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

2012
*
arXiv
*
pre-print

We prove

arXiv:1009.3460v3
fatcat:bt4lwqjlabchvfescnhj6tsjti
*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. ...##
###
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
*

We prove

doi:10.1145/1993636.1993644
dblp:conf/stoc/ChakrabartiR11
fatcat:ygjwlpjklzau5aqsfs7nranxoa
*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. ...##
###
An Optimal Lower Bound on the Communication Complexity of Gap-Hamming-Distance

2012
*
SIAM journal on computing (Print)
*

We prove

doi:10.1137/120861072
fatcat:vjaavyhvz5b4zhtrcvey7hneqy
*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. ...##
###
Better Gap-Hamming Lower Bounds via Better Round Elimination
[chapter]

2010
*
Lecture Notes in Computer Science
*

Subsequent to this result,

doi:10.1007/978-3-642-15369-3_36
fatcat:4oc3hu274nb4hjdnei77idwoay
*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. ...##
###
The Information Complexity of Hamming Distance

2014
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

In this work, we give new

doi:10.4230/lipics.approx-random.2014.465
dblp:conf/approx/BlaisBG14
fatcat:lysru52kuben7pj6xdneyt2eta
*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. ...##
###
The One-Way Communication Complexity of Dynamic Time Warping Distance
[article]

2019
*
arXiv
*
pre-print

We resolve

arXiv:1903.03520v1
fatcat:waggmcrupjeavli26pzahulcnq
*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. ...##
###
Better Gap-Hamming Lower Bounds via Better Round Elimination
[article]

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. ...

##
###
On the Communication Complexity of Distributed Clustering
[article]

2017
*
arXiv
*
pre-print

When

arXiv:1507.00026v3
fatcat:7yslnnm62vexvk7hz42y4rctmy
*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 ...##
###
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
*

Our techniques are based

doi:10.1137/1.9781611973082.1
dblp:conf/soda/JayramW11
fatcat:orw6y2xxvvdwlmqo5xx3oc4sm4
*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. ...##
###
Optimal Bounds for Johnson-Lindenstrauss Transforms and Streaming Problems with Subconstant Error

2013
*
ACM Transactions on Algorithms
*

Our techniques are based

doi:10.1145/2483699.2483706
fatcat:k5af42dlwbbyfl4bafy7zkjime
*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. ...##
###
On Computation of Performance Bounds of Optimal Index Assignment

2011
*
IEEE Transactions on Communications
*

But

doi:10.1109/tcomm.2011.081111.100300
fatcat:pr2gqrfmyrdfvlmg6d7bdnx764
*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 ...##
###
On Computation of Performance Bounds of Optimal Index Assignment

2010
*
2010 Data Compression Conference
*

But

doi:10.1109/dcc.2010.24
dblp:conf/dcc/WuMWW10
fatcat:pbfimymycje5hm3d7njj7ma2pm
*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 ...##
###
The One-Way Communication Complexity of Dynamic Time Warping Distance

2019
*
International Symposium on Computational Geometry
*

We resolve

doi:10.4230/lipics.socg.2019.16
dblp:conf/compgeom/BravermanCKWY19
fatcat:far4oxhsynggvdcjkymfmuzu6i
*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. ...##
###
Some Bounds on Communication Complexity of Gap Hamming Distance
[article]

2015
*
arXiv
*
pre-print

In this paper we obtain some

arXiv:1511.08854v2
fatcat:nnpztpyxprhujpastnmlxn2zse
*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 ...##
###
Arthur-Merlin Streaming Complexity
[chapter]

2013
*
Lecture Notes in Computer Science
*

As a part

doi:10.1007/978-3-642-39206-1_45
fatcat:snse57ose5glhefiz2zxrv6uuu
*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 ...
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