Related papers: Optimal construction of a layer-ordered heap

Selection on the Cartesian product is a classic problem in computer science. Recently, an optimal algorithm for selection on $X+Y$, based on soft heaps, was introduced. By combining this approach with layer-ordered heaps (LOHs), an…

The hierarchical overlap graph (HOG) is a graph that encodes overlaps from a given set P of n strings, as the overlap graph does. A best known algorithm constructs HOG in O(||P|| log n) time and O(||P||) space, where ||P|| is the sum of…

Motivated by the development of computer theory, the sorting algorithm is emerging in an endless stream. Inspired by decrease and conquer method, we propose a brand new sorting algorithmUltimately Heapsort. The algorithm consists of two…

The theoretical computation of isotopic distribution of compounds is crucial in many important applications of mass spectrometry, especially as machine precision grows. A considerable amount of good tools have been created in the last…

Selection on $X_1+X_2+\cdots + X_m$ is an important problem with many applications in areas such as max-convolution, max-product Bayesian inference, calculating most probable isotopes, and computing non-parametric test statistics, among…

Selection and sorting the Cartesian sum, $X+Y$, are classic and important problems. Here, a new algorithm is presented, which generates the top $k$ values of the form $X_i+Y_j$. The algorithm relies only on median-of-medians and is simple…

Learning composable policies for environments with complex rules and tasks is a challenging problem. We introduce a hierarchical reinforcement learning framework called the Logical Options Framework (LOF) that learns policies that are…

The first worst-case linear-time algorithm for selection was discovered in 1973; however, linear-time binary heap construction was first published in 1964. Here we describe another worst-case linear selection algorithm,which is simply…

We propose a novel hashing-based matching scheme, called Locally Optimized Hashing (LOH), based on a state-of-the-art quantization algorithm that can be used for efficient, large-scale search, recommendation, clustering, and deduplication.…

For many data-processing applications, a comprehensive set of efficient operations for the management of priority values is required. Indexed priority queues are particularly promising to satisfy this requirement by design. In this work, we…

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,…

We propose a simple linear-time on-line algorithm for constructing a position heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it…

The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparison-based, amortized-efficient heap…

Genome assembly is a fundamental problem in Bioinformatics, where for a given set of overlapping substrings of a genome, the aim is to reconstruct the source genome. The classical approaches to solving this problem use assembly graphs, such…

Learning to Optimize (L2O) stands at the intersection of traditional optimization and machine learning, utilizing the capabilities of machine learning to enhance conventional optimization techniques. As real-world optimization problems…

This paper describes a new and purely functional implementation technique of binary heaps. A binary heap is a tree-based data structure that implements priority queue operations (insert, remove, minimum/maximum) and guarantees at worst…

We introduce a new family of priority-queue data structures: partition-based simple heaps. The structures consist of $O(\log n)$ doubly-linked lists; order is enforced among data in different lists, but the individual lists are unordered.…

We consider the classic problem of designing heaps. Standard binary heaps run faster in practice than Fibonacci heaps but have worse time guarantees. Here we present a new type of heap, a layered heap, that runs faster in practice than both…

We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…

Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…