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Hardness of Constant-round Communication Complexity [article]

Shuichi Hirahara, Rahul Ilango, Bruno Loff
2021 Electronic colloquium on computational complexity  
In this work, we show that it is NP-hard to approximate the size (number of leaves) of the smallest constant-round protocol for a two-argument total Boolean function f : [N ] × [N ] → {0, 1}, when it is  ...  How difficult is it to compute the communication complexity of a two-argument total Boolean function f : [N ] × [N ] → {0, 1}, when it is given as an N × N binary matrix?  ...  The authors would also like to thank Igor Oliveira for helpful conversations about hardness of communication complexity.  ... 
dblp:journals/eccc/HiraharaIL21 fatcat:whafgy4hufajzfhgl6pnvlee24

Hardness of Constant-Round Communication Complexity

Shuichi Hirahara, Rahul Ilango, Bruno Loff, Valentine Kabanets
2021
In this work, we show that it is NP-hard to approximate the size (number of leaves) of the smallest constant-round protocol for a two-argument total Boolean function f:[N]×[N] → {0,1}, when it is given  ...  How difficult is it to compute the communication complexity of a two-argument total Boolean function f:[N]×[N] → {0,1}, when it is given as an N×N binary matrix?  ...  The authors would also like to thank Igor Oliveira for helpful conversations about hardness of communication complexity.  ... 
doi:10.4230/lipics.ccc.2021.31 fatcat:6xmuvrqnkrhrhnf5fgzqkbhwde

On Round-Efficient Argument Systems [chapter]

Hoeteck Wee
2005 Lecture Notes in Computer Science  
We consider the problem of constructing round-efficient public-coin argument systems, that is, interactive proof systems that are only computationally sound with a constant number of rounds.  ...  Next, we relate the existence of non-trivial 2-round argument systems to that of hard-on-average search problems in NP and that of efficient public-coin zero-knowledge arguments for NP.  ...  Necessity of hardness assumptions We present hardness assumptions that are necessary for 2-round argument systems for NP with subpolynomial communication complexity.  ... 
doi:10.1007/11523468_12 fatcat:x3k2vjcelzct5oggyjy2kujd3y

Constant Rounds Almost Linear Complexity Multi-party Computation for Prefix Sum [chapter]

Kazuma Ohara, Kazuo Ohta, Koutarou Suzuki, Kazuki Yoneyama
2014 Lecture Notes in Computer Science  
Moreover, as an application of the prefix sum protocol, we construct the first bit addition protocol with constant rounds and almost linear communication complexity.  ...  In this paper, we propose the first MPC protocol for prefix sum in general semigroups with constant 2d + 2dc rounds and almost linear O(l log * (c) l) communication complexity, where c is a constant, d  ...  The bit decomposition protocol, that converts a sharing of a finite field element to a sharing of bit representation of the element, makes it possible to compute these basic operations efficiently.  ... 
doi:10.1007/978-3-319-06734-6_18 fatcat:2semie5mgbgs3dlqamwexcekly

Equivalence Classes and Conditional Hardness in Massively Parallel Computations

Danupon Nanongkai, Michele Scquizzato, Michael Wagner
2020 International Conference on Principles of Distributed Systems  
These connections concern the class of problems solvable in a sublogarithmic amount of rounds in the MPC model, denoted by MPC(o(log N )), and some standard classes concerning space complexity, namely  ...  In this section we shall exploit the shortest path problem as a prototypical problem for which the fastest known MPC algorithm takes O(log n) rounds, and prove a collection of constant-round equivalences  ...  Hard bounds on the point-to-point communication lead to very strong round lower bounds in this model [41, 49, 50] .  ... 
doi:10.4230/lipics.opodis.2019.33 dblp:conf/opodis/NanongkaiS19 fatcat:hmemw6usqvfrdaqqqyd2vubgqi

The advantages of a new approach to defining the communication complexity for VLSI

Juraj Hromkovič
1988 Theoretical Computer Science  
HmmkoviZ (1) There are very hard problems (ianguages) that can be solved (recognized) within constant communication complexity.  ...  with small (constant) communication complexity.  ...  Cub65 and Waczulik 143 proved for two specific languages with constant communication complexity that the union of,these languages requires linear communication complexity.  ... 
doi:10.1016/0304-3975(88)90165-x fatcat:iejval5e3bbgzlg7zd2maqltkm

The communication complexity of distributed task allocation

Andrew Drucker, Fabian Kuhn, Rotem Oshman
2012 Proceedings of the 2012 ACM symposium on Principles of distributed computing - PODC '12  
We study the communication complexity and round complexity of the task allocation problem.  ...  n has a randomized communication complexity of Ω(n).  ...  Communication complexity.  ... 
doi:10.1145/2332432.2332443 dblp:conf/podc/DruckerKO12 fatcat:gq7nh4wbr5dcnfl3yplptptvvi

Page 1302 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
[Venkatesh, Srinivasan] (6-TIFR-STC; Mumbai) The communication complexity of pointer chasing.  ...  The upper bound even holds as long as at least k/2+1 rounds of communication are allowed. For k/2 rounds, an upper bound of O(n log'*/?-") n) is shown. 3.  ... 

Brief Announcement: A Note on Hardness of Diameter Approximation

Karl Bringmann, Sebastian Krinninger, Marc Herbstritt
2017 International Symposium on Distributed Computing  
We revisit the hardness of approximating the diameter of a network. In the CONGEST model, Ω(n) rounds are necessary to compute the diameter [Frischknecht et al. SODA'12]. Abboud et al.  ...  Ω(n) rounds.  ...  In our new lower bound, we make the connection to orthogonal vectors explicit: we consider a communication complexity version of orthogonal vectors that we show to be hard unconditionally by a reduction  ... 
doi:10.4230/lipics.disc.2017.44 dblp:conf/wdag/BringmannK17 fatcat:l2hybf7esjf2vokkszpiu5x6r4

Equivalence Classes and Conditional Hardness in Massively Parallel Computations [article]

Danupon Nanongkai, Michele Scquizzato
2020 arXiv   pre-print
These connections concern the class of problems solvable in a sublogarithmic amount of rounds in the MPC model, denoted by MPC(o(log N)), and some standard classes concerning space complexity, namely L  ...  So far, the only way to argue lower bounds for this model is to condition on conjectures about the hardness of some specific problems, such as graph connectivity on promise graphs that are either one cycle  ...  Hard bounds on the point-topoint communication lead to very strong round lower bounds in this model [65, 75, 76] .  ... 
arXiv:2001.02191v1 fatcat:dtcr7kglzfh67kjr2lfhr5v2ty

A hard-to-compress interactive task?

Mark Braverman
2013 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
Whether the information complexity of any interactive problem is close to its communication complexity is an important open problem.  ...  In this note we give an example of a sampling problem whose information and communication complexity we conjecture to be as much as exponentially far apart.  ...  The naïve protocol π 0 for S proceeds in rounds, where in odd rounds Alice samples the next symbol of s, and in even rounds Bob does.  ... 
doi:10.1109/allerton.2013.6736498 dblp:conf/allerton/Braverman13 fatcat:42d743ck4zd4nhpy4kz5a4viqe

The Complexity of Data Aggregation in Directed Networks [chapter]

Fabian Kuhn, Rotem Oshman
2011 Lecture Notes in Computer Science  
, even when the diameter of the network is constant.  ...  Our lower bounds are established by reduction from several well-known problems in communication complexity.  ...  For technical reasons, it seems unlikely that a two-party reduction of the style we used in this paper will yield a stronger lower bound, but perhaps multi-party communication complexity lower bounds could  ... 
doi:10.1007/978-3-642-24100-0_40 fatcat:otsjzwiusbgkrcdnimmoylp4xi

The Communication Complexity of Gap Hamming Distance [article]

Alexander A. Sherstov
2011 Electronic colloquium on computational complexity  
complexity of this problem.  ...  y 2 f0; 1g n are at Hamming distance less than n=2 p n or greater than n=2 C p n: In a recent tour de force, Chakrabarti and Regev (STOC '11) proved the long-conjectured ˝.n/ bound on the randomized communication  ...  ACKNOWLEDGMENTS The author is thankful to Amit Chakrabarti, Dmitry Gavinsky, Oded Regev, Thomas Vidick, Ronald de Wolf, and David Woodruff for their valuable feedback on an earlier version of this manuscript  ... 
dblp:journals/eccc/Sherstov11a fatcat:gwy5dgdov5bado4gyapfbqcrna

Arguments of Proximity [chapter]

Yael Tauman Kalai, Ron D. Rothblum
2015 Lecture Notes in Computer Science  
As our second result, assuming sufficiently hard cryptographic PRGs, we give a lower bound, showing that the parameters obtained both in the IPPs of Rothblum et al., and in our arguments of proximity,  ...  Finally, we observe that any one-round argument of proximity immediately yields a one-round delegation scheme (without proximity) where the verifier runs in linear time.  ...  Note that the communication complexity of (V , P 1 , . . . , P , crs) is equal to the communication complexity of (V, P 1 , . . . , P , crs), denoted by c.  ... 
doi:10.1007/978-3-662-48000-7_21 fatcat:5kuidvuiibcmjlmtv75r6oztsa

Interaction in Quantum Communication

H. Klauck, A. Nayak, A. Ta-Shma, D. Zuckerman
2007 IEEE Transactions on Information Theory  
We show that for any constant k, there is a problem such that its k+1 message classical communication complexity is exponentially smaller than its k message quantum communication complexity.  ...  This, in particular, proves a round hierarchy theorem for quantum communication complexity, and implies, via a simple reduction, an Omega(N^1/k) lower bound for k message quantum protocols for Set Disjointness  ...  ACKNOWLEDGMENT The authors wish to thank Jaikumar Radhakrishnan and Venkatesh Srinivasan for their input on the classical communication complexity of Pointer Jumping and the subproblem , Dorit Aharonov  ... 
doi:10.1109/tit.2007.896888 fatcat:f6imow53b5d4xijfh4hjtckrf4
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