Related papers: Sorting a Low-Entropy Sequence

We consider the problem of finding the $k^{th}$ highest element in a totally ordered set of $n$ elements (select), and partitioning a totally ordered set into the top $k$ and bottom $n-k$ elements (partition) using pairwise comparisons.…

The goal of this paper is to develop an estimate for the entropy of random long-range correlated symbolic sequences with elements belonging to a finite alphabet. As a plausible model, we use the high-order additive stationary ergodic Markov…

This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…

In this paper we approximate the radiative transfer equations by the method of moments, constructing mesoscopic approximations of arbitrary order of the otherwise microscopic system. To define the necessary closure a minimum entropy…

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…

This article introduces an adaptive sorting algorithm that can relocate elements accurately by substituting their values into a function which we name it the guessing function. We focus on building this function which is the mapping…

The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…

We investigate high-order finite difference schemes for the Hamilton-Jacobi equation continuum limit of nondominated sorting. Nondominated sorting is an algorithm for sorting points in Euclidean space into layers by repeatedly removing…

We study a generalization of the recently introduced order-preserving pattern matching, where instead of looking for an exact copy of the pattern, we only require that the relative order between the elements is the same. In our variant, we…

Preference orderings are orderings of a set of items according to the preferences (of judges). Such orderings arise in a variety of domains, including group decision making, consumer marketing, voting and machine learning. Measuring the…

We study the complexity of a fundamental algorithm for fairly allocating indivisible items, the round-robin algorithm. For $n$ agents and $m$ items, we show that the algorithm can be implemented in time $O(nm\log(m/n))$ in the worst case.…

In many real-world applications, data is not collected as one batch, but sequentially over time, and often it is not possible or desirable to wait until the data is completely gathered before analyzing it. Thus, we propose a framework to…

Encoding data structures store enough information to answer the queries they are meant to support but not enough to recover their underlying datasets. In this paper we give the first encoding data structure for the challenging problem of…

We consider the problem of inserting a new item into an ordered list of N-1 items. The length of an algorithm is measured by the number of comparisons it makes between the new item and items already on the list. Classically, determining the…

Generalized sorting problem, also known as sorting with forbidden comparisons, was first introduced by Huang et al. together with a randomized algorithm which requires $\tilde O(n^{3/2})$ probes. We study this problem with additional…

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…

Many tasks in natural language processing involve predicting structured outputs, e.g., sequence labeling, semantic role labeling, parsing, and machine translation. Researchers are increasingly applying deep representation learning to these…

We give optimal sorting algorithms in the evolving data framework, where an algorithm's input data is changing while the algorithm is executing. In this framework, instead of producing a final output, an algorithm attempts to maintain an…

Sorting is a fundamental problem in computer science. In the classical setting, it is well-known that $(1\pm o(1)) n\log_2 n$ comparisons are both necessary and sufficient to sort a list of $n$ elements. In this paper, we study the Noisy…

Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…