2018/10/03 by John Iacono, Stefan Langerman, Iacono, John +1
Computer Science · #Advanced Graph Theory Research #Algorithms and Data Compression #Optimization and Search Problems #cs.DS
paper · pdf · doi:10.48550/arxiv.1810.01785
An earlier version of this work appeared in the Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms
arxiv created 2018/10/03 · arxiv updated 2018/10/04
It is shown that the online binary search tree data structure GreedyASS performs asymptotically as well on a sufficiently long sequence of searches as any static binary search tree where each search begins from the previous search (rather than the root). This bound is known to be equivalent to assigning each item i in the search tree a positive weight wi and bounding the search cost of an item in the search sequence s1,…,sm by O(1+ log \frac ∑_min(si-1,si) ≤ x ≤ max(si-1,si)wx min(wsi,w_si-1) ) amortized. This result is the strongest finger-type bound to be proven for binary search trees. By setting the weights to be equal, one observes that our bound implies the dynamic finger bound. Compared to the previous proof of the dynamic finger bound for Splay trees, our result is significantly shorter, stronger, simpler, and has reasonable constants.