Improved Constant-Time Approximation Algorithms for Maximum Matchings and Other Optimization Problems

Yoshida, Yuichi; Yamamoto, Masaki; Ito, Hiro

doi:10.1137/110828691

Cited by 35 publications

(67 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Onak et al [ORRR12] gave a (2, εn)-approximation for the size of minimum vertex cover with running timeÕ(d · poly(1/ε)), which improves upon previous results by Parnas and Ron [PR07], Marko and Ron [MR09], Nguyen and Onak [NO08] and Yoshida, Yamamoto and Ito [YYI12].…”

Section: Other Related Worksupporting

confidence: 76%

“…(Most of such results are stated in terms of bounded maximum degree d, while they can generalized to graphs with bounded average degreed by ignoring all vertices with degree greater thand/ε.) Examples include (1, εn)approximation for maximal/maximum matching [NO08,YYI12], (O(logd/ε), εn)-approximation for maximum dominating set [PR07, NO08].…”

Section: Other Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Estimating Graph Parameters from Random Order Streams

Pan¹,

Sohler²

2018

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

View full text Add to dashboard Cite

show abstract

Section: Other Related Worksupporting

confidence: 76%

Section: Other Related Workmentioning

confidence: 99%

Estimating Graph Parameters from Random Order Streams

Pan¹,

Sohler²

2018

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

View full text Add to dashboard Cite

show abstract

“…Set Cover can also be considered as a generalization of the Vertex Cover problem. The estimation variant of Vertex Cover under the adjacency-list oracle model has been studied in [30,23,29,33]. Set Cover has been also studied in the sub-linear space context, most notably for the streaming model of computation [32,12,7,3,2,5,18,10,17].…”

Section: Related Workmentioning

confidence: 99%

“…Data access model. As in the prior work [28,33] on Set Cover, our algorithms and lower bounds assume that the input can be accessed via the adjacency-list oracle. 3 More precisely, the algorithm has access to the following two oracles:…”

Section: Introductionmentioning

confidence: 99%

Set Cover in Sub-linear Time

Indyk¹,

Mahabadi²,

Rubinfeld³

et al. 2018

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

View full text Add to dashboard Cite

We study the classic set cover problem from the perspective of sub-linear algorithms. Given access to a collection of m sets over n elements in the query model, we show that sub-linear algorithms derived from existing techniques have almost tight query complexities.On one hand, first we show an adaptation of the streaming algorithm presented in [17] to the sub-linear query model, that returns an α-approximate cover using O(m(n/k) 1/(α−1) + nk) queries to the input, where k denotes the value of a minimum set cover. We then complement this upper bound by proving that for lower values of k, the required number of queries is Ω(m(n/k) 1/(2α) ), even for estimating the optimal cover size. Moreover, we prove that even checking whether a given collection of sets covers all the elements would require Ω(nk) queries. These two lower bounds provide strong evidence that the upper bound is almost tight for certain values of the parameter k.On the other hand, we show that this bound is not optimal for larger values of the parameter k, as there exists a (1 + ε)-approximation algorithm with O(mn/kε 2 ) queries. We show that this bound is essentially tight for sufficiently small constant ε, by establishing a lower bound of Ω(mn/k) query complexity.Our lower-bound results follow by carefully designing two distributions of instances that are hard to distinguish. In particular, our first lower bound involves a probabilistic construction of a certain set system with a minimum set cover of size αk, with the key property that a small number of "almost uniformly distributed" modifications can reduce the minimum set cover size down to k. Thus, these modifications are not detectable unless a large number of queries are asked. We believe that our probabilistic construction technique might find applications to lower bounds for other combinatorial optimization problems.

show abstract

“…Namely an algorithm A is said to be an (α, β)-approximation algorithm for a graph parameter x * if A outputs a value x with αx * − β ≤ x ≤ x * . A sequence of works [19,21,22,27] obtained constant-query (2, n)-approximation algorithms for the minimum size of a vertex cover for any > 0. There is no direct relation to our result since, even if the correct value is constant, these algorithms may answer with a value of n. Namely, such approximation algorithms are particularly useful when the target value is relatively large.…”

Section: Related Workmentioning

confidence: 99%

Parameterized testability

Iwama

Yoshida

2014

Proceedings of the 5th Conference on Innovations in Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

This paper studies property testing for NP optimization problems with parameter k under the general graph model with an augmentation of random edge sampling capability. It is shown that a variety of such problems, including k-Vertex Cover, k-Feedback Vertex Set, k-Multicut, k-PathFree and k-Dominating Set, are constant-time testable if k is constant. It should be noted that the first four problems are fixed parameter tractable (FPT) and it turns out that algorithmic techniques for their FPT algorithms (branchand-bound search, color coding, etc.) are also useful for our testers. k-Dominating Set is W [2]-hard, but we can still test the property in constant time since the definition of -farness makes the problem trivial for non-sparse graphs that are the source of hardness for the original optimization problem. We also consider k-Odd Cycle Transversal, which is another well-known FPT problem, but we only give a sublinear-time tester when k is a constant.

show abstract

Improved Constant-Time Approximation Algorithms for Maximum Matchings and Other Optimization Problems

Cited by 35 publications

References 11 publications

Estimating Graph Parameters from Random Order Streams

Estimating Graph Parameters from Random Order Streams

Set Cover in Sub-linear Time

Parameterized testability

Contact Info

Product

Resources

About