounds on Quantum Multiparty Communication Complexity

Troy Lee, Gideon Schechtman, Adi Shraibman
2009 2009 24th Annual IEEE Conference on Computational Complexity  
We examine this question in the number-on-the-forehead model of multiparty communication complexity.  ...  Here we show how the γ2 norm can be also extended to lower bound quantum multiparty complexity.  ...  QUANTUM MULTIPARTY COMMUNICATION COMPLEXITY We now define the NOF model of quantum multiparty communication complexity (see also [Ker07] ).  ... 
doi:10.1109/ccc.2009.24 dblp:conf/coco/LeeSS09 fatcat:xdkmaizlw5am5bajl657r3lsdq

The multiparty communication complexity of set disjointness

Alexander A. Sherstov
2012 Proceedings of the 44th symposium on Theory of Computing - STOC '12  
communication complexity.  ...  This gives the first directproduct result for multiparty set disjointness, solving an open problem due to Beame et al. (2005).  ...  Multiparty communication. An excellent reference on communication complexity is the monograph by Kushilevitz and Nisan [37] .  ... 
doi:10.1145/2213977.2214026 dblp:conf/stoc/Sherstov12 fatcat:yxgki7gjzbd5zpysoicpvqb5ma

Lower Bounds on the Multiparty Communication Complexity

Pavol Ďuriš, José D.P. Rolim
1998 Journal of computer and system sciences (Print)  
We derive a general technique for obtaining lower bounds on the multiparty communication complexity of boolean functions.  ...  We extend the two-party method based on a crossing sequence argument introduced by Yao to the multiparty communication model.  ...  We generalize Yao's method for multiparty communication model as follows.  ... 
doi:10.1006/jcss.1997.1547 fatcat:ugcyqaftrzekpidhiyhsy6pwie

The Multiparty Communication Complexity of Set Disjointness

Alexander A. Sherstov
2016 SIAM journal on computing (Print)  
communication complexity.  ...  This gives the first directproduct result for multiparty set disjointness, solving an open problem due to Beame et al. (2005).  ...  Multiparty communication. An excellent reference on communication complexity is the monograph by Kushilevitz and Nisan [37] .  ... 
doi:10.1137/120891587 fatcat:xfd26qmotver7hde4m56nr3gze

Determinism vs. Nondeterminism in Multiparty Communication Complexity

Danny Dolev, Tomás Feder
1992 SIAM journal on computing (Print)  
Key words . communication complexity, multiparty communication 1 . Introduction . Our model of multiparty communication complexity is motivated by two basic earlier models .  ...  More precisely, we prove that the deterministic and the nondeterministic communication complexity of multiparty Boolean function evaluation are polynomially related.  ...  In this paper we studied communication complexity in a multiparty model . The approach is based on the two-party model and the decision tree model.  ... 
doi:10.1137/0221052 fatcat:ya772efzzrbjtehoiamm5qzvgu

Robust Multiparty Computation with Linear Communication Complexity [chapter]

Martin Hirt, Jesper Buus Nielsen
2006 Lecture Notes in Computer Science  
The total communication complexity in bits over the point-to-point channels is O(Snκ + n BC), where S is the size of the circuit being securely evaluated, κ is the security parameter and BC is the communication  ...  We present a robust multiparty computation protocol.  ...  Hence, the total communication complexity is O(|Circ|nκ + n BC) bits.  ... 
doi:10.1007/11818175_28 fatcat:up437ta445ejlet6vgfbs7q7t4

Position-Based Cryptography and Multiparty Communication Complexity [chapter]

Joshua Brody, Stefan Dziembowski, Sebastian Faust, Krzysztof Pietrzak
2017 Lecture Notes in Computer Science  
We first show that an answer to this question would resolve a long standing open problem in multiparty communication complexity: finding a function that is hard to compute with low communication complexity  ...  Our results indicate that constructing improved provably secure protocols for PBC requires a better understanding of multiparty communication complexity.  ...  For every t take n such that n > t. (1) Multiparty communication complexity A brief introduction to the multiparty complexity was already given in Sect. 1.1.  ... 
doi:10.1007/978-3-319-70500-2_3 fatcat:wj6pm5zah5chrcrcicdgx4w6fm
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