The approximability of shortest path-based graph orientations of protein-protein interaction networks.

The graph orientation problem calls for orienting the edges of an undirected graph so as to maximize the number of prespecified source-target vertex pairs that admit a directed path from the source to the target. Most algorithmic approaches to this problem share a common preprocessing step, in which the input graph is reduced to a tree by repeatedly contracting its cycles. Although this reduction is valid from an algorithmic perspective, the assignment of directions to the edges of the contracted cycles becomes arbitrary and, consequently, the connecting source-target paths may be arbitrarily long. In the context of biological networks, the connection of vertex pairs via shortest paths is highly motivated, leading to the following variant: Given an undirected graph and a collection of source-target vertex pairs, assign directions to the edges so as to maximize the number of pairs that are connected by a shortest (in the original graph) directed path. Here we study this variant, provide strong inapproximability results for it, and propose approximation algorithms for the problem, as well as for relaxations where the connecting paths need only be approximately shortest.

Optimal codon randomization via mathematical programming.

Codon randomization via degenerate oligonucleotides is a widely used approach for generating protein libraries. We use integer programming methodology to model and solve the problem of computing the minimal mixture of oligonucleotides required to induce an arbitrary target probability over the 20 standard amino acids. We consider both randomization via conventional degenerate oligonucleotides, which incorporate at each position of the randomized codon certain nucleotides in equal probabilities, and randomization via spiked oligonucleotides, which admit arbitrary nucleotide distribution at each of the codon's positions. Existing methods for computing such mixtures rely on various heuristics.

Modeling the impact of changing patient transportation systems on peri-operative process performance in a large hospital: insights from a computer simulation study.

Transportation of patients is a key hospital operational activity. During a large construction project, our patient admission and prep area will relocate from immediately adjacent to the operating room suite to another floor of a different building. Transportation will require extra distance and elevator trips to deliver patients and recycle transporters (specifically: personnel who transport patients). Management intuition suggested that starting all 52 first cases simultaneously would require many of the 18 available elevators. To test this, we developed a data-driven simulation tool to allow decision makers to simultaneously address planning and evaluation questions about patient transportation. We coded a stochastic simulation tool for a generalized model treating all factors contributing to the process as JAVA objects. The model includes elevator steps, explicitly accounting for transporter speed and distance to be covered. We used the model for sensitivity analyses of the number of dedicated elevators, dedicated transporters, transporter speed and the planned process start time on lateness of OR starts and the number of cases with serious delays (i.e., more than 15 min). Allocating two of the 18 elevators and 7 transporters reduced lateness and the number of cases with serious delays. Additional elevators and/or transporters yielded little additional benefit. If the admission process produced ready-for-transport patients 20 min earlier, almost all delays would be eliminated. Modeling results contradicted clinical managers' intuition that starting all first cases on time requires many dedicated elevators. This is explained by the principle of decreasing marginal returns for increasing capacity when there are other limiting constraints in the system.