Universal Limit Laws for Depths in Random Trees

Random binary search trees, b-ary search trees, median-of-(2k+1) trees, quadtrees, simplex trees, tries, and digital search trees are special cases of random split trees. For these trees, we offer a universal law of large numbers and a limit law for the depth of the last inserted point, as well as a law of large numbers for the height. Key words. binary search tree, data structures, expected time analysis, depth of a node, random tree, law of large numbers AMS subject classifications. 68Q25, 68P05, 60F05, 60C05 PII. S0097539795283954 Random split trees. We introduce a model for a random tree that is sufficiently general that it encompasses many important families of random trees, such as random binary search trees, random m-ary search trees, random fringe-balanced trees, random median-of-(2k + 1) trees, random quadtrees, and random simplex trees. A skeleton tree Tb of branch factor b is an infinite rooted position tree, in which each node has b children, numbered 1 through b. A spli...

• Type: Journal
• Year: 1998
• Where: SIAMCOMP
• Authors: Luc Devroye
• Keywords: Binary Search Trees, Random, Search Trees, SIAMCOMP 1998