Sublinear time approximation of the cost of a metric <i>k</i>-nearest neighbor graph

Czumaj, Artur; Sohler, Christian

doi:10.1137/1.9781611975994.180

Cited by 4 publications

(3 citation statements)

References 28 publications

(43 reference statements)

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“…Noting from Algorithm 5 that f • n = Xn/k, inequality (12) implies that with probability 1 − 2/n 4 , To achieve the high probability bound on the time-complexity, as in the proofs of Theorems 1.2 and 1.3, we run Θ(log n) instances of Algorithm 5 in parallel and return the output of the instance that terminates first. By Markov's inequality, each instance terminates in time O(n/ε 3 ) with a constant probability.…”

Section: The Final Algorithm For the Adjacency Matrix Query Modelmentioning

confidence: 99%

“…Although at the first glance it may seem impossible to do much without reading the whole input, numerous sublinear-time algorithms have been designed over the years for various optimization problems. In addition to matching and vertex cover, which have been studied extensively in the area [25,23,26,24,19,9], the list includes estimating the weight/size of minimum spanning tree (MST) [8,10], traveling salesman problem (TSP) [9], k-nearest neighbor graph [12], graph's average degree [15,18], as well as problems such as vertex coloring [2], metric linear sampling [13], and many others. (This is by no means a comprehensive list of all the prior works.)…”

Section: Introductionmentioning

confidence: 99%

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Time-Optimal Sublinear Algorithms for Matching and Vertex Cover

Behnezhad¹

2021

Preprint

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We present a near-tight analysis of the average "query complexity"-à la Nguyen and Onak [FOCS'08]-of the randomized greedy maximal matching algorithm, improving over the bound of Yoshida, Yamamoto and Ito [STOC'09]. For any n-vertex graph of average degree d, this leads to the following sublinear-time algorithms for estimating the size of maximum matching and minimum vertex cover, all of which are provably time-optimal up to logarithmic factors:This (nearly) matches an Ω(n) time lower bound for any multiplicative approximation and is, notably, the first (2 + ε)-approximation that runs in o(n 2 ) time for all graphs.• A (2, εn)-approximation in O(( d + 1)/ε 2 ) time using adjacency list queries. This (nearly) matches an Ω( d+1) lower bound of Parnas and Ron [TCS'07] which holds for any (O(1), εn)-approximation, and improves over the bounds of Yoshida et al. [STOC'09], Onak, Ron, Rosen, and Rubinfeld [SODA'12], and Kapralov, Mitrovic, Norouzi-Fard, and Tardos [SODA'20]: The former two take at least quadratic time in the degree and so can take Ω(n 2 ) time, and the latter obtains a much larger approximation.• A (2, εn)-approximation in O(n/ε 3 ) time using adjacency matrix queries. This (nearly) matches an Ω(n) time lower bound in this model and improves over the O(n √ n)-time (2, εn)-approximate algorithm of Chen, Kannan, and Khanna [ICALP'20]. It also turns out that any non-trivial multiplicative approximation in the adjacency matrix model requires Ω(n 2 ) time, so the additive εn error is necessary too.As immediate corollaries, one can obtain improved sublinear time estimators for the size of (variants of) TSP by plugging the third result into the framework of Chen et al. [ICALP'20]. Additionally, our improved analysis of randomized greedy maximal matching gives an improved maximal matching algorithm in the Adaptive Massively Parallel Computation (AMPC) model.

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Section: The Final Algorithm For the Adjacency Matrix Query Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Time-Optimal Sublinear Algorithms for Matching and Vertex Cover

Behnezhad¹

2021

Preprint

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“…The K-Nearest Neighbor method uses data classification techniques that are divided into clusters (Agrawal, 2019). Prediction results can be calculated based on the distance closest to the sample data (Gou et al, 2019) (Czumaj & Sohler, 2020). This research will predict the graduation time of the students with the K-Nearest Neighbor algorithm.…”

Section: Introductionmentioning

confidence: 99%

Analysis K-Nearest Neighbor Algorithm for Improving Prediction Student Graduation Time

Muliono

Lubis

Khairina

2020

SinkrOn

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Higher education plays a major role in improving the quality of education in Indonesia. The BAN-PT institution established by the government has a standard of higher education accreditation and study program accreditation. With the 4.0-based accreditation instrument, it encourages university leaders to improve the quality and quality of their education. One indicator that determines the accreditation of study programs is the timely graduation of students. This study uses the K-Nearest Neighbor algorithm to predict student graduation times. Students' GPA at the time of the seventh semester will be used as training data, and data of students who graduate are used as sample data. K-Nearest Neighbor works in accordance with the given sample data. The results of prediction testing on 60 data for students of 2015-2016, obtained the highest level of accuracy of 98.5% can be achieved when k = 3. Prediction results depend on the pattern of data entered, the more samples and training data used, the calculation of the K-Nearest Neighbor algorithm is also more accurate.

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Time-Optimal Sublinear Algorithms for Matching and Vertex Cover

Behnezhad

2022

2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)

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Sublinear time approximation of the cost of a metric k-nearest neighbor graph

Abstract: How to cite:Please refer to published version for the most recent bibliographic citation information. If a published version is known of, the repository item page linked to above, will contain details on accessing it.

Cited by 4 publications

References 28 publications

Time-Optimal Sublinear Algorithms for Matching and Vertex Cover

Time-Optimal Sublinear Algorithms for Matching and Vertex Cover

Analysis K-Nearest Neighbor Algorithm for Improving Prediction Student Graduation Time

Time-Optimal Sublinear Algorithms for Matching and Vertex Cover

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