We introduce simulated packing and cracking as a technique for evaluating partisan-gerrymandering measures. apply it to historical congressional legislative elections evaluate four measures: partisan bias, declination, efficiency gap, mean-median difference. While the gap recognizes in completely predictable manner (a fact that follows immediately from gap's definition) declination does very go...

this study investigates the correlations among the tensile strength, mineral composition, and textural features of twenty-ninesandstones from kouzestan province. the regression analyses as well as artificial neural network (ann) are also applied to evaluatethe correlations. the results of simple regression analyses show no correlation between mineralogical features and tensile strength.however,...

We introduce and study the batched bin packing problem (BBPP), a bin packing problem in which items become available for packing incrementally, one batch at a time. A batched algorithm must pack a batch before the next batch becomes known. A batch may contain several items; the special case when each batch consists of merely one item is the well-studied on-line bin packing problem. We obtain lo...

In this note we consider the familiar bin-packing problem and provide new worst-case results for a number of classical heuristics. We show that the first-fit and best-fit heuristics have an absolute performance ratio of no more than 1.75, and first-fit decreasing and best-fit decreasing heuristics have an absolute performance ratio of 1.5. The latter is the best possible absolute performance ra...

We address the Clarke and Wright (CW) savings algorithm proposed for the Capacitated Vehicle Routing Problem (CVRP). We first consider a recent enhancement which uses the put first larger items idea originally proposed for the bin packing problem and show that the conflicting idea of putting smaller items first has a comparable performance. Next, we propose a robust enhancement to the CW saving...

Evolutionary algorithms (EAs) often appear to be a ‘black box’, neither offering worst-case bounds nor any guarantee of optimality when used to solve individual problems. They can also take much longer than non-evolutionary methods. We try to address these concerns by using an EA, in particular the learning classi£er system XCS, to learn a solution process rather than to solve individual proble...

We prove that the First Fit bin packing algorithm is stable under the input distribution U {k − 2, k} for all k ≥ 3, settling an open question from the recent survey by Coffman, Garey, and Johnson [3]. Our proof generalizes the multi-dimensional Markov chain analysis used by Kenyon, Rabani, and Sinclair to prove that Best Fit is also stable under these distributions [11]. Our proof is motivated...

This paper studies the dynamic bin packing problem, in which items arrive and depart at arbitrary time. We want to pack a sequence of unit fractions items (i.e., items with sizes 1/w for some integer w ≥ 1) into unit-size bins such that the maximum number of bins used over all time is minimized. Tight and almost-tight performance bounds are found for the family of any-fit algorithms, including ...

We study a variant of the classical bin-packing problem, the ordered open-end bin-packing problem, where first a bin can be filled to a level above 1 as long as the removal of the last piece brings the bin’s level back to below 1 and second, the last piece is the largest-indexed piece among all pieces in the bin. We conduct both worst-case and average-case analyses for the problem. In the worst...