Related papers: Towards Optimal Sorting of 16 Elements
We examine sorting algorithms for $n$ elements whose basic operation is comparing $t$ elements simultaneously (a $t$-comparator). We focus on algorithms that use only a single round or two rounds -- comparisons performed in the second round…
When algorithms for sorting and searching are applied to keys that are represented as bit strings, we can quantify the performance of the algorithms not only in terms of the number of key comparisons required by the algorithms but also in…
We give the first sorting algorithm with bounds in terms of higher-order entropies: let $S$ be a sequence of length $m$ containing $n$ distinct elements and let (H_\ell (S)) be the $\ell$th-order empirical entropy of $S$, with (n^{\ell + 1}…
We study the problem of estimating the number of defective items in adaptive Group testing by using a minimum number of queries. We improve the existing algorithm and prove a lower bound that show that, for constant estimation, the number…
Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study a more general setting, in which some pairs of objects are incomparable. This generalization is relevant…
We consider the problem of sorting $n$ elements subject to persistent random comparison errors. In this problem, each comparison between two elements can be wrong with some fixed (small) probability $p$, and comparing the same pair of…
We introduce a new model to study algorithm design under unreliable information, and apply this model for the problem of finding the uncorrupted maximum element of a list containing $n$ elements, among which are $k$ corrupted elements.…
In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the large-scale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more…
Sorting algorithms have attracted a great deal of attention and study, as they have numerous applications to Mathematics, Computer Science and related fields. In this thesis, we first deal with the mathematical analysis of the Quicksort…
We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…
We give an efficient algorithm to enumerate all elements of a Pareto front in a multi-objective optimization problem in which the space of values is finite for all objectives. Our algorithm uses a feasibility check for a search space…
This paper establishes the exact comparison complexity of finding an element repeated $n$ times in a $2n$-element array containing $n+1$ distinct values, under the equality-comparison model with $O(1)$ extra space. We present a simple…
There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…
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 study problems with stochastic uncertainty information on intervals for which the precise value can be queried by paying a cost. The goal is to devise an adaptive decision tree to find a correct solution to the problem in consideration…
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 running maximum-minimum (max-min) filter computes the maxima and minima over running windows of size w. This filter has numerous applications in signal processing and time series analysis. We present an easy-to-implement online…
We consider the problem of partial order production: arrange the elements of an unknown totally ordered set T into a target partially ordered set S, by comparing a minimum number of pairs in T. Special cases include sorting by comparisons,…
Previous parallel sorting algorithms do not scale to the largest available machines, since they either have prohibitive communication volume or prohibitive critical path length. We describe algorithms that are a viable compromise and…
We prove that \Omega(n log(n)) comparisons are necessary for any quantum algorithm that sorts n numbers with high success probability and uses only comparisons. If no error is allowed, at least 0.110nlog_2(n) - 0.067n + O(1) comparisons…