Related papers: Pbit and other list sorting algorithms

Proportional apportionment is the problem of assigning seats to parties according to their relative share of votes. Divisor methods are the de-facto standard solution, used in many countries. In recent literature, there are two algorithms…

We give the first concise description of the fastest known suffix sorting algorithm in main memory, the DivSufSort by Yuta Mori. We then present an extension that also computes the LCP-array, which is competitive with the fastest known…

Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational…

We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…

An industrial grade Quicksort function along with its new algorithm is presented. Compared to 4 other well known implementations of Quicksort, the new algorithm reduces both the number of comparisons and swaps in most cases while staying…

We investigate distributed memory parallel sorting algorithms that scale to the largest available machines and are robust with respect to input size and distribution of the input elements. The main outcome is that four sorting algorithms…

While modern general-purpose computing systems have ample amounts of memory, it is still the case that embedded computer systems, such as in a refrigerator, are memory limited; hence, such embedded systems motivate the need for strictly…

We present two stable mergesort variants, "peeksort" and "powersort", that exploit existing runs and find nearly-optimal merging orders with practically negligible overhead. Previous methods either require substantial effort for determining…

Quantum computing can enable a variety of breakthroughs in research and industry in the future. Although some quantum algorithms already exist that show a theoretical speedup compared to the best known classical algorithms, the…

This work shows that the following problems are equivalent, both in theory and in practice: - median filtering: given an $n$-element vector, compute the sliding window median with window size $k$, - piecewise sorting: given an $n$-element…

We revisit the well-known problem of sorting under partial information: sort a finite set given the outcomes of comparisons between some pairs of elements. The input is a partially ordered set P, and solving the problem amounts to…

Recently, many results on the computational complexity of sorting algorithms were obtained using Kolmogorov complexity (the incompressibility method). Especially, the usually hard average-case analysis is ammenable to this method. Here we…

In our previous work there was some indication that Partition Sort could be having a more robust average case O(nlogn) complexity than the popular Quick Sort. In our first study in this paper, we reconfirm this through computer experiments…

The provably asymptotically fastest algorithm within a factor of 5 for formally described problems will be constructed. The main idea is to enumerate all programs provably equivalent to the original problem by enumerating all proofs. The…

One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem…

Conventional sorting algorithms make use of such data structures as array, file and list which define access methods of the items to be sorted. Such traditional methods as exchange sort, divide and conquer sort, selection sort and insertion…

The problem of ranking can be described as follows. We have a set of combinatorial objects $S$, such as, say, the k-subsets of n things, and we can imagine that they have been arranged in some list, say lexicographically, and we want to…

As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…

Sorting a set of items is a task that can be useful by itself or as a building block for more complex operations. The more sophisticated and fast sorting algorithms become asymptotically, the less efficient they are for small sets of items…

We engineer algorithms for sorting huge data sets on massively parallel machines. The algorithms are based on the multiway merging paradigm. We first outline an algorithm whose I/O requirement is close to a lower bound. Thus, in contrast to…