A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
Elements of information theory
Elements of information theory
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Sublinear time approximate clustering
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A Sublinear Time Approximation Scheme for Clustering in Metric Spaces
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Estimating the weight of metric minimum spanning trees in sublinear-time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
The price of being near-sighted
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
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
Distributed discovery of large near-cliques
Proceedings of the 28th ACM symposium on Principles of distributed computing
Minimum Entropy Combinatorial Optimization Problems
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Maintaining a large matching and a small vertex cover
Proceedings of the forty-second ACM symposium on Theory of computing
Distributed discovery of large near-cliques
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Counting stars and other small subgraphs in sublinear time
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The program of the mini-workshop
Property testing
Sublinear graph approximation algorithms
Property testing
Dynamic approximate vertex cover and maximum matching
Property testing
The program of the mini-workshop
Property testing
Sublinear graph approximation algorithms
Property testing
Dynamic approximate vertex cover and maximum matching
Property testing
Proceedings of the forty-third annual ACM symposium on Theory of computing
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
Space-efficient local computation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Discrete Mathematics
Converting online algorithms to local computation algorithms
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
No sublogarithmic-time approximation scheme for bipartite vertex cover
DISC'12 Proceedings of the 26th international conference on Distributed Computing
ACM Computing Surveys (CSUR)
Comparable dependencies over heterogeneous data
The VLDB Journal — The International Journal on Very Large Data Bases
Limits of local algorithms over sparse random graphs
Proceedings of the 5th conference on Innovations in theoretical computer science
Proceedings of the 5th conference on Innovations in theoretical computer science
| Hi-index | 5.23 |
For a given graph G over n vertices, let OPT"G denote the size of an optimal solution in G of a particular minimization problem (e.g., the size of a minimum vertex cover). A randomized algorithm will be called an @a-approximation algorithm with an additive error for this minimization problem if for any given additive error parameter @e0 it computes a value OPT@? such that, with probability at least 2/3, it holds that OPT"G@?OPT@?@?@a@?OPT"G+@en. Assume that the maximum degree or average degree of G is bounded. In this case, we show a reduction from local distributed approximation algorithms for the vertex cover problem to sublinear approximation algorithms for this problem. This reduction can be modified easily and applied to other optimization problems that have local distributed approximation algorithms, such as the dominating set problem. We also show that for the minimum vertex cover problem, the query complexity of such approximation algorithms must grow at least linearly with the average degree d@? of the graph. This lower bound holds for every multiplicative factor @a and small constant @e as long as d@?=O(n/@a). In particular this means that for dense graphs it is not possible to design an algorithm whose complexity is o(n).