Solving Sequential Greedy Problems Distributedly with Sub-Logarithmic Energy Cost
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912131528523776 |
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| author | Balliu, Alkida Fraigniaud, Pierre Olivetti, Dennis Rabie, Mikaël |
| author_facet | Balliu, Alkida Fraigniaud, Pierre Olivetti, Dennis Rabie, Mikaël |
| contents | We study the awake complexity of graph problems that belong to the class O-LOCAL, which includes a subset of problems solvable by sequential greedy algorithms, such as $(Δ+1)$-coloring and maximal independent set. It is known from previous work that, in $n$-node graphs of maximum degree $Δ$, any problem in the class O-LOCAL can be solved by a deterministic distributed algorithm with awake complexity $O(\logΔ+\log^\star n)$.
In this paper, we show that any problem belonging to the class O-LOCAL can be solved by a deterministic distributed algorithm with awake complexity $O(\sqrt{\log n}\cdot\log^\star n)$. This leads to a polynomial improvement over the state of the art when $Δ\gg 2^{\sqrt{\log n}}$, e.g., $Δ=n^ε$ for some arbitrarily small $ε>0$. The key ingredient for achieving our results is the computation of a network decomposition, that uses a small-enough number of colors, in sub-logarithmic time in the Sleeping model, which can be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving Sequential Greedy Problems Distributedly with Sub-Logarithmic Energy Cost Balliu, Alkida Fraigniaud, Pierre Olivetti, Dennis Rabie, Mikaël Distributed, Parallel, and Cluster Computing We study the awake complexity of graph problems that belong to the class O-LOCAL, which includes a subset of problems solvable by sequential greedy algorithms, such as $(Δ+1)$-coloring and maximal independent set. It is known from previous work that, in $n$-node graphs of maximum degree $Δ$, any problem in the class O-LOCAL can be solved by a deterministic distributed algorithm with awake complexity $O(\logΔ+\log^\star n)$. In this paper, we show that any problem belonging to the class O-LOCAL can be solved by a deterministic distributed algorithm with awake complexity $O(\sqrt{\log n}\cdot\log^\star n)$. This leads to a polynomial improvement over the state of the art when $Δ\gg 2^{\sqrt{\log n}}$, e.g., $Δ=n^ε$ for some arbitrarily small $ε>0$. The key ingredient for achieving our results is the computation of a network decomposition, that uses a small-enough number of colors, in sub-logarithmic time in the Sleeping model, which can be of independent interest. |
| title | Solving Sequential Greedy Problems Distributedly with Sub-Logarithmic Energy Cost |
| topic | Distributed, Parallel, and Cluster Computing |
| url | https://arxiv.org/abs/2410.20499 |