Connected dominating sets on dynamic geometric graphs

We propose algorithms for efficiently maintaining a constant-approximate minimum connected dominating set (MCDS) of a geometric graph under node insertions and deletions. Assuming that two nodes are adjacent in the graph iff they are within a fixed geometric distance, we show that an O(1)-approximate MCDS of a graph in Rd with n nodes can be maintained with polylogarithmic (in n) work per node insertion/deletion as compared with (n) work to maintain the optimal MCDS, even in the weaker kinetic setting. In our approach, we ensure that a topology change caused by inserting or deleting a node only affects the solution in a small neighborhood of that node, and show that a small set of range queries and bichromatic closest pair queries is then sufficient to efficiently repair the CDS.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Leonidas J. Guibas, Nikola Milosavljevic, Arik Motskin
• Keywords: CCCG 2010, Computational Geometry, Connected Dominating Set, Geometric Graph, Node Insertions