Concurrent online tracking of mobile users
SIGCOMM '91 Proceedings of the conference on Communications architecture & protocols
Proximity problems on moving points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A scalable location service for geographic ad hoc routing
MobiCom '00 Proceedings of the 6th annual international conference on Mobile computing and networking
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Parametric and Kinetic Minimum Spanning Trees
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
RoamHBA: maintaining group connectivity in sensor networks
Proceedings of the 3rd international symposium on Information processing in sensor networks
LLS: a locality aware location service for mobile ad hoc networks
Proceedings of the 2004 joint workshop on Foundations of mobile computing
MLS: an efficient location service for mobile ad hoc networks
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Distributed resource management and matching in sensor networks
IPSN '09 Proceedings of the 2009 International Conference on Information Processing in Sensor Networks
Deformable spanners and applications
Computational Geometry: Theory and Applications
Resilient and low stretch routing through embedding into tree metrics
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
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We study the problem of maintaining group communication between m mobile agents, tracked and helped by n static networked sensors. We develop algorithms to maintain a O(lg n)-approximation to the minimum Steiner tree of the mobile agents such that the maintenance message cost is on average O(lg n) per each hop an agent moves. The key idea is to extract a 'hierarchical well-separated tree (HST)' on the sensor nodes such that the tree distance approximates the sensor network hop distance by a factor of O(lg n). We then prove that maintaining the subtree of the mobile agents on the HST uses logarithmic messages per hop movement. With the HST we can also maintain O(lg n) approximate k-center for the mobile agents with the same message cost. Both the minimum Steiner tree and the k-center problems are NP-hard and our algorithms are the first efficient algorithms for maintaining approximate solutions in a distributed setting.