Maximal Intersection Queries in Randomized Graph Models

Hoffmann, Benjamin; Lifshits, Yury; Nowotka, Dirk

doi:10.1007/978-3-540-74510-5_24

Cited by 6 publications

(2 citation statements)

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“…(1) n random points on d-dimensional sphere, (2) n random strings of some fixed length in σ-size alphabet for Hamming/edit distance, (3) random texts generated by Zipf model [39], and (4) preferential attachment graphs with "number of joint friends" similarity.…”

Section: Directions For Further Workmentioning

confidence: 99%

Combinatorial Framework for Similarity Search

Lifshits

2009

2009 Second International Workshop on Similarity Search and Applications

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Abstract-We present an overview of the combinatorial framework for similarity search. An algorithm is combinatorial if only direct comparisons between two pairwise similarity values are allowed. Namely, the input dataset is represented by a comparison oracle that given any three points x, y, z answers whether y or z is closer to x. We assume that the similarity order of the dataset satisfies the four variations of the following disorder inequality: if x is the a'th most similar object to y and y is the b'th most similar object to z, then x is among the D(a + b) most similar objects to z, where D is a relatively small disorder constant. 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, and (2) they work for arbitrarily complicated data representations and similarity functions.Ranwalk, the first known combinatorial solution for nearest neighbors, is randomized, exact, zero-error algorithm with query time that is logarithmic in number of objects. But Ranwalk preprocessing time is quadratic. Later on, another solution, called combinatorial nets, was discovered. It is deterministic and exact algorithm with near-linear time and space complexity of preprocessing, and near-logarithmic time complexity of search. Combinatorial nets also have a number of side applications. For near-duplicate detection they lead to the first known deterministic algorithm that requires just nearlinear time + time proportional to the size of output. 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 number of steps. The later result is the first known work-around for Navarro's impossibility of generalizing Delaunay graphs.

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Section: Directions For Further Workmentioning

confidence: 99%

Combinatorial Framework for Similarity Search

Lifshits

2009

2009 Second International Workshop on Similarity Search and Applications

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“…With respect to the conference version of this paper we generalize the matching level theorem from regular queries to any query taken from the Zipf model [10].…”

Section: Querymentioning

confidence: 99%

Maximal Intersection Queries in Randomized Input Models

Hoffmann

Lifshits

et al. 2008

Theory Comput Syst

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Consider a family of sets and a single set, called the query set. How can one quickly find a member of the family which has a maximal intersection with the query set? Time constraints on the query and on a possible preprocessing of the set family make this problem challenging. Such maximal intersection queries arise in a wide range of applications, including web search, recommendation systems, and distributing on-line advertisements. In general, maximal intersection queries are computationally expensive. We investigate two well-motivated distributions over all families of sets and propose an algorithm for each of them. We show that with very high probability an almost optimal solution is found in time which is logarithmic in the size of the family. Moreover, we point out a threshold phenomenon on the probabilities of intersecting sets in each of our two input models which leads to the efficient algorithms mentioned above.

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Efficient similarity search on multidimensional space of biometric databases

Jayaraman

Gupta

2021

Neurocomputing

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Maximal Intersection Queries in Randomized Graph Models

Cited by 6 publications

References 6 publications

Combinatorial Framework for Similarity Search

Combinatorial Framework for Similarity Search

Maximal Intersection Queries in Randomized Input Models

Efficient similarity search on multidimensional space of biometric databases

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