TY - GEN

T1 - Random k-out subgraph leaves only O(n/k) inter-component edges

AU - Holm, Jacob

AU - King, Valerie

AU - Thorup, Mikkel

AU - Zamir, Or

AU - Zwick, Uri

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - communication complexity

KW - Connected components

KW - Random subgraph

U2 - 10.1109/FOCS.2019.00058

DO - 10.1109/FOCS.2019.00058

M3 - Article in proceedings

AN - SCOPUS:85078476801

BT - Proceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019

PB - IEEE

T2 - 60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019

Y2 - 9 November 2019 through 12 November 2019

ER -