Streaming and Fully Dynamic Centralized Algorithms for Constructing and Maintaining Sparse Spanners

We present a streaming algorithm for constructing sparse spanners and show that our algorithm out-performs significantly the state-of-the-art algorithm for this task [20]. Specifically, the processing time-per-edge of our algorithm is drastically smaller than that of the algorithm of [20], and all other efficiency parameters of our algorithm are no greater (and some of them are strictly smaller) than the respective parameters for the state-of-the-art algorithm. We also devise a fully dynamic centralized algorithm maintaining sparse spanners. This algorithm has a very small incremental update time, and a non-trivial decremental update time. To our knowledge, this is the first fully dynamic centralized algorithm for maintaining sparse spanners that provides non-trivial bounds on both incremental and decremental update time for a wide range of stretch parameter t.

• Type: Conference
• Year: 2007
• Where: ICALP
• Authors: Michael Elkin
• Keywords: Algorithm, Dynamic Centralized Algorithm, ICALP 2007, Sparse Spanners, Theoretical Computer Science