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An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance
[article]
2012
arXiv
pre-print
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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
2011
Proceedings of the 43rd annual ACM symposium on Theory of computing - STOC '11
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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
2012
SIAM journal on computing (Print)
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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]
2010
Lecture Notes in Computer Science
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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
2014
International Workshop on Approximation Algorithms for Combinatorial Optimization
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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]
2019
arXiv
pre-print
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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]
2009
arXiv
pre-print
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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]
2017
arXiv
pre-print
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2015 pre-print arXiv:1507.00026v2 fatcat:zyectcvddvhbdkkadugyx32zmeOther Versions
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]
2011
Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms
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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
2013
ACM Transactions on Algorithms
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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
2011
IEEE Transactions on Communications
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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
2010
2010 Data Compression Conference
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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
2019
International Symposium on Computational Geometry
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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]
2015
arXiv
pre-print
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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]
2013
Lecture Notes in Computer Science
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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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