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Disorder inequality

Navin Goyal, Yury Lifshits, Hinrich Schütze
2008 Proceedings of the international conference on Web search and web data mining - WSDM '08  
Combinatorial algorithms for nearest neighbor search have two important advantages: (1) they do not map similarity values to artificial distance values and do not use triangle inequality for the latter  ...  Disorder constant D(S) of a set S is defined to ensure the following inequality: if x is the a'th most similar object to z and y is the b'th most similar object to z, then x is among the D(S) · (a + b)  ...  Also, what is analogue of disorder inequality for bichromatic nearest neighbor search?  ... 
doi:10.1145/1341531.1341538 dblp:conf/wsdm/GoyalLS08 fatcat:bszhij3n6raq5bkgzl4e5sstt4

Combinatorial Framework for Similarity Search

Yury Lifshits
2009 2009 Second International Workshop on Similarity Search and Applications  
For any dataset with small disorder combinatorial nets can be used to construct a visibility graph: the one in which greedy routing deterministically converges to the nearest neighbor of a target in logarithmic  ...  Combinatorial algorithms for nearest neighbor search have two important advantages: (1) they do not map similarity values to artificial distance values and do not use triangle inequality for the latter  ...  ACKNOWLEDGMENT Author thanks Navin Goyal, Hinrich Schútze and Shengyu Zhang for their invaluable help in studies of the combinatorial framework.  ... 
doi:10.1109/sisap.2009.31 dblp:conf/sisap/Lifshits09 fatcat:juawmerbo5dsdlz2b74ucjeg5e

Combinatorial Algorithms for Nearest Neighbors, Near-Duplicates and Small-World Design [chapter]

Yury Lifshits, Shengyu Zhang
2009 Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms  
nearest neighbor of a target in logarithmic number of steps.  ...  For nearest neighbor search we present deterministic and exact algorithm with almost linear time and space complexity of preprocessing, and near-logarithmic time complexity of search.  ...  We put these examples to Appendix A. Nearest Neighbor Search in the Combinatorial Framework Recall that the Nearest Neighbor Search problem is as follows.  ... 
doi:10.1137/1.9781611973068.36 fatcat:ih4qq6udu5g6pp5l4qmgyrahyi

Approximate Nearest Neighbor Search through Comparisons [article]

Dominique Tschopp, Suhas Diggavi
2009 arXiv   pre-print
This paper addresses the problem of finding the nearest neighbor (or one of the R-nearest neighbors) of a query object q in a database of n objects.  ...  In contrast with most existing approaches, we can only access the "hidden" space in which the objects live through a similarity oracle.  ...  The authors of [1] and [2] work with a combinatorial framework for nearest neighbor search, which defines approximates inequalities for ranks analogous to the triangle inequality for distances.  ... 
arXiv:0909.2194v1 fatcat:wjwloke2ezb2rhlhwxfpapdxga

Randomized Algorithms for Comparison-based Search

Dominique Tschopp, Suhas N. Diggavi, Payam Delgosha, Soheil Mohajer
2011 Neural Information Processing Systems  
We show the importance of a characterization: combinatorial disorder D which defines approximate triangle inequalities on ranks.  ...  The main problem we study is how to search the database for the nearest neighbor (NN) of a query, while minimizing the questions.  ...  More precisely, we prove a lower bound on the average search time to retrieve the nearest neighbor of a query point for randomized algorithms in the combinatorial framework. Theorem 1.  ... 
dblp:conf/nips/TschoppDDM11 fatcat:tr7bxjirkzaahdlgmxgsvwrzqu

Fundamentals of the problem

Edgar Chávez, Gonzalo Navarro
2010 SIGSPATIAL Special  
+ , a set of k elements of U nearest to q.  ...  The most basic ones are (a) range query (q, r), for q ∈ X and r ∈ R + , returns {u ∈ U, d(q, u) ≤ r}, the dataset objects at distance within r of q; and (b) k-nearest neighbor query nn(q, k), for k ∈ N  ...  nearest neighbor search.  ... 
doi:10.1145/1862413.1862415 fatcat:m76assblozac7afs64r62avaca

Facebrowsing: Search and navigation through comparisons

Dominique Tschopp, Suhas Diggavi
2010 2010 Information Theory and Applications Workshop (ITA)  
We develop nearest-neighbor search algorithms and analyze its performance for such an oracles.  ...  This paper addresses the problem of finding the nearest neighbor (or one of the R-nearest neighbors) of a query object in a database which is only accessible through a comparison oracle.  ...  ACKNOWLEDGEMENTS We would like to thank Matthias Grossglauser for early discussions on image database navigation that led to the formulation of the facebrowsing application.  ... 
doi:10.1109/ita.2010.5454139 dblp:conf/ita/TschoppD10 fatcat:br4i4tmksncmlfa3ujhugiu5oy

Universal two-time correlations, out-of-time-ordered correlators, and Leggett-Garg inequality violation by edge Majorana fermion qubits

F. J. Gómez-Ruiz, J. J. Mendoza-Arenas, F. J. Rodríguez, C. Tejedor, L. Quiroga
2018 Physical review B  
, which provide direct experimental alternatives to the quantitative analysis of the system regime, either normal or topological.  ...  Finally, we find that violations of Leggett-Garg inequalities can indicate the topological-normal phase transition by looking at different qubits formed by pairing local and non-local edge Majorana fermions  ...  The single site fermion occupation operator is denoted bŷ n j =ĉ † jĉ j , the chemical potential is µ, taken as uniform along the chain, ω is the hopping amplitude between nearest-neighbor sites (we assume  ... 
doi:10.1103/physrevb.97.235134 fatcat:6mbul5uerrcczk2tovdltlsp7i

Weak chaos in the disordered nonlinear Schrödinger chain: Destruction of Anderson localization by Arnold diffusion

D.M. Basko
2011 Annals of Physics  
Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization.  ...  The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators.  ...  Acknowledgements The author is grateful to I. L. Aleiner, B. L. Altshuler, S. Flach, and O. M. Yevtushenko for helpful discussions.  ... 
doi:10.1016/j.aop.2011.02.004 fatcat:647cbxhpmzdjhimetmoyxvgjg4

The Random Link Approximation for the Euclidean Traveling Salesman Problem

N. J. Cerf, J. Boutet de Monvel, O. Bohigas, O. C. Martin, A. G. Percus
1997 Journal de Physique I  
Working with periodic boundary conditions and inspired by a remarkable universality in the kth nearest neighbor distribution, we find for the average optimum tour length = beta_E(d) N^1-1/d [1+O(1/N)]  ...  For d=1,2,3, numerical results show that the random link approximation is a good one, with a discrepancy of less than 2.1 argue that the approximation is exact up to O(1/d^2) and give a conjecture for  ...  In fact, since a tour at best links a city with its two nearest neighbors, this bound can be improved upon by summing, over all i, the mean of i's nearest and next-nearest neighbor distances.  ... 
doi:10.1051/jp1:1997129 fatcat:hupxzeaovzajdeacqsyh4ldvle

Machine learning, phase stability, and disorder with the Automatic Flow Framework for Materials Discovery [article]

Corey Oses
2018 arXiv   pre-print
superconductors to thermoelectrics.  ...  of phase diagrams and properties of disordered materials.  ...  ., the volume as a function of nearest neighbor distance cubed, as shown in Figure 2 .23.  ... 
arXiv:1811.08464v1 fatcat:kaxykm2hgzb5dlbhqonarctbv4

Statistics of energy levels and eigenfunctions in disordered systems

A Mirlin
2000 Physics reports  
Fluctuations of the conductance and of the local intensity of a classical wave radiated by a point-like source in the quasi-1D geometry are also studied within the sigma-model approach.  ...  Calculations are based on the supermatrix sigma-model approach.  ...  Summation in the first term of Eq.(5.7) goes over the pairs ij of nearest neighbors.  ... 
doi:10.1016/s0370-1573(99)00091-5 fatcat:sak3z3hfgjdi3b5uvslgcc6rfu

On nonmetric similarity search problems in complex domains

Tomáš Skopal, Benjamin Bustos
2011 ACM Computing Surveys  
For a long time, the database-oriented applications of similarity search employed the definition of similarity restricted to metric distances.  ...  In fact, retrieval of semantically unstructured data entities requires a form of aggregated qualification that selects entities relevant to a query.  ...  Such a class is searched, to which the query object is "nearest" -there is an assumption the nearest neighbor is located in the "nearest class".  ... 
doi:10.1145/1978802.1978813 fatcat:36ld4nxcm5c6bnu7dtvvhavh4a

The Traveling Salesman and Related Stochastic Problems [article]

A. G. Percus
1998 arXiv   pre-print
Finally, we look at the related geometric issue of nearest neighbor distances, and find some remarkable universalities.  ...  We study the stochastic version of the problem, taking the locations of cities and the distances separating them to be random variables drawn from an ensemble.  ...  Acknowledgments We are grateful to J. Houdayer and E. Bogomolny for sharing with us their numerous and valuable insights on this topic, and to O. Bohigas for having introduced us to the problem.  ... 
arXiv:cond-mat/9803104v1 fatcat:5aplldbcozhczkm6dknxxivu4e

The stochastic traveling salesman problem: Finite size scaling and the cavity prediction [article]

A. G. Percus, O. C. Martin
1998 arXiv   pre-print
Finally, we note a surprising result concerning the distribution of kth-nearest neighbor links in optimal tours, and invite a theoretical understanding of this phenomenon.  ...  We discuss a theoretical approach, the cavity method, that has been proposed for finding the optimal tour length over this random ensemble, given the assumption of replica symmetry.  ...  Acknowledgments Thanks go to J. Houdayer  ... 
arXiv:cond-mat/9802295v2 fatcat:eioy5e6nwza2niazbn7wpe4v5e
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