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Shortest Paths and Distances with Differential Privacy
[article]
2016
arXiv
pre-print
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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]
2010
Lecture Notes in Computer Science
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• 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
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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
2003
Computational geometry
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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]
2021
arXiv
pre-print
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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]
2012
Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms
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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]
2018
arXiv
pre-print
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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
2009
IEEE Transactions on Pattern Analysis and Machine Intelligence
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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
2012
Journal of Computational Neuroscience
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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]
2017
arXiv
pre-print
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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
2000
Physical Review D, Particles and fields
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2000 accepted arXiv:gr-qc/0008059v2 fatcat:oqlbnpxip5gg3kd3456fsqbtuaOther Versions
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
2003
Bioinformatics
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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
2015
Pattern Recognition
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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
2020
Scandinavian Workshop on Algorithm Theory
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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
2019
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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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 δ ≡ δ 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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