TY - GEN

T1 - Approximating the Arboricity in Sublinear Time

AU - Eden, Talya

AU - Mossel, Saleet

AU - Ron, Dana

N1 - Publisher Copyright:
Copyright © 2022 by SIAM.

PY - 2022

Y1 - 2022

N2 - We consider the problem of approximating the arboricity of a graph G = (V, E), which we denote by arb(G), in sublinear time, where the arboricity of a graph is the minimal number of forests required to cover its edge set. An algorithm for this problem may perform degree and neighbor queries, and is allowed a small error probability. We design an algorithm that outputs an estimate , such that with probability 1-1/poly(n), arb(G) ≤ ≤ clog2 n-arb(G), where n = |V| and c is a constant. The expected query complexity and running time of the algorithm are O(n/arb(G)) · poly(log n), and this upper bound also holds with high probability. This bound is optimal for such an approximation up to a poly (log n) factor. For the closely related problem of finding the densest subgraph, Bhattacharya et al. (STOC, 2015) showed that there exists a factor-2 approximation algorithm that runs in time O(n) · poly (log n). In a follow up work, McGregor et al. (MFCS, 2015) improved the approximation factor to (1 + ?) with the same complexity.

AB - We consider the problem of approximating the arboricity of a graph G = (V, E), which we denote by arb(G), in sublinear time, where the arboricity of a graph is the minimal number of forests required to cover its edge set. An algorithm for this problem may perform degree and neighbor queries, and is allowed a small error probability. We design an algorithm that outputs an estimate , such that with probability 1-1/poly(n), arb(G) ≤ ≤ clog2 n-arb(G), where n = |V| and c is a constant. The expected query complexity and running time of the algorithm are O(n/arb(G)) · poly(log n), and this upper bound also holds with high probability. This bound is optimal for such an approximation up to a poly (log n) factor. For the closely related problem of finding the densest subgraph, Bhattacharya et al. (STOC, 2015) showed that there exists a factor-2 approximation algorithm that runs in time O(n) · poly (log n). In a follow up work, McGregor et al. (MFCS, 2015) improved the approximation factor to (1 + ?) with the same complexity.

UR - http://www.scopus.com/inward/record.url?scp=85130710318&partnerID=8YFLogxK

M3 - פרסום בספר כנס

AN - SCOPUS:85130710318

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 2404

EP - 2425

BT - ACM-SIAM Symposium on Discrete Algorithms, SODA 2022

PB - Association for Computing Machinery

Y2 - 9 January 2022 through 12 January 2022

ER -