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- W3192035920 abstract "We provide a deterministic scheme for solving any decidable problem in the distributed {sleeping model}. The sleeping model is a generalization of the standard message-passing model, with an additional capability of network nodes to enter a sleeping state occasionally. As long as a vertex is in the awake state, it is similar to the standard message-passing setting. However, when a vertex is asleep it cannot receive or send messages in the network nor can it perform internal computations. On the other hand, sleeping rounds do not count towards {awake complexity.} Awake complexity is the main complexity measurement in this setting, which is the number of awake rounds a vertex spends during an execution. In this paper we devise algorithms with worst-case guarantees on the awake complexity. We devise a deterministic scheme with awake complexity of $O(log n)$ for solving any decidable problem in this model by constructing a structure we call { Distributed Layered Tree}. This structure turns out to be very powerful in the sleeping model, since it allows one to collect the entire graph information within a constant number of awake rounds. Moreover, we prove that our general technique cannot be improved in this model, by showing that the construction of distributed layered trees itself requires $Omega(log n)$ awake rounds. Another result we obtain in this work is a deterministic scheme for solving any problem from a class of problems, denoted O-LOCAL, in $O(log Delta + log^*n)$ awake rounds. This class contains various well-studied problems, such as MIS and $(Delta+1)$-vertex-coloring." @default.
- W3192035920 created "2021-08-16" @default.
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- W3192035920 date "2021-08-04" @default.
- W3192035920 modified "2023-09-27" @default.
- W3192035920 title "Deterministic Logarithmic Completeness in the Distributed Sleeping Model" @default.
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