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- W3042983256 abstract "In a recent breakthrough, Charalampopoulos, Gawrychowski, Mozes, and Weimann (STOC 2019) showed that exact distance queries on planar graphs could be answered in $n^{o(1)}$ time by a data structure occupying $n^{1+o(1)}$ space, i.e., up to $o(1)$ terms, optimal exponents in time (0) and space (1) can be achieved simultaneously. Their distance query algorithm is recursive: it makes successive calls to a point-location algorithm for planar Voronoi diagrams, which involves many recursive distance queries. The depth of this recursion is non-constant and the branching factor logarithmic, leading to $(log n)^{omega(1)} = n^{o(1)}$ query times. In this paper we present a new way to do point-location in planar Voronoi diagrams, which leads to a new exact distance oracle. At the two extremes of our space-time tradeoff curve we can achieve either $n^{1+o(1)}$ space and $log^{2+o(1)}n$ query time, or $nlog^{2+o(1)}n$ space and $n^{o(1)}$ query time. All previous oracles with $tilde{O}(1)$ query time occupy space $n^{1+Omega(1)}$, and all previous oracles with space $tilde{O}(n)$ answer queries in $n^{Omega(1)}$ time." @default.
- W3042983256 created "2020-07-23" @default.
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- W3042983256 date "2020-07-16" @default.
- W3042983256 modified "2023-10-14" @default.
- W3042983256 title "Planar Distance Oracles with Better Time-Space Tradeoffs" @default.
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- W3042983256 doi "https://doi.org/10.48550/arxiv.2007.08585" @default.
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