A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Very simple methods for all pairs network flow analysis
SIAM Journal on Computing
A Fast Algorithm for Optimally Increasing the Edge Connectivity
SIAM Journal on Computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Global min-cuts in RNC, and other ramifications of a simple min-out algorithm
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Some optimal inapproximability results
Journal of the ACM (JACM)
Testing the diameter of graphs
Random Structures & Algorithms
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Tight Bounds for Testing Bipartiteness in General Graphs
SIAM Journal on Computing
Approximating the Minimum Spanning Tree Weight in Sublinear Time
SIAM Journal on Computing
Additive Approximation for Edge-Deletion Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Tolerant property testing and distance approximation
Journal of Computer and System Sciences
Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
Estimating the distance to a monotone function
Random Structures & Algorithms
Testing versus Estimation of Graph Properties
SIAM Journal on Computing
Approximating average parameters of graphs
Random Structures & Algorithms
Testing Triangle-Freeness in General Graphs
SIAM Journal on Discrete Mathematics
Tolerant locally testable codes
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
The program of the mini-workshop
Property testing
Introduction to testing graph properties
Property testing
Sublinear graph approximation algorithms
Property testing
The program of the mini-workshop
Property testing
Introduction to testing graph properties
Property testing
Sublinear graph approximation algorithms
Property testing
Towards privacy for social networks: a zero-knowledge based definition of privacy
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Introduction to testing graph properties
Studies in complexity and cryptography
An efficient partitioning oracle for bounded-treewidth graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Discrete Mathematics
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We address the problem of approximating the distance of bounded-degree and general sparse graphs from having some predetermined graph property P. That is, we are interested in sublinear algorithms for estimating the fraction of edge modifications (additions or deletions) that must be performed on a graph so that it obtains P. This fraction is taken with respect to a given upper bound m on the number of edges. In particular, for graphs with degree bound d over n vertices, m = dn. To perform such an approximation the algorithm may ask for the degree of any vertex of its choice, and may ask for the neighbors of any vertex. The problem of estimating the distance to having a property was first explicitly addressed by Parnas et al. [2006]. In the context of graphs this problem was studied by Fischer and Newman [2007] in the dense graphs model. In this model the fraction of edge modifications is taken with respect to n2, and the algorithm may ask for the existence of an edge between any pair of vertices of its choice. Fischer and Newman showed that every graph property that has a testing algorithm in this model, with query complexity independent of the size of the graph, also has a distance approximation algorithm with query complexity that is independent of the size of graph. In this work we focus on bounded-degree and general sparse graphs, and give algorithms for all properties shown to have efficient testing algorithms by Goldreich and Ron [2002]. Specifically, these properties are k-edge connectivity, subgraph freeness (for constant-size subgraphs), being an Eulerian graph, and cycle freeness. A variant of our subgraph-freeness algorithm approximates the size of a minimum vertex cover of a graph in sublinear time. This approximation improves on a recent result of Parnas and Ron [2007].