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Shortest Paths and Distances with Differential Privacy [article]

Adam Sealfon
2016 arXiv   pre-print
In our model, two weight functions w,w' are considered to be neighboring if they have ℓ_1 distance at most one.  ...  We are concerned with the approximation error, the difference between the length of the released path or released distance and the length of the shortest path or actual distance.  ...  Acknowledgments I am grateful to Salil Vadhan and Shafi Goldwasser for their guidance and encouragement throughout this project.  ... 
arXiv:1511.04631v2 fatcat:g6boiv7rgzcehp4k37i4nzx3iy

Algorithms for Forest Pattern Matching [chapter]

Kaizhong Zhang, Yunkun Zhu
2010 Lecture Notes in Computer Science  
• Edit Operations • General change l 1 l 2 delete l 1 l 1 l 2 insert l 1 l 1 l 2 distance function γ: (1) γ(a, b) ≥ 0; (2) γ(a, b) = γ(b, a); (3) γ(a, c) ≤ γ(a, b) + γ(b, c); (4) γ(a, b) = 0 if δ(F 1  ...  Sequence Approximate Pattern Matching (SAPM) Introduction Forest Edit Distance Finding A Most Similar Closed Subforest • Problem Statement • Sequence Approximate Pattern Matching • Finding  ... 
doi:10.1007/978-3-642-13509-5_1 fatcat:zxeagrov6jcm7l3bqd6yi4bieq

Subject Index

2005 Journal of Discrete Algorithms  
problem, 448 Annuli Optimizing a constrained convex polygonal annu- lus, 1 Approximate string matching Indexing text with approximate q-grams, 157; Bit- parallel (δ, γ )-matching and suffix automata  ...  hop count on ATM tree networks, 101 Bioinformatics Distributed suffix trees, 176 Bit-parallelism Bit-parallel (δ, γ )-matching and suffix automata, 198; Bit-parallel approximate string matching  ... 
doi:10.1016/s1570-8667(05)00042-0 fatcat:phytlwupp5hmtddg3ffue5546u

Approximate congruence in nearly linear time

Piotr Indyk, Suresh Venkatasubramanian
2003 Computational geometry  
Using a novel application of Hall's Theorem to reduce the geometric matching problem to a combinatorial matching problem, we present near-linear time approximation schemes for minimising this distance  ...  This result yields improved algorithms for approximate congruence, and may be of independent interest.  ...  All our results are for computing the approximate generalized bottleneck distance under translations.  ... 
doi:10.1016/s0925-7721(02)00095-0 fatcat:pirpfzdebvcwxbhlcbbknxrepy

Approximate Nearest Neighbors in the Space of Persistence Diagrams [article]

Brittany Terese Fasy, Xiaozhou He, Zhihui Liu, Samuel Micka, David L. Millman, Binhai Zhu
2021 arXiv   pre-print
Furthermore, as the lattice parameter decreases, searching our data structure yields a six-approximation of the nearest diagram in Γ in O((mlogn+m^2)logτ) time and a constant factor approximation of the  ...  Given a set Γ of n (M,m)-bounded persistence diagrams, each with at most m points, we snap-round the points of each diagram to points on a cubical lattice and produce a key for each possible snap-rounding  ...  Sheehy for directing us to additional searching approaches and feedback on early drafts, and Brendan Mumey for the discussions related to this research and pointing out the paper by Heffernan and Schirra  ... 
arXiv:1812.11257v2 fatcat:2glpbegjwjdihk2terugdwldhi

Algorithms for the Transportation Problem in Geometric Settings [chapter]

R. Sharathkumar, Pankaj K. Agarwal
2012 Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms  
Suppose we run the primal-dual algorithm on A and B, under a distance function d(·, ·).  ...  a∈A da = b∈B s b = U and let d(·, ·) be a distance function. Suppose the diameter of A ∪ B is ∆ under d(·, ·), and ε > 0 is a parameter.  ... 
doi:10.1137/1.9781611973099.29 dblp:conf/soda/SharathkumarA12 fatcat:ltatcgniv5fxfiwik2o5w6cnu4

Approximating (k,ℓ)-center clustering for curves [article]

Kevin Buchin, Anne Driemel, Joachim Gudmundsson, Michael Horton, Irina Kostitsyna, Maarten Löffler, Martijn Struijs
2018 arXiv   pre-print
This result also holds when k=1, and the NP-hardness extends to the case that ℓ=∞, i.e., for the problem of computing the minimum-enclosing ball under the Fréchet distance.  ...  Our constructions yield different bounds for one and two-dimensional curves and the discrete and continuous Fréchet distance.  ...  As d DF (γ(s), c * ) ≤ 1, there exists a matching between γ(s) and c * such that all matched pairs have distance at most 1.  ... 
arXiv:1805.01547v2 fatcat:j2t2v3ywwbfpdpejzy4tytho6y

Time Warp Edit Distance with Stiffness Adjustment for Time Series Matching

P.-F. Marteau
2009 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Compared to Edit Distance, Dynamic Time Warping, Longest Common Subsequnce and Edit Distance with Real Penalty, TWED has proven to be quite effective on the considered experimental task.  ...  To define the "edit operations" we use the paradigm of a graphical editing process and end up with a dynamic programming algorithm that we call Time Warp Edit Distance (TWED).  ...  Proposition 3: γ λ δ , is an increasing function of γ λ and : ) , ( ) , ( , ' ' 0 , 0 ' , ' , 2 Y X Y X U Y X γ λ γ λ δ δ γ γ λ λ γ λ ≤ ∈ ∀ ≥ ∀ ≥ ∀ > ≥ ∀ The proof is given in [25] . D.  ... 
doi:10.1109/tpami.2008.76 pmid:19110495 fatcat:mdalo7eyefc33nn7dwhztc4soa

Estimating summary statistics in the spike-train space

Wei Wu, Anuj Srivastava
2012 Journal of Computational Neuroscience  
To directly capture and analyze the average and variability in the observation space of the spike trains, we focus on a data-driven approach where statistics are defined and computed in a function space  ...  Based on the definition of a "Euclidean" metric, a recent paper introduced the notion of the mean of a set of spike trains and developed an efficient algorithm to compute it under some restrictive conditions  ...  Acknowledgements This research is supported in part by the grants NSF IIS-0916154 to WW and NSF DMS-0915003, ONR N00014-09-1-0664, and AFOSR FA9550-06-1-0324 to AS. We thank Prof.  ... 
doi:10.1007/s10827-012-0427-3 pmid:23053864 fatcat:4cnbs45jf5dadcouf3qqdw2ysi

Approximation of LRU Caches Miss Rate: Application to Power-law Popularities [article]

Christian Berthet
2017 arXiv   pre-print
Fagin, we give a closed-form expression for the approximated Miss Rate (MR) of LRU Caches assuming a power-law popularity.  ...  In addition, we bring a new analysis of the conditions (cache relative size, popularity parameter) under which the ratio of LRU MR to Static MR is worst-case.  ...  In Section 3 we introduce Fagin approximation for LRU Miss Rate under IRM and see how it has been recently rediscovered under the "Che's approximation" label.  ... 
arXiv:1705.10738v1 fatcat:utprdvnqhfcbzavearlzqqjzqm

Gravitational wave chirp search: Economization of post-Newtonian matched filter bank via cardinal interpolation

R. P. Croce, Th. Demma, V. Pierro, I. M. Pinto, D. Churches, B. S. Sathyaprakash
2000 Physical Review D, Particles and fields  
match) is 0.97.  ...  Gravitational radiation emitted during this phase will have to be dug out of noise by matched-filtering (correlating) the detector output with a bank of several 10^5 templates, making the computational  ...  Pinto wishes to thank the TAMA staff at NAO and in particular prof. Fujimoto Masa-Katsu and prof. Kawamura Seiji for gracious hospitality and stimulating discussions. D. Churches and B.S.  ... 
doi:10.1103/physrevd.62.121101 fatcat:zyeufns5inhwnpyszjefvfm45y

Detecting protein sequence conservation via metric embeddings

E. Halperin, J. Buhler, R. Karp, R. Krauthgamer, B. Westover
2003 Bioinformatics  
We first propose a new distance function on peptides derived from a given score matrix.  ...  Given two databases, one must find all pairs of proteins that align with high score under a biologically meaningful substitution score matrix, such as a BLOSUM matrix (Henikoff and Henikoff, 1992) .  ...  ACKNOWLEDGEMENTS The first, third and fourth authors were supported in part by NSF grants CCR-9820951 and CCR-0121555 and DARPA cooperative agreement F30602-00-2-0601.  ... 
doi:10.1093/bioinformatics/btg1016 pmid:12855448 fatcat:alv3vpswnzbopiwwjxmd2nvtbe

Integral invariants for space motion trajectory matching and recognition

Zhanpeng Shao, Youfu Li
2015 Pattern Recognition  
Then a non-linear distance of the integral invariants is defined to measure the similarity for trajectory matching and recognition.  ...  Experimental results on trajectory matching and sign recognition show the effectiveness and robustness of the proposed integral invariants in motion trajectory matching and recognition.  ...  A distance function between their integral invariants is defined to measure the similarity between them to match, cluster, and classify motion trajectories.  ... 
doi:10.1016/j.patcog.2015.02.029 fatcat:ru2rhjzxzzh3hiusm4n3a6ycmy

On the Hardness of Computing an Average Curve

Kevin Buchin, Anne Driemel, Martijn Struijs, Susanne Albers
2020 Scandinavian Workshop on Algorithm Theory  
We show this under the discrete and continuous Fréchet and Dynamic Time Warping (DTW) distance.  ...  We study the complexity of clustering curves under k-median and k-center objectives in the metric space of the Fréchet distance and related distance measures.  ...  Our approximation algorithms rely on the fact that good approximations have small distance to some optimal solution and that we can search a bounded space (the set of balls surrounding the vertices) for  ... 
doi:10.4230/lipics.swat.2020.19 dblp:conf/swat/BuchinDS20 fatcat:v2vpa6a4yzb35embffcm52i2ia

Beam emittance preservation using Gaussian density ramps in a beam-driven plasma wakefield accelerator

M. D. Litos, R. Ariniello, C. E. Doss, K. Hunt-Stone, J. R. Cary
2019 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
Small longitudinal variations of the plasma density n p and/or the beam Lorentz factor γ b lead to the approximation k β k β,0 (1 − δ/2), where δδ n − δ γ − (3/4)δ 2 n + (9/4)δ 2 γ − (1/2)δ n δ γ to  ...  second order in δ n and δ γ .  ... 
doi:10.1098/rsta.2018.0181 fatcat:rxe7yxjxkjg6nonizru6ttw2km
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