On Solving Problems of Substantially Super-linear Complexity in $N^{o(1)}$ Rounds in the MPC Model

Andrzej Lingas

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arXiv · 2605.03376

On Solving Problems of Substantially Super-linear Complexity in $N^{o(1)}$ Rounds in the MPC Model

Andrzej Lingas

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Abstract

We study the possibility of designing $N^{o(1)}$-round protocols for problems of substantially super-linear polynomial-time (sequential) complexity in the model of Massively Parallel Computation, where $N$ is the input size. We show that if the machines are not equipped with relatively large local memory and their number does not exceed $N$, then the exponent of the average time complexity of the local computation performed by a machine in a round (in terms of local memory size) in such protocols must be larger than the exponent of the time complexity of the given problem.

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BibTeX RIS

Andrzej Lingas. 2026-05-05. On Solving Problems of Substantially Super-linear Complexity in $N^{o(1)}$ Rounds in the MPC Model. https://arxiv.org/abs/2605.03376

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