Related papers: A Probabilistic Approach to The Perfect Sum Proble…
Given a set $Z$ of $n$ positive integers and a target value $t$, the Subset Sum problem asks whether any subset of $Z$ sums to $t$. A textbook pseudopolynomial time algorithm by Bellman from 1957 solves Subset Sum in time $O(nt)$. This has…
In this article, we consider the Euclidean dispersion problems. Let $P=\{p_{1}, p_{2}, \ldots, p_{n}\}$ be a set of $n$ points in $\mathbb{R}^2$. For each point $p \in P$ and $S \subseteq P$, we define $cost_{\gamma}(p,S)$ as the sum of…
Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference. They have been developed for linear algebra, optimization, integration and differential equation simulation. PNMs naturally incorporate prior…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
We consider the problem of repetitive scenario design where one has to solve repeatedly a scenario design problem and can adjust the sample size (number of scenarios) to obtain a desired level of risk (constraint violation probability). We…
We present new approximation schemes for bin packing based on the following two approaches: (1) partitioning the given problem into mostly identical sub-problems of constant size and then construct a solution by combining the solutions of…
We convert, within polynomial-time and sequential processing, NP-Complete Problems into a problem of deciding feasibility of a given system S of linear equations with constants and coefficients of binary-variables that are 0, 1, or -1. S is…
The vertex cover problem is a famous combinatorial problem, and its complexity has been heavily studied. While a 2-approximation can be trivially obtained for it, researchers have not been able to approximate it better than 2-\textit{o}(1).…
We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex solution. We analyze various probability…
We consider a discrete version of the Witsenhausen problem where all random variables are bounded and take on integer values. Our main goal is to understand the complexity of computing good strategies given the distributions for the initial…
The modular subset sum problem consists of deciding, given a modulus $m$, a multiset $S$ of $n$ integers in $0..m-1$, and a target integer $t$, whether there exists a subset of $S$ with elements summing to $t \mod m $, and to report such a…
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…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
This paper discloses a simple algorithm for encrypting text messages, based on the NP-completeness of the subset sum problem, such that the similarity between encryptions is roughly proportional to the semantic similarity between their…
Quantization for a probability distribution refers to the idea of estimating a given probability by a discrete probability supported by a finite number of points. In this paper, firstly a general approach to this process is outlined using…
We present a new generalization of the bin covering problem that is known to be a strongly NP-hard problem. In our generalization there is a positive constant $\Delta$, and we are given a set of items each of which has a positive size. We…
Consider the classical Min-Sum Set Cover problem: We are given a universe $\mathcal{U}$ of $n$ elements and a collection $\mathcal{S}$ of $k$ subsets of $\mathcal{U}$. Moreover, a cost function is associated with each set. The goal is to…
Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…