Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams

Chitnis, Rajesh; Cormode, Graham; Esfandiari, Hossein; Hajiaghayi, MohammadTaghi; McGregor, Andrew; Monemizadeh, Morteza; Vorotnikova, Sofya

doi:10.1137/1.9781611974331.ch92

Cited by 69 publications

(147 citation statements)

References 35 publications

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“…Although G has a perfect matching, the subgraph between the first n/2 vertices of A and the last n/2 vertices of B has Ω(n 2 ) edges, and the algorithm is very likely to pick these edges in the matching. A result by Chitnis et al [3] shows that the maximum matching can be found in the streaming model with a memory of sizeÕ(k 2 ) where k is the cardinality of the maximum matching. Therefore, if µ(G) ≤ √ n, using their algorithm we can find the exact solution using a memory of sizeÕ(n).…”

Section: Preliminariesmentioning

confidence: 99%

Approximate Maximum Matching in Random Streams

Farhadi¹,

Hajiaghayi²,

Mai³

et al. 2020

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

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In this paper, we study the problem of finding a maximum matching in the semi-streaming model when edges arrive in a random order. In the semi-streaming model, an algorithm receives a stream of edges and it is allowed to have a memory ofÕ(n) 1 where n is the number of vertices in the graph. A recent inspiring work by Assadi et al. [1] shows that there exists a streaming algorithm with the approximation ratio of 2 3 that usesÕ(n 1.5 ) memory. However, the memory of their algorithm is much larger than the memory constraint of the semi-streaming algorithms. In this work, we further investigate this problem in the semi-streaming model, and we present simple algorithms for approximating maximum matching in the semi-streaming model. Our main results are as follows.• We show that there exists a single-pass deterministic semi-streaming algorithm that finds a 3 5 (= 0.6) approximation of the maximum matching in bipartite graphs usingÕ(n) memory. This result significantly outperforms the state-of-the-art result of Konrad [15] that finds a 0.539 approximation of the maximum matching usingÕ(n) memory.• By giving a black-box reduction from finding a matching in general graphs to finding a matching in bipartite graphs, we show there exists a single-pass deterministic semistreaming algorithm that finds a 6 11 (≈ 0.545) approximation of the maximum matching in general graphs, improving upon the state-of-art result 0.506 approximation by Gamlath et al. [9]. notion to hide logarithmic factors.2 With high probability

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Section: Preliminariesmentioning

confidence: 99%

Approximate Maximum Matching in Random Streams

Farhadi¹,

Hajiaghayi²,

Mai³

et al. 2020

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

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“…In particular, our and Assadi et al [3]'s procedures are similar to the one in [11], which is aimed to for reducing space complexity of packing problems in streaming setting, but these conduct different analysis and provide different guarantees.…”

Section: Vertex Sparsification Lemmamentioning

confidence: 99%

Stochastic Packing Integer Programs with Few Queries

Maehara¹,

Yamaguchi²

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the task is to find a good solution by conducting a small number of queries. We propose a general framework of adaptive and non-adaptive algorithms for this problem, and provide a unified methodology for analyzing the performance of those algorithms. We also demonstrate our framework by applying it to a variety of stochastic combinatorial optimization problems such as matching, matroid, and stable set problems.

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“…The problem of MWM was also considered in other streaming models, such as the MapReduce model [8,15], the sliding-window model [8,9] and the turnstile stream model (allowing deletions as well as insertions) [1,5,7,14]. More general submodular-function matching problems in the semi-streaming model have been considered by Varadaraja and by Chakrabarti and Kale [6,18].…”

Section: Introductionmentioning

confidence: 99%

A (2 + ∊)-Approximation for Maximum Weight Matching in the Semi-Streaming Model

Paz¹,

Schwartzman²

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We present a simple deterministic single-pass (2 + )-approximation algorithm for the maximum weight matching problem in the semi-streaming model. This improves upon the currently best known approximation ratio of (3.5 + ).Our algorithm uses O(n log 2 n) space for constant values of . It relies on a variation of the local-ratio theorem, which may be of independent interest in the semi-streaming model.

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Kernelization via Sampling with Applications to Finding Matchings and Related Problems in Dynamic Graph Streams

Cited by 69 publications

References 35 publications

Approximate Maximum Matching in Random Streams

Approximate Maximum Matching in Random Streams

Stochastic Packing Integer Programs with Few Queries

A (2 + ∊)-Approximation for Maximum Weight Matching in the Semi-Streaming Model

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