# Distributed Large Independent Sets in One Round on Bounded-Independence Graphs

@inproceedings{Halldrsson2015DistributedLI, title={Distributed Large Independent Sets in One Round on Bounded-Independence Graphs}, author={Magn{\'u}s M. Halld{\'o}rsson and Christian Konrad}, booktitle={DISC}, year={2015} }

We present a randomized one-round, single-bit messages, distributed algorithm for the maximum independent set problem in polynomially bounded-independence graphs with poly-logarithmic approximation factor. Bounded-independence graphs capture various models of wireless networks such as the unit disc graphs model and the quasi unit disc graphs model. For instance, on unit disc graphs, our achieved approximation ratio is $$\mathrm {O} \frac{\log n}{\log \log n}^2$$.
A starting point of our work…

## 9 Citations

Approximating the Caro-Wei Bound for Independent Sets in Graph Streams

- Computer Science, MathematicsISCO
- 2018

Streaming algorithms and a lower bound for approximating the Caro-Wei bound itself are given.

Independent Set Size Approximation in Graph Streams

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The results show that $\beta(G)$ can be approximated accurately, based on a provided lower bound on $\beta$, and an $\Omega(n/\beta)$ lower bound is shown on any algorithm that approximates $\beta$ up to a constant factor.

A Unified Sparsification Approach for Matching Problems in Graphs of Bounded Neighborhood Independence

- Computer ScienceSPAA
- 2020

A unified and surprisingly simple approach for producing (1+ε)-approximate matchings, for arbitrarily small ε >0, and shows that, with high probability, GΔ is a (1-ε)-matching sparsifier for G, i.e., the maximum matching size of GΓ is within a factor of 1+ε from that of G.

Optimal deterministic distributed algorithms for maximal independent set in geometric graphs

- Computer Science, MathematicsJ. Parallel Distributed Comput.
- 2019

When Algorithms for Maximal Independent Set and Maximal Matching Run in Sublinear Time

- Mathematics, Computer ScienceICALP
- 2019

The results suggest that even though MIS and MM do not admit sublinear-time algorithms in general graphs, one can still solve both problems in sublinear time for a wide range of beta(G) << n.

Brief Announcement: Local Independent Set Approximation

- MathematicsPODC
- 2016

We show that the first phase of the Linial-Saks network decomposition algorithm gives a randomized distributed O(nε)-approximation algorithm for the maximum independent set problem that operates in…

On the Microscopic View of Time and Messages

- Computer Science
- 2017

The basics of computing at the microscopic level are discussed, describing simple but powerful computational tools, and analyzing their use.

## References

SHOWING 1-10 OF 23 REFERENCES

An optimal maximal independent set algorithm for bounded-independence graphs

- Computer ScienceDistributed Computing
- 2010

A novel distributed algorithm for the maximal independent set problem that solves the connected dominating set problem for unit disk graphs in O(log* n) time, exponentially faster than the state-of-the-art algorithm.

Nearly optimal bounds for distributed wireless scheduling in the SINR model

- Computer ScienceDistributed Computing
- 2014

A randomized distributed scheduling algorithm proposed by Kesselheim and Vöcking achieves O(logn)-approximation, an improvement of a logarithmic factor, which matches the best ratio known for centralized algorithms and holds in arbitrary metric space and for every length-monotone and sublinear power assignment.

Locality in Distributed Graph Algorithms

- Mathematics, Computer ScienceSIAM J. Comput.
- 1992

This model focuses on the issue of locality in distributed processing, namely, to what extent a global solution to a computational problem can be obtained from locally available data.

On the Locality of Some NP-Complete Problems

- Computer Science, MathematicsICALP
- 2012

The first local algorithm for an NP-complete problem is devised, with high probability, an O(n1/2+e ·χ)-coloring within O(1) rounds, where e>0 is an arbitrarily small constant, and χ is the chromatic number of the input graph.

Linear degree extractors and the inapproximability of max clique and chromatic number

- Computer Science, MathematicsSTOC '06
- 2006

New extractors which require only log n + O(1) additional random bits for sources with constant entropy rate are constructed, and dispersers, which are similar to one-sided extractors, are built, which use an arbitrarily small constant times log n additional Randomness Extractor to within n1-ε are NP-hard.

Ad-hoc networks beyond unit disk graphs

- Computer ScienceDIALM-POMC '03
- 2003

It is proved that in Quasi Unit Disk Graphs flooding is an asymptotically message-optimal routing technique, and the geometric routing algorithm being more efficient above all in dense networks, and classic geometric routing is possible with the same performance guarantees as for Unit Diskgraphs if d = 1/v2.

Fast Distributed Approximations in Planar Graphs

- Mathematics, Computer ScienceDISC
- 2008

We give deterministic distributed algorithms that given i¾?> 0 find in a planar graph G, (1±i¾?)-approximations of a maximum independent set, a maximum matching, and a minimum dominating set. The…

What cannot be computed locally!

- Computer SciencePODC '04
- 2004

Time lower bounds are given for the distributed approximation of minimum vertex cover (MVC) and related problems such as minimum dominating set (MDS) and the construction of maximal matchings and maximal independent sets.

Streaming Algorithms for Independent Sets

- Computer ScienceICALP
- 2010

These results form the first treatment of the classic IS problem in the streaming setting, and a new output-efficient streaming model is proposed, that is more restrictive than semi-streaming but more flexible than classic streaming.

Wireless scheduling with power control

- Computer ScienceTALG
- 2012

Improved approximation is obtained for a bidirectional variant of the scheduling problem, partial answers are given to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2-dimensional Euclidean plane to doubling metrics.