Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Distance oracles are data structures that provide fast (possibly approximate) ansrs to shortest-path and distance queries in graphs. The tradeoff beten the space requirements and the query time of distance oracles is of particular interest and the main focus of this paper. Unless stated otherwise,  assume all graphs to be planar and undirected.#R##N##R##N#In FOCS 2001 (J. ACM 2004), Thorup introduced approximate distance oracles for planar graphs (concurrent with Klein, SODA 2002). Thorup proved that, for any e > 0 and for any undirected planar graph G = (V,E) on n = |V| nodes, there exists a (1 + e)--approximate distance oracle using space O(ne−1 log n) such that approximate distance queries can be ansred in time O(e−1).#R##N##R##N#,  aim at reducing the polynomial dependency on e−1 and log n, getting the first improvement in the query time--space tradeoff. To simplify the statement of our bounds,  define O(·) to hide log log n and log(1/e) factors.#R##N##R##N#•  provide the first oracle with a time--space product that is subquadratic in e−1.  obtain an oracle with space O(n log n) and query time O(e−1).#R##N##R##N#• For unighted graphs  show how the logarithmic dependency on n can be removed.  obtain an oracle with space O(n) and query time O(e−1). This bound also holds for graphs with polylogarithmic average edge length, which may be a quite reasonable assumption, e.g., for road networks.
['Ken-ichi Kawarabayashi', 'Christian Sommer', 'Mikkel Thorup']
I am writing a research paper on a idea More compact oracles for approximate distances in undirected planar graphs
[{"from": "human", "value": "I am writing a research paper on a idea More compact oracles for approximate distances in undirected planar graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Distance oracles are data structures that provide fast (possibly approximate) ansrs to shortest-path and distance queries in graphs. The tradeoff beten the space requirements and the query time of distance oracles is of particular interest and the main focus of this paper. Unless stated otherwise,  assume all graphs to be planar and undirected.#R##N##R##N#In FOCS 2001 (J. ACM 2004), Thorup introduced approximate distance oracles for planar graphs (concurrent with Klein, SODA 2002). Thorup proved that, for any e > 0 and for any undirected planar graph G = (V,E) on n = |V| nodes, there exists a (1 + e)--approximate distance oracle using space O(ne\u22121 log n) such that approximate distance queries can be ansred in time O(e\u22121).#R##N##R##N#,  aim at reducing the polynomial dependency on e\u22121 and log n, getting the first improvement in the query time--space tradeoff. To simplify the statement of our bounds,  define O(\u00b7) to hide log log n and log(1/e) factors.#R##N##R##N#\u2022  provide the first oracle with a time--space product that is subquadratic in e\u22121.  obtain an oracle with space O(n log n) and query time O(e\u22121).#R##N##R##N#\u2022 For unighted graphs  show how the logarithmic dependency on n can be removed.  obtain an oracle with space O(n) and query time O(e\u22121). This bound also holds for graphs with polylogarithmic average edge length, which may be a quite reasonable assumption, e.g., for road networks."}]