Random k-out subgraph leaves only O(n/k) inter-component edges
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Each vertex of an arbitrary simple graph on n vertices chooses k random incident edges. What is the expected number of edges in the original graph that connect different connected components of the sampled subgraph? We prove that the answer is O(n/k), when k ≥ c log n, for some large enough c. We conjecture that the same holds for smaller values of k, possibly for any k ≥ 2. Such a result is best possible for any k ≥ 2. As an application, we use this sampling result to obtain a one-way communication protocol with private randomness for finding a spanning forest of a graph in which each vertex sends only O (√n log n) bits to a referee.
Original language | English |
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Title of host publication | Proceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019 |
Number of pages | 14 |
Publisher | IEEE |
Publication date | 2019 |
Article number | 8948658 |
ISBN (Electronic) | 9781728149523 |
DOIs | |
Publication status | Published - 2019 |
Event | 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019 - Baltimore, United States Duration: 9 Nov 2019 → 12 Nov 2019 |
Conference
Conference | 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019 |
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Land | United States |
By | Baltimore |
Periode | 09/11/2019 → 12/11/2019 |
Sponsor | IEEE Computer Society Technical Committee on Mathematical Foundations of Computing |
- communication complexity, Connected components, Random subgraph
Research areas
Links
- https://arxiv.org/pdf/1909.11147.pdf
Submitted manuscript
ID: 237757204