Related papers: Hardness Amplification of Optimization Problems
Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for…
We present a complete classification of the distributed computational complexity of local optimization problems in directed cycles for both the deterministic and the randomized LOCAL model. We show that for any local optimization problem…
The direct product problem is a fundamental question in complexity theory which seeks to understand how the difficulty of computing a function on each of k independent inputs scales with k. We prove the following direct product theorem…
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
While research in robust optimization has attracted considerable interest over the last decades, its algorithmic development has been hindered by several factors. One of them is a missing set of benchmark instances that make algorithm…
In this paper, we tackle the resolution of chance-constrained problems reformulated via Sample Average Approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program cursed with…
We survey the average-case complexity of problems in NP. We discuss various notions of good-on-average algorithms, and present completeness results due to Impagliazzo and Levin. Such completeness results establish the fact that if a certain…
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…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We study an assortment optimization problem under a multi-purchase choice model in which customers choose a bundle of up to one product from each of two product categories. Different bundles have different utilities and the bundle price is…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…
We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various…
Optimization problems pervade essentially every scientific discipline and industry. Many such problems require finding a solution that maximizes the number of constraints satisfied. Often, these problems are particularly difficult to solve…
We prove new hardness amplification results for Learning Parity with Noise ($\mathsf{LPN}$) and its sparse variants. In $\mathsf{LPN}_{\eta,n,m}$, the goal is to recover a secret $\vec s\in\mathbb{F}_2^n$ from $m$ noisy linear samples…
We consider a robust version of the revenue maximization problem, where a single seller wishes to sell $n$ items to a single unit-demand buyer. In this robust version, the seller knows the buyer's marginal value distribution for each item…
A strong direct product theorem states that if we want to compute $k$ independent instances of a function, using less than $k$ times the resources needed for one instance, then the overall success probability will be exponentially small in…
The ``sample amplification'' problem formalizes the following question: Given $n$ i.i.d. samples drawn from an unknown distribution $P$, when is it possible to produce a larger set of $n+m$ samples which cannot be distinguished from $n+m$…
Distribution networks with periodically repeating events often hold great promise to exploit economies of scale. Joint replenishment problems are a fundamental model in inventory management, manufacturing, and logistics that capture these…
The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…