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An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance [article]

Amit Chakrabarti, Oded Regev
2012 arXiv   pre-print
We prove an optimal Ω(n) lower bound on the randomized communication complexity of the much-studied Gap-Hamming-Distance problem.  ...  The Gap-Hamming-Distance problem is a communication problem, wherein Alice and Bob receive n-bit strings x and y, respectively.  ...  Acknowledgments We thank Bo'az Klartag for referring us to [Bar01] , Thomas Vidick for comments on an earlier draft and David Woodruff for encouraging us to include a proof of Theorem 2.7.  ... 
arXiv:1009.3460v3 fatcat:bt4lwqjlabchvfescnhj6tsjti

An optimal lower bound on the communication complexity of gap-hamming-distance

Amit Chakrabarti, Oded Regev
2011 Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11  
We prove an optimal Ω(n) lower bound on the randomized communication complexity of the much-studied GAP-HAMMING-DISTANCE problem.  ...  This was begun in the aforementioned work of Indyk and Woodruff [IW03], who showed a linear lower bound on the communication complexity of a somewhat artificial variant of GHD in the one-way model, i.e  ...  Acknowledgments We thank Bo'az Klartag for referring us to [Bar01] and Thomas Vidick for comments on an earlier draft.  ... 
doi:10.1145/1993636.1993644 dblp:conf/stoc/ChakrabartiR11 fatcat:ygjwlpjklzau5aqsfs7nranxoa

An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance

Amit Chakrabarti, Oded Regev
2012 SIAM journal on computing (Print)  
We prove an optimal Ω(n) lower bound on the randomized communication complexity of the much-studied GAP-HAMMING-DISTANCE problem.  ...  This was begun in the aforementioned work of Indyk and Woodruff [IW03], who showed a linear lower bound on the communication complexity of a somewhat artificial variant of GHD in the one-way model, i.e  ...  Acknowledgments We thank Bo'az Klartag for referring us to [Bar01] and Thomas Vidick for comments on an earlier draft.  ... 
doi:10.1137/120861072 fatcat:vjaavyhvz5b4zhtrcvey7hneqy

Better Gap-Hamming Lower Bounds via Better Round Elimination [chapter]

Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, Ronald de Wolf
2010 Lecture Notes in Computer Science  
Subsequent to this result, the bound has been improved by some of us to the optimal Ω(n), independent of k, by using different techniques. 1 Introduction The communication complexity of the Gap-Hamming  ...  One of the few basic problems whose randomized communication complexity is not yet well-understood, is the Gap Hamming Distance (GHD) problem, defined as follows.  ...  Acknowledgments We thank Ishay Haviv for discussions during the early stages of this work.  ... 
doi:10.1007/978-3-642-15369-3_36 fatcat:4oc3hu274nb4hjdnei77idwoay

The Information Complexity of Hamming Distance

Eric Blais, Joshua Brody, Badih Ghazi, Marc Herbstritt
2014 International Workshop on Approximation Algorithms for Combinatorial Optimization  
In this work, we give new lower bounds on the communication complexity of the Hamming distance function by establishing new bounds on its information complexity.  ...  With a simple padding argument, their result gives a general lower bound of (min{d, n≠d}) bits on the communication complexity of Ham n,d . 1 Recently, there has been much interest in the Gap-Hamming Distance  ...  Acknowledgments The authors would like to thank Madhu Sudan for very helpful discussions. They also wish to thank the anonymous referees for much valuable feedback.  ... 
doi:10.4230/lipics.approx-random.2014.465 dblp:conf/approx/BlaisBG14 fatcat:lysru52kuben7pj6xdneyt2eta

The One-Way Communication Complexity of Dynamic Time Warping Distance [article]

Vladimir Braverman, Moses Charikar, William Kuszmaul, David P. Woodruff, Lin F. Yang
2019 arXiv   pre-print
We resolve the randomized one-way communication complexity of Dynamic Time Warping (DTW) distance.  ...  We show that there is an efficient one-way communication protocol using O(n/α) bits for the problem of computing an α-approximation for DTW between strings x and y of length n, and we prove a lower bound  ...  Lower Bounds In this section, we present lower bounds for the one-way communication complexity of α-DTW.  ... 
arXiv:1903.03520v1 fatcat:waggmcrupjeavli26pzahulcnq

Better Gap-Hamming Lower Bounds via Better Round Elimination [article]

Joshua Brody, Amit Chakrabarti, Oded Regev, Thomas Vidick, Ronald de Wolf
2009 arXiv   pre-print
Gap Hamming Distance is a well-studied problem in communication complexity, in which Alice and Bob have to decide whether the Hamming distance between their respective n-bit inputs is less than n/2-sqrt  ...  This lower bound has an exponentially better dependence on the number of rounds than the previous best bound, due to Brody and Chakrabarti.  ...  Acknowledgments We thank Ishay Haviv for discussions during the early stages of this work.  ... 
arXiv:0912.5276v1 fatcat:grtayendy5doxfbjgbczyp4syi

On the Communication Complexity of Distributed Clustering [article]

Qin Zhang
2017 arXiv   pre-print
When the input is distributed across a large number of machines and the number of clusters k is small, our lower bounds match the current best upper bounds up to a logarithmic factor.  ...  In this paper we give a first set of communication lower bounds for distributed clustering problems, in particular, for k-center, k-median and k-means.  ...  We include the details of the simulation for completeness. Protocol Π ′ for 2n-TWO-BIT on input Y ∼ ϕ using protocol Π for 2n-GAP-XOR  ... 
arXiv:1507.00026v3 fatcat:7yslnnm62vexvk7hz42y4rctmy

Optimal Bounds for Johnson-Lindenstrauss Transforms and Streaming Problems with Sub-Constant Error [chapter]

T.S. Jayram, David Woodruff
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
Our techniques are based on lower bounding the information cost of a novel one-way communication game and yield the first space lower bounds in a data stream model that depend on the error probability  ...  Finally, we give an application to one-way communication complexity under product distributions, showing that unlike in the case of constant δ, the VC-dimension does not characterize the complexity when  ...  Our results come from lower-bounding the information cost of a novel one-way communication complexity problem.  ... 
doi:10.1137/1.9781611973082.1 dblp:conf/soda/JayramW11 fatcat:orw6y2xxvvdwlmqo5xx3oc4sm4

Optimal Bounds for Johnson-Lindenstrauss Transforms and Streaming Problems with Subconstant Error

T. S. Jayram, David P. Woodruff
2013 ACM Transactions on Algorithms  
Our techniques are based on lower bounding the information cost of a novel one-way communication game and yield the first space lower bounds in a data stream model that depend on the error probability  ...  Finally, we give an application to one-way communication complexity under product distributions, showing that unlike in the case of constant δ, the VC-dimension does not characterize the complexity when  ...  Our results come from lower-bounding the information cost of a novel one-way communication complexity problem.  ... 
doi:10.1145/2483699.2483706 fatcat:k5af42dlwbbyfl4bafy7zkjime

On Computation of Performance Bounds of Optimal Index Assignment

Xiaolin Wu, Hans D. Mittelmann, Xiaohan Wang, Jia Wang
2011 IEEE Transactions on Communications  
But optimal design of index assignment is an instance of quadratic assignment problem (QAP), one of the hardest optimization problems in the NP-complete class.  ...  The strength of the resulting lower bounds is validated by comparing them against the upper bounds produced by heuristic index assignment algorithms.  ...  The main idea is to decompose the distance matrix of codewords or the Hamming adjacency matrix into two positive semidefinite matrices, and then obtain the lower bound on the performance of optimal index  ... 
doi:10.1109/tcomm.2011.081111.100300 fatcat:pr2gqrfmyrdfvlmg6d7bdnx764

On Computation of Performance Bounds of Optimal Index Assignment

Xiaolin Wu, Hans D. Mittelmann, Xiaohan Wang, Jia Wang
2010 2010 Data Compression Conference  
But optimal design of index assignment is an instance of quadratic assignment problem (QAP), one of the hardest optimization problems in the NP-complete class.  ...  The strength of the resulting lower bounds is validated by comparing them against the upper bounds produced by heuristic index assignment algorithms.  ...  The main idea is to decompose the distance matrix of codewords or the Hamming adjacency matrix into two positive semidefinite matrices, and then obtain the lower bound on the performance of optimal index  ... 
doi:10.1109/dcc.2010.24 dblp:conf/dcc/WuMWW10 fatcat:pbfimymycje5hm3d7njj7ma2pm

The One-Way Communication Complexity of Dynamic Time Warping Distance

Vladimir Braverman, Moses Charikar, William Kuszmaul, David P. Woodruff, Lin F. Yang, Michael Wagner
2019 International Symposium on Computational Geometry  
We resolve the randomized one-way communication complexity of Dynamic Time Warping (DTW) distance.  ...  We show that there is an efficient one-way communication protocol using O(n/α) bits for the problem of computing an α-approximation for DTW between strings x and y of length n, and we prove a lower bound  ...  Woodruff would like to thank the Simons Institute for the Theory of Computing where part of this work was done.  ... 
doi:10.4230/lipics.socg.2019.16 dblp:conf/compgeom/BravermanCKWY19 fatcat:far4oxhsynggvdcjkymfmuzu6i

Some Bounds on Communication Complexity of Gap Hamming Distance [article]

Alexander Kozachinskiy
2015 arXiv   pre-print
In this paper we obtain some bounds on communication complexity of Gap Hamming Distance problem (GHD^n_L, U): Alice and Bob are given binary string of length n and they are guaranteed that Hamming distance  ...  As an application of this result for every c < 2 we prove a Ω(n(2 - c)^2/p) lower bound on the space complexity of any c-approximate deterministic p-pass streaming algorithm for computing the number of  ...  As an application of this result for every c < 2 we prove a Ω n(2−c) 2 p lower bound on the space complexity of any c-approximate deterministic p-pass streaming algorithm for computing the number of distinct  ... 
arXiv:1511.08854v2 fatcat:nnpztpyxprhujpastnmlxn2zse

Arthur-Merlin Streaming Complexity [chapter]

Tom Gur, Ran Raz
2013 Lecture Notes in Computer Science  
As a part of the proof of the lower bound for the Distinct Elements problem, we show a new lower bound of Ω ( √ n) on the MA communication complexity of the Gap Hamming Distance problem, and prove its  ...  We also prove a lower bound, showing that every MA streaming algorithm for the Distinct Elements problem that uses s bits of space and a proof of size w, satisfies s · w = Ω(n).  ...  Lower bound In order to prove our lower bound on the MA communication complexity of Gap Hamming Distance, we first show a lower bound on the MA communication complexity of Gap Orthogonality, a problem  ... 
doi:10.1007/978-3-642-39206-1_45 fatcat:snse57ose5glhefiz2zxrv6uuu
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