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- Hosam M. Mahmoud, Mark Daniel Ward
- Appl. Math. Lett.
- 2012

Wederive exactmoments of the number of 2-protected nodes in binary search trees grown from random permutations. Furthermore, we show that a properly normalized version of this tree parameter converges to a Gaussian limit. © 2012 Elsevier Ltd. All rights reserved.

We analyze a fringe tree parameter w in a variety of settings, utilizing a variety of methods from the analysis of algorithms and data structures. Given a tree t and one of its leaves a, the w(t, a) parameter denotes the number of internal nodes in the subtree rooted at a’s father. The closely-related w(t, a) parameter denotes the number of leaves,… (More)

In this report, we prove that under a Markovian model of order one, the average depth of suffix trees of index n is asymptotically similar to the average depth of tries (a.k.a. digital trees) built on n independent strings. This leads to an asymptotic behavior of (log n)/h + C for the average of the depth of the suffix tree, where h is the entropy of the… (More)

- Hosam M. Mahmoud, Mark Daniel Ward
- J. Applied Probability
- 2015

We investigate protected nodes in random recursive trees. The exact mean of the number of such nodes is obtained by recurrence, and a linear asymptotic equivalent follows. A nonlinear recurrence for the variance shows that the variance grows linearly, too. It follows that the number of protected nodes in a random recursive tree, upon proper scaling,… (More)

- Jeffrey Gaither, Mark Daniel Ward
- ANALCO
- 2013

We derive an asymptotic expression for the variance of the number of 2-protected nodes (neither leaves nor parents of leaves) in a binary trie. In an unbiased trie on n leaves we find, for example, that the variance is approximately .934n plus small fluctuations (also of order n); but our result covers the general (biased) case as well. Our proof relies on… (More)

- Stefano Lonardi, Wojciech Szpankowski, Mark Daniel Ward
- IEEE Transactions on Information Theory
- 2007

We propose a joint source-channel coding algorithm capable of correcting some errors in the popular Lempel-Ziv'77 (LZ'77) scheme without introducing any measurable degradation in the compression performance. This can be achieved because the LZ'77 encoder does not completely eliminate the redundancy present in the input sequence. One source of redundancy can… (More)

- Irina Gheorghiciuc, Mark Daniel Ward
- 2007

We consider words with letters from a q-ary alphabet A . The kth subword complexity of a word w ∈ A∗ is the number of distinct subwords of length k that appear as contiguous subwords of w. We analyze subword complexity from both combinatorial and probabilistic viewpoints. Our first main result is a precise analysis of the expected kth subword complexity of… (More)

- Mark Daniel Ward
- 2012

We study the fringe of random recursive trees, by analyzing the joint distribution of the counts of uncorrelated motifs. Our approach allows for finite and countably infinite collections. To be able to deal with the collection when it is infinitely countable, we use measure-theoretic themes. Each member of a collection of motifs occurs a certain number of… (More)

We investigate the average similarity of random strings as captured by the average number of “cousins” in the underlying tree structures. Analytical techniques including poissonization and the Mellin transform are used for accurate calculation of the mean. The string alphabets we consider are m– ary, and the corresponding trees are m–ary trees. Certain… (More)

- James Allen Fill, Svante Janson, Mark Daniel Ward
- Electr. J. Comb.
- 2012

Wilf’s Sixth Unsolved Problem asks for any interesting properties of the set of partitions of integers for which the (nonzero) multiplicities of the parts are all different. We refer to these as Wilf partitions. Using f(n) to denote the number of Wilf partitions, we establish lead-order asymptotics for ln f(n).