Approximate Distance Queries in Disk Graphs

Martin Fürer, Shiva Prasad Kasiviswanathan

Abstract: We present efficient algorithms for approximately answering distance queries in disk graphs. Let G be a disk graph with n vertices and m edges. For any fixed ε> 0, we show that G can be preprocessed in \(O(m\sqrt{n}\epsilon^{-1}+m\epsilon^{-2}\log S)\) time, constructing a data structure of size O(n 3/2 ε − 1+nε − 2logS), such that any subsequent distance query can be answered approximately in \(O(\sqrt{n}\epsilon^{-1}+\epsilon^{-2}\log S)\) time. Here S is the ratio between the largest and smallest radius. The estimate produced is within an additive error which is only ε times the longest edge on some shortest path.

External IDs:dblp:conf/waoa/FurerK06