Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
Testing Euclidean minimum spanning trees in the plane
ACM Transactions on Algorithms (TALG)
Separating Sublinear Time Computations by Approximate Diameter
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Approximating the distance to properties in bounded-degree and general sparse graphs
ACM Transactions on Algorithms (TALG)
Counting stars and other small subgraphs in sublinear time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Local graph exploration and fast property testing
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Property testing
Sublinear graph approximation algorithms
Property testing
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
Analyzing graph structure via linear measurements
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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
Approximating average parameters of graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Distance approximation in bounded-degree and general sparse graphs
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Research paper: The saga of minimum spanning trees
Computer Science Review
SIAM Journal on Discrete Mathematics
A dense hierarchy of sublinear time approximation schemes for bin packing
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
Constant-Time approximation algorithms for the knapsack problem
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Constant-time algorithms for sparsity matroids
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Property testing in sparse directed graphs: strong connectivity and subgraph-freeness
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Proceedings of the 5th conference on Innovations in theoretical computer science
| Hi-index | 0.00 |
We present a probabilistic algorithm that, given a connected graph G (represented by adjacency lists) of average degree d, with edge weights in the set{1,...,w}, and given a parameter $0G with a relative error of at most $\eps$. Note that the running time does not depend on the number of vertices in G. We also prove a nearly matching lower bound of $\Omega( dw \varepsilon^{-2} )$ on the probe and time complexity of any approximation algorithm for MST weight.The essential component of our algorithm is a procedure for estimating in time $O(d\eps^{-2}\log \frac{d}\varepsilon)$ the number of connected components of an unweighted graph to within an additive error of $\varepsilon n$. (This becomes $O(\eps^{-2}\log \frac{1}\varepsilon)$ for $d=O(1)$.) The time bound is shown to be tight up to within the $\log \frac{d}\varepsilon$ factor. Our connected-components algorithm picks $O(1/\varepsilon^2)$ vertices in the graph and then grows "local spanning trees" whose sizes are specified by a stochastic process. From the local information collected in this way, the algorithm is able to infer, with high confidence, an estimate of the number of connected components. We then show how estimates on the number of components in various subgraphs of G can be used to estimate the weight of its MST.