· 2014
Limits of local algorithms over sparse random graphs
- 109citations
- 2014year
Short summary
Local algorithms, which compute graph properties using only local information, cannot find near-maximum independent sets in sparse random d-regular graphs, refuting a prior conjecture. The best they can achieve is an independent set that is at least 1/2 + 1/(2√2) (approx. 0.853) times the size of the maximum, asymptotically as d approaches infinity.
AI-generated from the title and abstract; the full text is not read.
Key points
- Local algorithms use only local information and randomness to compute global graph features.
- A conjecture implied local algorithms could find near-maximum independent sets in sparse random d-regular graphs.
- This paper shows local algorithms produce independent sets at most 0.853 times the size of the maximum, asymptotically.
- The result holds for sparse random d-regular graphs as d approaches infinity.
AI-generated from the title and abstract; the full text is not read.
Abstract
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the global structure, while also potentially using some randomness. Research over the years has shown that such algorithms can be surprisingly powerful in terms of computing structures like large independent sets in graphs locally. These algorithms have also been implicitly considered in the work on graph limits, where a conjecture due to Hatami, Lovász and Szegedy [17] implied that local algorithms may be able to compute near-maximum independent sets in (sparse) random d-regular graphs. In this paper we refute this conjecture and show that every independent set produced by local algorithms is smaller that the largest one by a multiplicative factor of at least 1/2+1/(2√2) ≈ .853, asymptotically as d → ∞.
The authors' abstract, as published at the source., 2014 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics