Adding range restriction capability to dynamic data structures
Journal of the ACM (JACM)
SIAM Journal on Computing
Discrete Mathematics - Topics on domination
Euclidean minimum spanning trees and bichromatic closest pairs
Discrete & Computational Geometry
On calculating connected dominating set for efficient routing in ad hoc wireless networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
Data structures for mobile data
Journal of Algorithms
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Message-optimal connected dominating sets in mobile ad hoc networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Smooth kinetic maintenance of clusters
Proceedings of the nineteenth annual symposium on Computational geometry
PTAS for Minimum Connected Dominating Set in Unit Ball Graph
WASA '08 Proceedings of the Third International Conference on Wireless Algorithms, Systems, and Applications
Approximation algorithms for unit disk graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
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We propose algorithms for efficiently maintaining a constant-approximate minimum connected dominating set (MCDS) of a geometric graph under node insertions and deletions, and under node mobility. Assuming that two nodes are adjacent in the graph if and only if they are within a fixed geometric distance, we show that an O(1)-approximate MCDS of a graph in R^d with n nodes can be maintained in O(log^2^dn) time per node insertion or deletion. We also show that @W(n) time per operation is necessary to maintain exact MCDS. This lower bound holds even for d=1, even for randomized algorithms, and even when running time is amortized over a sequence of insertions/deletions, or over continuous motion. The crucial fact is that a single operation may affect the entire exact solution, while an approximate solution is affected only in a small neighborhood of the node that was inserted or deleted. In the approximate case, we show how to compute these local changes by a few range searching queries and a few bichromatic closest pair queries.