Fast distributed approximation algorithms for vertex cover and set cover in anonymous networks

Authors:
Matti Åstrand;Jukka Suomela
Affiliations:
Helsinki Institute for Information Technology HIIT, University of Helsinki, Helsinki, Finland;Helsinki Institute for Information Technology HIIT, University of Helsinki, Helsinki, Finland
Venue:
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Year:
2010

Citing 25
Cited 8

Deterministic coin tossing with applications to optimal parallel list ranking

Information and Control
Computing on an anonymous ring

Journal of the ACM (JACM)
Parallel symmetry-breaking in sparse graphs

SIAM Journal on Discrete Mathematics
Distributed program checking: a paradigm for building self-stabilizing distributed protocols (extended abstract)

SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Locality in distributed graph algorithms

SIAM Journal on Computing
Linear programming without the matrix

STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
A primal-dual parallel approximation technique applied to weighted set and vertex covers

Journal of Algorithms
What Can Be Computed Locally?

SIAM Journal on Computing
Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases

IEEE Transactions on Parallel and Distributed Systems
Self-stabilization

Self-stabilization
On the Distributed Complexity of Computing Maximal Matchings

SIAM Journal on Discrete Mathematics
An Effective Characterization of Computability in Anonymous Networks

DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Local and global properties in networks of processors (Extended Abstract)

STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Local computations on static and dynamic graphs

ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
What cannot be computed locally!

Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Some simple distributed algorithms for sparse networks

Distributed Computing
The price of being near-sighted

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Constant-time distributed dominating set approximation

Distributed Computing
Fault-Tolerant Clustering in Ad Hoc and Sensor Networks

ICDCS '06 Proceedings of the 26th IEEE International Conference on Distributed Computing Systems
Vertex cover might be hard to approximate to within 2-ε

Journal of Computer and System Sciences
Dynamic networks are as fast as static networks

SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Distributed weighted vertex cover via maximal matchings

ACM Transactions on Algorithms (TALG)
A simple local 3-approximation algorithm for vertex cover

Information Processing Letters
Distributed and parallel algorithms for weighted vertex cover and other covering problems

Proceedings of the 28th ACM symposium on Principles of distributed computing
A local 2-approximation algorithm for the vertex cover problem

DISC'09 Proceedings of the 23rd international conference on Distributed computing

Distributed algorithms for edge dominating sets

Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Deterministic dominating set construction in networks with bounded degree

ICDCN'11 Proceedings of the 12th international conference on Distributed computing and networking
Analysing local algorithms in location-aware quasi-unit-disk graphs

Discrete Applied Mathematics
Distributed maximal matching: greedy is optimal

PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Lower bounds for local approximation

PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Weak models of distributed computing, with connections to modal logic

PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Survey of local algorithms

ACM Computing Surveys (CSUR)
Lower bounds for local approximation

Journal of the ACM (JACM)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a distributed algorithm that finds a maximal edge packing in O(Δ + log* W) synchronous communication rounds in a weighted graph, independent of the number of nodes in the network; here Δ is the maximum degree of the graph and W is the maximum weight. As a direct application, we have a distributed 2-approximation algorithm for minimum-weight vertex cover, with the same running time. We also show how to find an $f$-approximation of minimum-weight set cover in O(f2k2 + fk log* W) rounds; here k is the maximum size of a subset in the set cover instance, f is the maximum frequency of an element, and W is the maximum weight of a subset. The algorithms are deterministic, and they can be applied in anonymous networks.