Fast and Compact Exact Distance Oracle for Planar Graphs
2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)(2017)
摘要
For a given a graph, a distance oracle is a data structure that answers distance queries between pairs of vertices. We introduce an O(n
5/3
)-space distance oracle which answers exact distance queries in O(log n) time for n-vertex planar edge-weighted digraphs. All previous distance oracles for planar graphs with truly subquadratic space (i.e., space O(n
2-ϵ)
for some constant ϵ > 0) either required query time polynomial in n or could only answer approximate distance queries. Furthermore, we show how to trade-off time and space: for any S ≥ n
3/2
, we show how to obtain an S-space distance oracle that answers queries in time O( n
5/2/S3/2
logn). This is a polynomial improvement over the previous planar distance oracles with o(n
1/4
) query time.
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关键词
O-space distance oracle,query time polynomial,answer distance queries,S-space distance oracle,approximate distance queries,truly subquadratic space,n-vertex planar edge-weighted digraphs,exact distance queries,data structure,planar graphs
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