We consider an algorithmic problem that arises in manufacturing applications. The input is a sequence of objects of various types. The scheduler is fed the objects in the sequence one by one, and is equipped with a finite buffer. The goal of the scheduler/sorter is to maximally reduce the number of type transitions. We give the first polynomial-time constant approximation algorithm for this problem. We prove several lemmas about the combinatorial structure of optimal solutions that may be useful in future research, and we show that the unified algorithm based on the local ratio lemma performs well for a slightly larger class of problems than was apparently previously known.

The relative worst-order ratio is a measure of the quality of online algorithms. In contrast to the competitive ratio, this measure compares two online algorithms directly instead of using an intermediate comparison with an optimal offline algorithm. In this paper, we apply the relative worst-order ratio to online algorithms for several common variants of the bin packing problem. We mainly consider pairs of algorithms that are not distinguished by the competitive ratio and show that the relative worst-order ratio prefers the intuitively better algorithm of each pair.

The relative worst order ratio is a measure for the quality of online algorithms. Unlike the competitive ratio, it compares algorithms directly without involving an optimal offline algorithm. The measure has been successfully applied to problems like paging and bin packing. In this paper, we apply it to machine scheduling. We show that for preemptive scheduling, the measure separates multiple pairs of algorithms which have the same competitive ratios; with the relative worst order ratio, the algorithm which is "intuitively better" is also provably better. Moreover, we show one such example for non-preemptive scheduling.

Relative worst order analysis is a supplement or alternative to competitive analysis which has been shown to give results more in accordance with observed behavior of online algorithms for a range of different online problems. The contribution of this paper is twofold. First, it adds the static list accessing problem to the collection of online problems where relative worst order analysis gives better results. Second, and maybe more interesting, it adds the non-trivial supplementary proof technique of list factoring to the theoretical toolbox for relative worst order analysis.

Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider