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Novel Characteristi...
Abstract
Ämnesord
Stäng
- We investigate characteristics of random split trees introduced by Devroye [SIAM J Comput 28, 409-432, 1998]; split trees include e. g., binary search trees, m-ary search trees, quadtrees, median of (2k + 1)-trees, simplex trees, tries and digital search trees. More precisely: We use renewal theory in the studies of split trees, and use this theory to prove several results about split trees. A split tree of cardinality n is constructed by distributing n balls (which often represent data) to a subset of nodes of an infinite tree. One of our main results is a relation between the deterministic number of balls n and the random number of nodes N. In [5] there is a central limit law for the depth of the last inserted ball so that most nodes are close to depth lnn/mu + O(root lnn), where mu is some constant depending on the type of split tree; we sharpen this result by finding an upper bound for the expected number of nodes with depths >= lnn/mu - ln(1/2+epsilon) n or depths <= lnn/mu + ln(1/2+epsilon) n for any choice of epsilon > 0. We also find the first asymptotic of the variances of the depths of the balls in the tree.
Ämnesord
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
Nyckelord
- Random Trees
- Split Trees
- Renewal Theory
- Discrete mathematics
- Diskret matematik
- Mathematics
- Matematik
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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