Fully dynamic search trees for an extension of the BSP model
Armin Bäumker, Wolfgang Dittrich · 1996
We present parallel algorithms that maintain a 2-3 tree under insertions and deletions. The algorithms are designed for an extension of Valiant's BSP model, BSP*, that and reduction of the overhead involved in communication. The BSP*-model is introduced by Baumker et al. in [2]. Our analysis of the data structure goes beyond standard asymptotic analysis: We use Valiant's notion of c-optimality. Intuitively c-optimal algorithms tend to speedup p=c with growing input size (p denotes the number of processors), where the communication time is asymptotically smaller than the computation time. Our first approach allows 1-optimal searching and amortized c-optimal insertion and deletion for a small constant c. The second one allows 2-optimal searching, and c-optimal deletion and insertion for a small constant c. Both results hold with probability 1 \\Gamma o(1) for wide ranges of BSP*- parameters, where the ranges become larger with growing input sizes. The first approach allows much larger...