相关论文: Sorting using complete subintervals and the maximu…

The cornerstone of any algorithm computing all repetitions in a string of length n in O(n) time is the fact that the number of runs (or maximal repetitions) is O(n). We give a simple proof of this result. As a consequence of our approach,…

Consider a branching random walk evolving in a macroscopic time-inhomogeneous environment, that scales with the length $n$ of the process under study. We compute the first two terms of the asymptotic of the maximal displacement at time $n$.…

A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…

A novel integer sorting technique was proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms which requires only constant amount of additional memory. The technique was inspired from one…

The n-way number partitioning problem, a fundamental challenge in combinatorial optimization, has significant implications for applications such as fair division and machine scheduling. Despite these problems being NP-hard, many…

This note examines a problem in enumerative and asymptotic combinatorics involving the classical structure of integer compositions. What is sought is an analysis on average and in distribution of the length of the longest run of consecutive…

We investigate the order of the variance of the optimal alignments score of two independent iid binary random words having the same length. The letters are equiprobable, but the scoring function is such that one letter has a larger score…

Let $A$ be a sequence of $n \geq 0$ real numbers. A subsequence of $A$ is a sequence of contiguous elements of $A$. A \emph{maximum scoring subsequence} of $A$ is a subsequence with largest sum of its elements, which can be found in O(n)…

We study parallel comparison-based algorithms for finding all equivalence classes of a set of $n$ elements, where sorting according to some total order is not possible. Such scenarios arise, for example, in applications, such as in…

Mergesort is one of the few efficient sorting algorithms and, despite being the oldest one, often still the method of choice today. In contrast to some alternative algorithms, it always runs efficiently using O(n log n) element comparisons…

We continue the study of selection and sorting of $n$ numbers under the adversarial comparator model, where comparisons can be adversarially tampered with if the arguments are sufficiently close. We derive a randomized sorting algorithm…

We study very simple sorting algorithms based on a probabilistic comparator model. In our model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared…

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 the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower…

Sorting networks are oblivious sorting algorithms with many practical applications and rich theoretical properties. Propositional encodings of sorting networks are a key tool for proving concrete bounds on the minimum number of comparators…

A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…

A novel integer value-sorting technique is proposed replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. It requires only constant amount of additional memory. The technique is inspired from…

Maximizing monotone submodular functions under cardinality constraints is a classic optimization task with several applications in data mining and machine learning. In this paper we study this problem in a dynamic environment with…

Determining the maximum number of edges in an intersecting hypergraph on a fixed ground set under additional constraints is one of the central topics in extremal combinatorics. In contrast, there are few results on analogous problems…

In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are…