Erin Mcleish

McGill University | McGill

We study the merging process when Kruskal's algorithm is run with random graphs as inputs. Our aim is to analyze this process when the underlying graph is the complete graph on n vertices lying in [0,1] (d) , and edge set weighted with the Euclidean distance. The height of the binary tree explaining the merging process is proved to be I similar to(...

Musical cyclic rhythms with a cycle length (timespan) of 8 or 16 pulses are called binary; those with 6 or 12 pulses are called ternary. The process of mapping a ternary rhythm of, say 12 pulses, to a rhythm of 16 pulses, such that musicologically salient properties are preserved is termed binarization. By analogy, the converse process of mapping a...

We extend results about heights of random trees (Devroye, JACM 33 (1986) 489–498, SIAM J COMP 28 (1998) 409–432). In this paper, a general split tree model is considered in which the normalized subtree sizes of nodes converge in distribution. The height of these trees is shown to be in probability asymptotic to clog n for some constant c. We apply...

We consider a model of random trees similar to the split trees of Devroye (SIAM J. Comput. 28(2), 409–432, 1998) in which a set of items is recursively partitioned. Our model allows for more flexibility in the choice of the partitioning procedure, and has weighted edges. We prove that for this model, the height H n of a random tree is asymptotic t...

Let S={s1,…,sn} be a set of points in the plane. The Oja depth of a query point θ with respect to S is the sum of the areas of all triangles (θ,si,sj). This depth may be computed in O(nlogn) time in the RAM model of computation. We show that a matching lower bound holds in the algebraic decision tree model. This bound also applies to the computatio...

We present an algorithm for hashing � αnelements into a table with n separate chains that requires O(1) deterministic worst-case insert time, and O(1) expected worst-case search time for constant α. We exploit the connection between two-way chaining and random graph theory in our techniques. 1. Introduction. In classical uniform hashing with chaini...