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- W2964319962 abstract "In the distributed setting, the only existing constructions of textit{sparse skeletons}, (i.e., subgraphs with $O(n)$ edges) either use randomization or large messages, or require $Omega(D)$ time, where $D$ is the hop-diameter of the input graph $G$. We devise the first deterministic distributed algorithm in the CONGEST model (i.e., uses small messages) for constructing linear-size skeletons in time $2^{O(sqrt{{log n}cdot{log{log n}}})}$. We can also compute a linear-size spanner with stretch $polylog(n)$ in low deterministic polynomial time, i.e., $O(n^rho)$ for an arbitrarily small constant $rho >0$, in the CONGEST model. Yet another algorithm that we devise runs in $O({log n})^{kappa-1}$ time, for a parameter $kappa=1,2,dots,$ and constructs an $O({log n})^{kappa-1}$ spanner with $O(n^{1+1/kappa})$ edges. All our distributed algorithms are lightweight from the computational perspective, i.e., none of them employs any heavy computations." @default.
- W2964319962 created "2019-07-30" @default.
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- W2964319962 date "2019-07-25" @default.
- W2964319962 modified "2023-09-27" @default.
- W2964319962 title "Fast Deterministic Constructions of Linear-Size Spanners and Skeletons." @default.
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