具有改进查询时间-空间权衡的平面图近似距离预言机
数据结构与算法
2016-01-06 v1
摘要
我们考虑边加权n顶点无向平面图的近似距离预言机。给定固定 epsilon > 0，我们提出一种 (1+epsilon)-近似距离预言机，其空间为 O(n(loglog n)^2)，查询时间为 O((loglog n)^3)。这将Thorup (FOCS 2001, J. ACM 2004) 和 Klein (SODA 2002) 的预言机在查询时间与空间的最优乘积从 O(n log n) 改进至 O(n(loglog n)^5)。
引用
@article{arxiv.1601.00839,
title = {Approximate Distance Oracles for Planar Graphs with Improved Query Time-Space Tradeoff},
author = {Christian Wulff-Nilsen},
journal= {arXiv preprint arXiv:1601.00839},
year = {2016}
}
备注
20 pages, 9 figures of which 2 illustrate pseudo-code. This is the SODA 2016 version but with the definition of C_i in Phase I fixed and the analysis slightly modified accordingly. The main change is in the subsection bounding query time and stretch for Phase I