In this paper, we consider two types of inverse sorting problems. The first type is an inverse sorting problem under weighted Hamming distance with bound constraints, which can be solved in O(n) time. The second type is a family of partial inverse sorting problems which we can further divide into two kinds, with free positions and with fixed positions. We show that both types of partial inverse...

Abstract— Sorting Networks are cost-effective multistage interconnection networks with sorting capabilities. These networks theoretically consume Θ(NlogN) comparisons. However, the fastest implementable sorting networks built so far consume Θ(NlogN) comparisons, and generally, use the Merge-sorting strategy to sort the input. An 18-element network using the Merge-sorting strategy needs at least...

We propose new sequential sorting operations by adapting techniques and methods used for designing parallel sorting algorithms. Although the norm is to parallelize a sequential algorithm to improve performance, we adapt a contrarian approach: we employ parallel computing techniques to speed up sequential sorting. Our methods can also work for multi-core sorting with minor adjustments that do no...

Numerous experiments on CHO cells have shown that endosomes are composed of separate vesicular and tubulovesicular compartments, such as the sorting endosome, the recycling compartment, and the late endosome. However, Hopkins et al. (Nature 346, 335-339, 1990) have reported that endosomes in HEp2 human carcinoma cells form an extensive tubular reticulum. To resolve their observations with previ...

distribution centers (dcs) play important role in maintaining the uninterrupted flow of goods and materials between the manufacturers and their customers.this paper proposes a mathematical model as the bi-objective capacitated multi-vehicle allocation of customers to distribution centers. an evolutionary algorithm named non-dominated sorting ant colony optimization (nsaco) is used as the optimi...

We present new parallel sorting networks for 17 to 20 inputs. For 17, 19, and 20 inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on 17, 19, and 20 channels. The networks were obtained using a combination of hand-crafted first layers and a...

We consider the problem of sorting elements on a series of stacks, introduced by Tarjan and Knuth. We improve the asymptotic lower bound for the number of stacks necessary to sort n elements to 0.561 log 2 n+O(1). This is the first significant improvement since the previous lower bound, 1 2 log 2 n+O(1), was established by Knuth in 1972.