Approximating the Minimum Spanning Tree Weight in Sublinear Time
SIAM Journal on Computing
Approximating the Weight of the Euclidean Minimum Spanning Tree in Sublinear Time
SIAM Journal on Computing
Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
Every minor-closed property of sparse graphs is testable
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximating average parameters of graphs
Random Structures & Algorithms
Constant-Time Approximation Algorithms via Local Improvements
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Approximating the distance to properties in bounded-degree and general sparse graphs
ACM Transactions on Algorithms (TALG)
An improved constant-time approximation algorithm for maximum~matchings
Proceedings of the forty-first annual ACM symposium on Theory of computing
Testing Hereditary Properties of Nonexpanding Bounded-Degree Graphs
SIAM Journal on Computing
Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time
SIAM Journal on Computing
Local Graph Partitions for Approximation and Testing
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Parameter testing in bounded degree graphs of subexponential growth
Random Structures & Algorithms
Counting stars and other small subgraphs in sublinear time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the forty-third annual ACM symposium on Theory of computing
Every property of hyperfinite graphs is testable
Proceedings of the forty-third annual ACM symposium on Theory of computing
Proceedings of the 5th conference on Innovations in theoretical computer science
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We give a nearly optimal sublinear-time algorithm for approximating the size of a minimum vertex cover in a graph G. The algorithm may query the degree deg(v) of any vertex v of its choice, and for each 1 ≤ i ≤ deg(v), it may ask for the ith neighbor of v. Letting VCopt(G) denote the minimum size of vertex cover in G, the algorithm outputs, with high constant success probability, an estimate [EQUATION] such that [EQUATION], where ε is a given additive approximation parameter. We refer to such an estimate as a (2, ε)-estimate. The query complexity and running time of the algorithm are Õ([EQUATION] · poly(1/ε)), where d denotes the average vertex degree in the graph. The best previously known sublinear algorithm, of Yoshida et al. (STOC 2009), has query complexity and running time O(d4/ε2), where d is the maximum degree in the graph. Given the lower bound of Ω(d) (for constant ε) for obtaining such an estimate (with any constant multiplicative factor) due to Parnas and Ron (TCS 2007), our result is nearly optimal. In the case that the graph is dense, that is, the number of edges is Θ(n2), we consider another model, in which the algorithm may ask, for any pair of vertices u and v, whether there is an edge between u and v. We show how to adapt the algorithm that uses neighbor queries to this model and obtain an algorithm that outputs a (2, ε)-estimate of the size of a minimum vertex cover whose query complexity and running time are Õ(n) · poly(1/ε).