Related papers: Selection on $X_1 + X_1 + \cdots X_m$ via Cartesia…
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…
We use soft heaps to obtain simpler optimal algorithms for selecting the $k$-th smallest item, and the set of~$k$ smallest items, from a heap-ordered tree, from a collection of sorted lists, and from $X+Y$, where $X$ and $Y$ are two…
The layer-ordered heap (LOH) is a simple, recently proposed data structure used in optimal selection on $X+Y$, thealgorithm with the best known runtime for selection on $X_1+X_2+\cdots+X_m$, and the fastest method in practice for computing…
Chazelle [JACM00] introduced the soft heap as a building block for efficient minimum spanning tree algorithms, and recently Kaplan et al. [SOSA2019] showed how soft heaps can be applied to achieve simpler algorithms for various selection…
In this paper we provide efficient algorithms for approximate $\mathcal{C}^m(\mathbb{R}^n, \mathbb{R}^D)-$selection. In particular, given a set $E$, constants $M_0 > 0$ and $0 <\tau \leq \tau_{\max}$, and convex sets $K(x) \subset…
Collecting the most informative data from a large dataset distributed over a network is a fundamental problem in many fields, including control, signal processing and machine learning. In this paper, we establish a connection between…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
Although a large number of optimization algorithms have been proposed for black box optimization problems, the no free lunch theorems inform us that no algorithm can beat others on all types of problems. Different types of optimization…
Convex composition optimization is an emerging topic that covers a wide range of applications arising from stochastic optimal control, reinforcement learning and multi-stage stochastic programming. Existing algorithms suffer from…
An inherently parallel algorithm is proposed that efficiently performs selection: finding the K-th largest member of a set of N members. Selection is a common component of many more complex algorithms and therefore is a widely studied…
Let X[0..n-1] and Y[0..m-1] be two sorted arrays, and define the mxn matrix A by A[j][i]=X[i]+Y[j]. Frederickson and Johnson gave an efficient algorithm for selecting the k-th smallest element from A. We show how to make this algorithm…
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…
An algorithm is presented that efficiently solves the selection problem: finding the k-th smallest member of a set. Relevant to a divide-and-conquer strategy, the algorithm also partitions a set into small and large valued subsets. Applied…
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,…
A wide variety of optimization techniques, both exact and heuristic, tend to be biased samplers. This means that when attempting to find multiple uncorrelated solutions of a degenerate Boolean optimization problem a subset of the solution…
The smooth heap is a recently introduced self-adjusting heap [Kozma, Saranurak, 2018] similar to the pairing heap [Fredman, Sedgewick, Sleator, Tarjan, 1986]. The smooth heap was obtained as a heap-counterpart of Greedy BST, a binary search…
We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within…
This paper investigates the optimal signal detection problem with a particular interest in large-scale multiple-input multiple-output (MIMO) systems. The problem is NP-hard and can be solved optimally by searching the shortest path on the…
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…