On Solving Problems of Substantially Super-linear Complexity in $N^{o(1)}$ Rounds in the MPC Model
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917461090107392 |
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| author | Lingas, Andrzej |
| author_facet | Lingas, Andrzej |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03376 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Solving Problems of Substantially Super-linear Complexity in $N^{o(1)}$ Rounds in the MPC Model Lingas, Andrzej Distributed, Parallel, and Cluster Computing Computational Complexity Data Structures and Algorithms F.2.2 F.2.2 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. |
| title | On Solving Problems of Substantially Super-linear Complexity in $N^{o(1)}$ Rounds in the MPC Model |
| topic | Distributed, Parallel, and Cluster Computing Computational Complexity Data Structures and Algorithms F.2.2 F.2.2 |
| url | https://arxiv.org/abs/2605.03376 |