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Tight Cell-Probe Bounds for Online Hamming Distance Computation [article]

Raphael Clifford, Markus Jalsenius, Benjamin Sach
2012 arXiv   pre-print
We show tight bounds for online Hamming distance computation in the cell-probe model with word size w.  ...  The task is to output the Hamming distance between a fixed string of length n and the last n symbols of a stream.  ...  We thank Kasper Green Larssen in particular for pointing out that the cell-probe lower bounds we give are in fact tight.  ... 
arXiv:1207.1885v3 fatcat:ybari7qv7zcznc7yvsywz2cs24

Tight Cell-Probe Bounds for Online Hamming Distance Computation [chapter]

Raphaël Clifford, Markus Jalsenius, Benjamin Sach
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
We show tight bounds for online Hamming distance computation in the cell-probe model with word size w.  ...  The task is to output the Hamming distance between a fixed string of length n and the last n symbols of a stream.  ...  We thank Kasper Green Larsen in particular for pointing out that the cell-probe lower bounds we give are in fact tight. We also thank the anonymous reviewers for their helpful comments.  ... 
doi:10.1137/1.9781611973105.48 dblp:conf/soda/CliffordJS13 fatcat:bk7iqzfwlzhp5i5sny37q24sg4

Time Bounds for Streaming Problems

Raphaël Clifford, Markus Jalsenius, Benjamin Sach
2019 Theory of Computing  
We give tight cell-probe bounds for the time to compute convolution, multiplication and Hamming distance in a stream.  ...  We argue that these bounds are in fact tight within the cell probe model.  ...  As we discussed above, our lower bounds for all three problems are also tight within the cell-probe model for the online problems.  ... 
doi:10.4086/toc.2019.v015a002 dblp:journals/toc/CliffordJS19 fatcat:fnvfj6gqfzazlgw6uecuhsqeda

Time Bounds for Streaming Problems [article]

Raphael Clifford, Markus Jalsenius, Benjamin Sach
2014 arXiv   pre-print
We give tight cell-probe bounds for the time to compute convolution, multiplication and Hamming distance in a stream.  ...  We argue that these bound are in fact tight within the cell probe model.  ...  We thank Kasper Green Larsen in particular for pointing out that the cell-probe lower bounds we give are in fact tight.  ... 
arXiv:1412.6935v1 fatcat:yxxsxlx6bfe3tmtv22lxzb5eja

Cell-Probe Lower Bounds for Bit Stream Computation

Raphaël Clifford, Markus Jalsenius, Benjamin Sach, Marc Herbstritt
2016 European Symposium on Algorithms  
We revisit the complexity of online computation in the cell probe model.  ...  Cell probe bounds of Ω(δ lg n/w) have previously been shown for both convolution and Hamming distance in this setting, where δ is the size of a symbol in bits and w ∈ Ω(lg n) is the cell size in bits.  ...  Online pattern matching is particularly suited to study in this setting and cell probe lower bounds have previously been shown for different measures of distance including Hamming distance, inner product  ... 
doi:10.4230/lipics.esa.2016.31 dblp:conf/esa/CliffordJS16 fatcat:v2hohoxbljfyli3ddnrto4mlte

The complexity of computation in bit streams [article]

Raphael Clifford, Markus Jalsenius, Benjamin Sach
2015 arXiv   pre-print
We revisit the complexity of online computation in the cell probe model.  ...  Cell probe bounds of Ω(δn/w) have previously been shown for both convolution and Hamming distance in this setting, where δ is the size of a symbol in bits and w∈Ω(n) is the cell size in bits.  ...  Online pattern matching is particularly suited to study in this setting and cell probe lower bounds have previously been shown for different measures of distance including Hamming distance, inner product  ... 
arXiv:1504.00834v1 fatcat:hdw2okkdjremflekbl6b4uanhi

Lower Bounds for Oblivious Near-Neighbor Search [article]

Kasper Green Larsen and Tal Malkin and Omri Weinstein and Kevin Yeo
2019 arXiv   pre-print
For the natural setting of d = Θ( n), our result implies an Ω̃(^2 n) lower bound, which is a quadratic improvement over the highest (non-oblivious) cell-probe lower bound for ANN.  ...  We prove an Ω(d n/ ( n)^2) lower bound on the dynamic cell-probe complexity of statistically oblivious approximate-near-neighbor search (ANN) over the d-dimensional Hamming cube.  ...  The seminal work of Larsen and Nielsen [LN18] presented the first cell-probe lower bound for oblivious data structures, in which they proved a (tight) Ω(lg n) lower bound for ORAMs. Jacob et al.  ... 
arXiv:1904.04828v1 fatcat:r3hafauyw5cuhfdvsejv3narsm

Generalizing the Pigeonhole Principle for Similarity Query Processing in Hamming Space

Jianbin Qin, Chuan Xiao, Yaoshu Wang, Wei Wang, Xuemin Lin, Yoshiharu Ishikawa, Guoren Wang
2019 IEEE Transactions on Knowledge and Data Engineering  
A distance search in Hamming space finds binary vectors whose Hamming distances are no more than a threshold from a query vector.  ...  Based on the new principle, we develop a tight constraint of candidates and devise cost-aware methods for partitioning and threshold allocation to optimize query processing.  ...  We choose the sub-partitioning method to compute the candidate number for Hamming distance join, because the machine learning method requires an offline training and does not work for an index built online  ... 
doi:10.1109/tkde.2019.2899597 fatcat:lmwphgcixfhchbluk3sklcdel4

GPH: Similarity Search in Hamming Space

Jianbin Qin, Yaoshu Wang, Chuan Xiao, Wei Wang, Xuemin Lin, Yoshiharu Ishikawa
2018 2018 IEEE 34th International Conference on Data Engineering (ICDE)  
A similarity search in Hamming space finds binary vectors whose Hamming distances are no more than a threshold from a query vector.  ...  Based on the new principle, we first develop a tight constraint of candidates, and then devise cost-aware methods for dimension partitioning and threshold allocation to optimize query processing.  ...  We thank the authors of [11] for kindly providing their source codes.  ... 
doi:10.1109/icde.2018.00013 dblp:conf/icde/QinWXWLI18 fatcat:culbmr66hjfdfa7rgnbloynfxu

Equivalence of Systematic Linear Data Structures and Matrix Rigidity [article]

Sivaramakrishnan Natarajan Ramamoorthy, Cyrus Rashtchian
2019 arXiv   pre-print
Finally, we prove a cell probe lower bound for the vector-matrix-vector problem in the high error regime, improving a result of Chattopadhyay, Koucký, Loff, and Mukhopadhyay.  ...  Recently, Dvir, Golovnev, and Weinstein have shown that sufficiently strong lower bounds for linear data structures would imply new bounds for rigid matrices.  ...  Special thanks to Paul, Anup, Makrand and Amir for the encouragement to write up these results.  ... 
arXiv:1910.11921v1 fatcat:wxgwve7l35f5fgvrk4gxnddy2m

Equivalence of Systematic Linear Data Structures and Matrix Rigidity

Sivaramakrishnan Natarajan Ramamoorthy, Cyrus Rashtchian, Michael Wagner
2020 Innovations in Theoretical Computer Science  
ACM Subject Classification Theory of computationCell probe models and lower bounds; Theory of computation → Circuit complexity  ...  Finally, we prove a cell probe lower bound for the vector-matrix-vector problem in the high error regime, improving a result of Chattopadhyay, Koucký, Loff, and Mukhopadhyay.  ...  Special thanks to Paul, Anup, Makrand and Amir for the encouragement to write up these results.  ... 
doi:10.4230/lipics.itcs.2020.35 dblp:conf/innovations/RamamoorthyR20 fatcat:wfes7y25c5acdmvjcske5vnaoy

Practical linear-space Approximate Near Neighbors in high dimension [article]

Georgia Avarikioti, Ioannis Z. Emiris, Ioannis Psarros, Georgios Samaras
2016 arXiv   pre-print
In a recently accepted paper, optimal bounds have been achieved for any c>1 ALRW17.  ...  Given an LSH family of functions for some metric space, we randomly project points to the Hamming cube of dimension n, where n is the number of input points.  ...  value for the Hamming distance is ρ = 1/c ± o(1).  ... 
arXiv:1612.07405v1 fatcat:qwc4rcdhcjaxxbtuqljmpep77y

Hobbes: optimized gram-based methods for efficient read alignment

Athena Ahmadi, Alexander Behm, Nagesh Honnalli, Chen Li, Lingjie Weng, Xiaohui Xie
2011 Nucleic Acids Research  
We introduce Hobbes, a new gram-based program for aligning short reads, supporting Hamming and edit distance.  ...  or edit distance, respectively.  ...  ACKNOWLEDGEMENTS We thank Jacob Biesinger and Daniel Newkirk for testing Hobbes and providing valuable feedback. We also thank Knut Reinert and the rest of the SeqAn team for helpful discussions.  ... 
doi:10.1093/nar/gkr1246 pmid:22199254 pmcid:PMC3315303 fatcat:l33rgyjf75cmtmqbyptggh5dpi

Hashing for Similarity Search: A Survey [article]

Jingdong Wang, Heng Tao Shen, Jingkuan Song, Jianqiu Ji
2014 arXiv   pre-print
Similarity search (nearest neighbor search) is a problem of pursuing the data items whose distances to a query item are the smallest from a large database.  ...  functions without exploring the data distribution and learning to hash, which learns hash functions according the data distribution, and review them from various aspects, including hash function design and distance  ...  Recent study in [105] provides more lower bound analysis for Hamming distance, Euclidean distance, and Jaccard distance.  ... 
arXiv:1408.2927v1 fatcat:reknwesjnbafvcbouyudrzp4rq

Distributed PCP Theorems for Hardness of Approximation in P [article]

Amir Abboud, Aviad Rubinstein, Ryan Williams
2017 arXiv   pre-print
All our inapproximability factors are nearly-tight.  ...  In particular, for the first two problems we obtain nearly-polynomial factors of 2^( n)^1-o(1); only (1+o(1))-factor lower bounds (under SETH) were known before.  ...  This work was done in part at the Simons Institute for the Theory of Computing. We are also grateful to the organizers of Dagstuhl Seminar 16451 for a special collaboration opportunity.  ... 
arXiv:1706.06407v2 fatcat:xzapmrglobah5bgxdw7igrpvz4
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