Almost Optimal Distance Oracles for Planar Graphs
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We present new tradeoffs between space and query-time for exact distance oracles in directed weighted planar graphs. These tradeoffs are almost optimal in the sense that they are within polylogarithmic, sub-polynomial or arbitrarily small polynomial factors from the naïve linear space, constant query-time lower bound. These tradeoffs include: (i) an oracle with space Õ(n^1+ϵ) and query-time Õ(1) for any constant ϵ>0, (ii) an oracle with space Õ(n) and query-time Õ(n^ϵ) for any constant ϵ>0, and (iii) an oracle with space n^1+o(1) and query-time n^o(1).
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