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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)

- Jeffrey Gaither, Yushi Homma, Mark Sellke, Mark Daniel Ward
- 2012

We use probabilistic and combinatorial tools on strings to discover the average number of 2-protected nodes in tries and in suffix trees. Our analysis covers both the uniform and non-uniform cases. For instance, in a uniform trie with n leaves, the number of 2-protected nodes is approximately 0.803n, plus small first-order fluctuations. The 2-protected… (More)

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

Dedicated to the memory of Philippe Flajolet Keywords: Binary search trees Random structure Combinatorial probability Asymptotic analysis a b s t r a c t We derive exact moments 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… (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)

- 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)

- 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)

We consider a serialized coin-tossing leader election algorithm that proceeds in rounds until a winner is chosen, or all contestants are eliminated. The analysis allows for either biased or fair coins. We find the exact distribution for the duration of any fixed contestant; asymptotically it turns out to be a geometric distribution. Rice's method (an… (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). 1 The Problem Herbert S. Wilf was an expert… (More)

- Adam D Harper Smith, Sarah L Coakley, Mark D Ward, Andrew W Macfarlane, Peter S Friedmann, Neil P Walsh
- Brain, behavior, and immunity
- 2011

Little is known about the influence of exercise on induction and elicitation phases of in vivo immunity in humans. We used experimental contact-hypersensitivity, a clinically relevant in vivo measure of T cell-mediated immunity, to investigate the effects of exercise on induction and elicitation phases of immune responses to a novel antigen. The effects of… (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)