Datensatz

Zusammenfassung

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 $\R^d$ with $n$ nodes can be maintained with polylogarithmic (in $n$) work per node insertion/deletion as compared with $\Omega(n)$ 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.