Mark Daniel Ward

Learn More
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)
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)
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)
— We propose a joint source-channel coding algorithm capable of correcting some errors in the popular Lempel-Ziv'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 be(More)
We consider a sequence of n geometric random variables and interpret the outcome as an urn model. For a given parameter m, we treat several parameters like what is the largest urn containing at least (or exactly) m balls, or how many urns contain at least m balls, etc. Many of these questions have their origin in some computer science problems. Identifying(More)
In a suffix tree, the multiplicity matching parameter (MMP) M n is the number of leaves in the subtree rooted at the branching point of the (n + 1)st insertion. Equivalently, the MMP is the number of pointers into the database in the Lempel-Ziv '77 data compression algorithm. We prove that the MMP asymptotically follows the logarithmic series distribution(More)
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)
This paper complements the analysis of Louchard and Prodinger [LP08] on the number of rounds in a coin-flipping selection algorithm that occurs in the presence of a demon. We precisely analyze a very different aspect of the selection algorithm, using different methods of analysis. Specifically, we obtain precise descriptions of the distribution and all(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)