The interval ordering problem

For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by earlier intervals in the ordering). This problem is motivated by an application in molecular biology that concerns the determination of the structure of the backbone of a protein. We present polynomial-time algorithms for several natural special cases of the problem that cover the situation where the interval boundaries are agreeably ordered and the situation where the interval set is laminar. Also the bottleneck variant of the problem is shown to be solvable in polynomial time. Finally we prove that the general problem is NP-hard, and that the existence of a constant-factor-approximation algorithm is unlikely

Frequentist Hypothesis Testing with Background Uncertainty

We consider the standard Neyman-Pearson hypothesis test of a signal-plus-background hypothesis and background-only hypothesis in the presence of uncertainty on the background-only prediction. Surprisingly, this problem has not been addressed in the recent conferences on statistical techniques in high-energy physics -- although the its confidence-interval equivalent has been. We discuss the issues of power, similar tests, coverage, and ordering rules. The method presented is compared to the Cousins-Highland technique, the ratio of Poisson means, and ``profile'' method.Comment: Talk from PhyStat2003, Stanford, Ca, USA, September 2003, 4 pages, LaTeX, 2 eps figures. PSN WEMT00

On the Economic Order Quantity Model With Transportation Costs

We consider an economic order quantity type model with unit out-of-pocket holding costs, unitopportunity costs of holding, fixed ordering costs and general transportation costs. For these models, we analyzethe associated optimization problem and derive an easy procedure for determining a bounded interval containingthe optimal cycle length. Also for a special class of transportation functions, like the carload discount schedule, wespecialize these results and give fast and easy algorithms to calculate the optimal lot size and the correspondingoptimal order-up-to-level.EOQ-type model;exact solution;transportation cost function;upper bounds