Simple Linear-Size Additive Emulators
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913188141858816 |
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| author | Hoppenworth, Gary |
| author_facet | Hoppenworth, Gary |
| contents | Given an input graph $G = (V, E)$, an additive emulator $H = (V, E', w)$ is a sparse weighted graph that preserves all distances in $G$ with small additive error. A recent line of inquiry has sought to determine the best additive error achievable in the sparsest setting, when $H$ has a linear number of edges. In particular, the work of [Kogan and Parter, ICALP 2023], following [Pettie, ICALP 2007], constructed linear size emulators with $+O(n^{0.222})$ additive error. It is known that the worst-case additive error must be at least $+Ω(n^{2/29})$ due to [Lu, Vassilevska Williams, Wein, and Xu, SODA 2022].
We present a simple linear-size emulator construction that achieves additive error $+O(n^{0.191})$. Our approach extends the path-buying framework developed by [Baswana, Kavitha, Mehlhorn, and Pettie, SODA 2005] and [Vassilevska Williams and Bodwin, SODA 2016] to the setting of sparse additive emulators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_17886 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Simple Linear-Size Additive Emulators Hoppenworth, Gary Data Structures and Algorithms Given an input graph $G = (V, E)$, an additive emulator $H = (V, E', w)$ is a sparse weighted graph that preserves all distances in $G$ with small additive error. A recent line of inquiry has sought to determine the best additive error achievable in the sparsest setting, when $H$ has a linear number of edges. In particular, the work of [Kogan and Parter, ICALP 2023], following [Pettie, ICALP 2007], constructed linear size emulators with $+O(n^{0.222})$ additive error. It is known that the worst-case additive error must be at least $+Ω(n^{2/29})$ due to [Lu, Vassilevska Williams, Wein, and Xu, SODA 2022]. We present a simple linear-size emulator construction that achieves additive error $+O(n^{0.191})$. Our approach extends the path-buying framework developed by [Baswana, Kavitha, Mehlhorn, and Pettie, SODA 2005] and [Vassilevska Williams and Bodwin, SODA 2016] to the setting of sparse additive emulators. |
| title | Simple Linear-Size Additive Emulators |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2310.17886 |