Massively Parallel Ruling Set Made Deterministic
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910657609203712 |
|---|---|
| author | Giliberti, Jeff Parsaeian, Zahra |
| author_facet | Giliberti, Jeff Parsaeian, Zahra |
| contents | We study the deterministic complexity of the $2$-Ruling Set problem in the model of Massively Parallel Computation (MPC) with linear and strongly sublinear local memory.
Linear MPC: We present a constant-round deterministic algorithm for the $2$-Ruling Set problem that matches the randomized round complexity recently settled by Cambus, Kuhn, Pai, and Uitto [DISC'23], and improves upon the deterministic $O(\log \log n)$-round algorithm by Pai and Pemmaraju [PODC'22]. Our main ingredient is a simpler analysis of CKPU's algorithm based solely on bounded independence, which makes its efficient derandomization possible.
Sublinear MPC: We present a deterministic algorithm that computes a $2$-Ruling Set in $\tilde O(\sqrt{\log n})$ rounds deterministically. Notably, this is the first deterministic ruling set algorithm with sublogarithmic round complexity, improving on the $O(\log Δ+ \log \log^* n)$-round complexity that stems from the deterministic MIS algorithm of Czumaj, Davies, and Parter [TALG'21]. Our result is based on a simple and fast randomness-efficient construction that achieves the same sparsification as that of the randomized $\tilde O(\sqrt{\log n})$-round LOCAL algorithm by Kothapalli and Pemmaraju [FSTTCS'12]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Massively Parallel Ruling Set Made Deterministic Giliberti, Jeff Parsaeian, Zahra Data Structures and Algorithms Distributed, Parallel, and Cluster Computing We study the deterministic complexity of the $2$-Ruling Set problem in the model of Massively Parallel Computation (MPC) with linear and strongly sublinear local memory. Linear MPC: We present a constant-round deterministic algorithm for the $2$-Ruling Set problem that matches the randomized round complexity recently settled by Cambus, Kuhn, Pai, and Uitto [DISC'23], and improves upon the deterministic $O(\log \log n)$-round algorithm by Pai and Pemmaraju [PODC'22]. Our main ingredient is a simpler analysis of CKPU's algorithm based solely on bounded independence, which makes its efficient derandomization possible. Sublinear MPC: We present a deterministic algorithm that computes a $2$-Ruling Set in $\tilde O(\sqrt{\log n})$ rounds deterministically. Notably, this is the first deterministic ruling set algorithm with sublogarithmic round complexity, improving on the $O(\log Δ+ \log \log^* n)$-round complexity that stems from the deterministic MIS algorithm of Czumaj, Davies, and Parter [TALG'21]. Our result is based on a simple and fast randomness-efficient construction that achieves the same sparsification as that of the randomized $\tilde O(\sqrt{\log n})$-round LOCAL algorithm by Kothapalli and Pemmaraju [FSTTCS'12]. |
| title | Massively Parallel Ruling Set Made Deterministic |
| topic | Data Structures and Algorithms Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2406.12727 |