Novel Techniques for the Zero-Forcing and p-Median Graph Location Problems

This thesis presents new methods for solving two graph location problems, the p-Median problem and the zero-forcing problem. For the p-median problem, I present a branch decomposition based method that finds the best p-median solution that is limited to some input support graph. The algorithm can be used to either find an integral solution from a fractional linear programming solution, or it can be used to improve on the solutions given by a pool of heuristics. In either use, the algorithm compares favorably in running time or solution quality to state-of-the-art heuristics. For the zero-forcing problem, this thesis gives both theoretical and computational results. In the theoretical section, I show that the branchwidth of a graph is a lower bound on its zero-forcing number, and I introduce new bounds on the zero-forcing iteration index for cubic graphs. This thesis also introduces a special type of graph structure, a zero-forcing fort, that provides a powerful tool for the analysis and modeling of zero-forcing problems. In the computational section, I introduce multiple integer programming models for finding minimum zero-forcing sets and integer programming and combinatorial branch and bound methods for finding minimum connected zero-forcing sets. While the integer programming methods do not perform better than the best combinatorial method for the basic zero-forcing problem, they are easily adapted to the connected zero-forcing problem, and they are the best methods for the connected zero-forcing problem

Rationale, design, implementation, and baseline characteristics of patients in the DIG trial: A large, simple, long-term trial to evaluate the effect of digitalis on mortality in heart failure

This article provides a detailed overview of the rationale for key aspects of the protocol of the Digitalis Investigation Group (DIG) trial. It also highlights unusual aspects of the study implementation and the baseline characteristics. The DIG trial is a large, simple, international placebo-controlled trial whose primary objective is to determine the effect of digoxin on all cause mortality in patients with clinical heart failure who are in sinus rhythm and whose ejection fraction is less than or equal to 0.45. An ancillary study examines the effect in those with an ejection fraction > 0.45. Key aspects of the trial include the simplicity of the design, broad eligibility criteria, essential data collection, and inclusion of various types of centers. A total of 302 centers in the United States and Canada enrolled 7788 patients between February 1991 and September 1993. Follow-up continued until December 1995 with the results available in Spring 1996