# Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space

@article{Czumaj2020GraphSF, title={Graph Sparsification for Derandomizing Massively Parallel Computation with Low Space}, author={Artur Czumaj and Peter Davies and Merav Parter}, journal={Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures}, year={2020} }

Massively Parallel Computation (MPC) is an emerging model which distills core aspects of distributed and parallel computation. It was developed as a tool to solve (typically graph) problems in systems where input is distributed over many machines with limited space. Recent work has focused on the regime in which machines have sublinear (in n, number of nodes in the input graph) space, with randomized algorithms presented for the fundamental problems of Maximal Matching and Maximal Independent…

## 16 Citations

### Deterministic massively parallel connectivity

- Computer Science, MathematicsSTOC
- 2022

A deterministic MPC low local space algorithm that in O(logD + loglogn) rounds determines connected components of the input graph is presented, which matches the complexity of state of the art randomized algorithms for this task.

### Optimal Deterministic Massively Parallel Connectivity on Forests

- Computer ScienceArXiv
- 2022

This work gives an algorithm that identifies connected components in O(logD) deterministic rounds and yields a deterministic forest-rooting algorithm with the same runtime and memory bounds as the above algorithm, which can be verified by checking the O(1)-radius neighborhood of each node.

### Massively Parallel Computation in a Heterogeneous Regime

- Computer Science, MathematicsPODC
- 2022

It is shown that even a single large machine suffices to circumvent most of the conditional hardness results for the sublinear regime, and it is observed that the best known near-linear MPC algorithms for several other graph problems can be transformed to work in the heterogeneous MPC model with a single near- linear machine.

### Improved Deterministic Connectivity in Massively Parallel Computation

- Computer ScienceDISC
- 2022

A deterministic connectivity algorithm that matches all the parameters of the randomized algorithm and reduces the local computation time to nearly linear is presented, which is the first to have eﬃcient local computation in low-memory MPC.

### Exponential Speedup Over Locality in MPC with Optimal Memory

- Computer Science, MathematicsDISC
- 2022

This work provides a method that, given the complexity of an LCL problem in the LOCAL model, automatically provides an exponentially faster algorithm for the low-space MPC setting that uses optimal global memory, that is, truly linear.

### Massively Parallel Correlation Clustering in Bounded Arboricity Graphs

- Computer ScienceDISC
- 2021

This paper studies the problem of correlation clustering in bounded arboricity graphs with respect to the Massively Parallel Computation (MPC) model, and develops a 3-approximation algorithm that runs in O (log λ · log logn) MPC rounds in the sublinear memory regime.

### Improved Deterministic (Δ+1) Coloring in Low-Space MPC

- Computer Science, MathematicsPODC
- 2021

The Chang-Li-Pettie algorithm runs in T_local =poly(loglog n) rounds, which sets the state-of-the-art randomized round complexity for the problem in the local model, and employs a combination of tools, notably pseudorandom generators (PRG) and bounded-independence hash functions.

### Brief Announcement: A Randomness-efficient Massively Parallel Algorithm for Connectivity

- Computer SciencePODC
- 2021

The Connectivity algorithm is an instantiation of a general method for converting randomized algorithms in the PRAM model to highly randomness-efficient MPC algorithms and achieves a super-polynomial saving in randomness complexity.

### Sample-and-Gather: Fast Ruling Set Algorithms in the Low-Memory MPC Model

- Computer ScienceFSTTCS
- 2020

It is shown that a $\beta$-ruling set can be computed in the low-memory MPC model with $O(n^\eps)$ memory-per-machine in $\tilde{O}(\beta \cdot \log^{1/(2^{\beta+1}-2)} \Delta)$ rounds, whp.

### Deterministic graph coloring in the streaming model

- Computer Science, MathematicsSTOC
- 2022

It is proved that there is no deterministic single-pass semi-streaming algorithm that given a graph G with maximum degree Δ, can output a proper coloring of G using any number of colors which is sub-exponential in Δ.

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