On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
A unified geometric approach to graph separators
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Introduction to VLSI Systems
Planar Spanners and Approximate Shortest Path Queries among Obstacles in the Plane
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
Minimum energy disjoint path routing in wireless ad-hoc networks
Proceedings of the 9th annual international conference on Mobile computing and networking
Journal of the ACM (JACM)
Well-Separated Pair Decomposition for the Unit-Disk Graph Metric and Its Applications
SIAM Journal on Computing
Coverage in wireless ad hoc sensor networks
IEEE Transactions on Computers
IEEE Journal on Selected Areas in Communications
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Spanners for geometric intersection graphs
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
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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(n3/2ε−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. The algorithm uses an efficient subdivision of the plane to construct a sparse graph having many of the same distance properties as the input disk graph. Additionally, the sparse graph has a small separator decomposition, which is then used to answer distance queries. The algorithm extends naturally to the higher dimensional ball graphs.