Related papers: The Optimal Arbitrary-Proportional Finite-Set-Part…
Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the…
We study set selection problems where the weights are uncertain. Instead of its exact weight, only an uncertainty interval containing its true weight is available for each element. In some cases, some solutions are universally optimal;…
We study the problem of partitioning a given simple polygon $P$ into a minimum number of connected polygonal pieces, each of bounded size. We describe a general technique for constructing such partitions that works for several notions of…
There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…
This paper addresses the challenges of storage and communication costs for large-scale datasets in resource-constrained edge devices by proposing a novel dataset quantization approach to reduce intra-sample redundancy. Unlike traditional…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of Min Sum Set Cover (MSSC), several…
Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…
Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there…
In the metric distortion problem, a set of voters and candidates lie in a common metric space, and a committee of $k$ candidates must be elected. The objective is to minimize a social cost, defined as a function of the distances between…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
A new challenge for learning algorithms in cyber-physical network systems is the distributed solution of big-data classification problems, i.e., problems in which both the number of training samples and their dimension is high. Motivated by…
Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…
We consider the SUBSET SUM problem and its important variants in this paper. In the SUBSET SUM problem, a (multi-)set $X$ of $n$ positive numbers and a target number $t$ are given, and the task is to find a subset of $X$ with the maximal…
In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…
The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting a good subset. We formulate…
Sortition is based on the idea of choosing randomly selected representatives for decision making. The main properties that make sortition particularly appealing are fairness -- all the citizens can be selected with the same probability --…
Feature selection is popular for obtaining small, interpretable, yet highly accurate prediction models. Conventional feature-selection methods typically yield one feature set only, which might not suffice in some scenarios. For example,…
Consider a collection of competing machine learning algorithms. Given their performance on a benchmark of datasets, we would like to identify the best performing algorithm. Specifically, which algorithm is most likely to rank highest on a…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…