Multilevel models are increasingly used to estimate models for hierarchical and repeated measures data. The authors discuss a model in which there is mediation at the lower level and the mediational links vary randomly across upper level units. One repeated measures example is a case in which a person's daily stressors affect his or her coping efforts, which affect his or her mood, and both lin...

1997 ii ACKNOWLEDGEMENTS We would like mostly to thank Mr. Peter Keenan, who was as much a partner as a supervisor, for his invaluable time and erudite guidance during the summer. We must also pay tribute to our parents for their encouragement and support, not only for the duration of this dissertation, but throughout the year. ABSTRACT The Capacitated Arc Routing Problem is a NP-hard arc routi...

The graph homomorphism problem (HOM) asks whether the vertices of a given n-vertex graph G can be mapped to the vertices of a given h-vertex graph H such that each edge of G is mapped to an edge of H. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the 2-CSP problem. In this paper, we prove several lower bounds for HOM under the Exponen...

We disprove Heilbronn's conjecture—that N points lying in the unit disc necessarily contain a triangle of area less than c/N. Introduction We think that the best account of the problem can be achieved by simply copying the corresponding paragraphs from Roth's paper [6]. "Let Pv, P2,..., Pn (where n ^ 3) be a distribution of n points in a (closed) disc of unit area, such that the minimum of the ...

We establish new lower bounds on the complexity of the following basic geometric problem, attributed to John Hopcroft: Given a set of n points and m hyperplanes in IR, is any point contained in any hyperplane? We de ne a general class of partitioning algorithms, and show that in the worst case, for all m and n, any such algorithm requires time (n logm + nm + m logn) in two dimensions, or (n log...

We consider the file maintenance problem (also called the online labeling problem) in which n integer items from the set {1, . . . , r} are to be stored in an array of size m ≥ n. The items are presented sequentially in an arbitrary order, and must be stored in the array in sorted order (but not necessarily in consecutive locations in the array). Each new item must be stored in the array before...

We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a function of the probabilities. Finding probabilities that maximize this expected value is shown to be equivalent to obtaining an optimal solution to the unique game...

Lower bounds for the condition numbers of the preconditioned systems are obtained for two-level additive Schwarz preconditioners for both second order and fourth order problems. They show that the known upper bounds are sharp in the case of a small overlap.