Mark Daniel Ward

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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)
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 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)
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)
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)
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).