Metric Sublinear Algorithms via Linear Sampling

Esfandiari, Hossein; Mitzenmacher, Michael

doi:10.1109/focs.2018.00011

Cited by 7 publications

(7 citation statements)

References 56 publications

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“…For the k-center and k-median problem there are approximation algorithms with a running time of O(nk) [20] as well as bi-criteria approximation algorithms [17]. The metric maximum cut problem can also be solved in sublinear time [10,17]. A recent result on linear sampling from metric spaces can be used to improve a number of previous results [10] like, for example, reduce the query complexity of maxcut.…”

Section: Lower Boundsmentioning

confidence: 99%

“…The metric maximum cut problem can also be solved in sublinear time [10,17]. A recent result on linear sampling from metric spaces can be used to improve a number of previous results [10] like, for example, reduce the query complexity of maxcut. The size of a maximum matching [23,31] and the vertex cover size [23,24] can also be approximated using sublinear time approximation algorithms.…”

Section: Lower Boundsmentioning

confidence: 99%

“…We condition on the event that all calls to algorithm EstimateVertexDegree provide the correct answer; by Lemma 5.4, this happens with probability at least 1 − 1/n 10 .…”

Section: Consistencymentioning

confidence: 99%

See 2 more Smart Citations

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

Czumaj¹,

Sohler²

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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Section: Lower Boundsmentioning

confidence: 99%

Section: Lower Boundsmentioning

confidence: 99%

See 1 more Smart Citation

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

Czumaj¹,

Sohler²

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Each node reveals its incident edges with probability p, which is the same as the independent cascade probability along each edge. Accessing the graph information by performing edge queries is a common technique in sublinear time algorithms that provide an output after inspecting a small portion of their input [2,3,15,23,30]. In the second model (Section 4), each query consists of a spread whereby a signal node is seeded and the identities of the resultant adopters is observed.…”

Section: Introductionmentioning

confidence: 99%

Seeding with Costly Network Information

Eckles

Esfandiari

Mossel

et al. 2022

Operations Research

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In the presence of contagion, decision makers strategize about where in a network to intervene (e.g., seeding a new product). A large literature has developed methods for approximately optimizing the choice of k seeds to cause the largest cascade of, for example, product adoption. However, it is often impractical to measure an entire social network. In “Seeding with Costly Network Information,” Eckles, Esfandiari, Mossel, and Rahimian develop and analyze algorithms for making a bounded number of queries of a social network and then selecting k seeds. They prove hardness results for this problem and provide almost tight approximation guarantees for their proposed algorithms under widely used models of contagion. One proposed algorithm is practical for both querying online social networks and structuring in-person surveys. This framework further allows reasoning about tradeoffs between spending budget on collecting more network data versus increasing the number of seeds.

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“…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%

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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Metric Sublinear Algorithms via Linear Sampling

Cited by 7 publications

References 56 publications

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

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

Seeding with Costly Network Information

Time-Optimal Sublinear Algorithms for Matching and Vertex Cover

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