Related papers: Optimal Grain Mixing is NP-Complete
Multihead weighing machines (MWMs) are ubiquitous in industry for fast and accurate packaging of a wide variety of foods and vegetables, small hardware items and office supplies. A MWM consists of a system of multiple hoppers that are…
We explore the clearing problem in the barter exchange market. The problem, described in the terminology of graph theory, is to find a set of vertex-disjoint, length-restricted cycles that maximize the total weight in a weighted digraph.…
We break the barrier of $3/2$ for the problem of online load balancing with known makespan, also known as bin stretching. In this problem, $m$ identical machines and the optimal makespan are given. The load of a machine is the total size of…
Vertical farming allows for year-round cultivation of a variety of crops, overcoming environmental limitations and ensuring food security. This closed and highly controlled system allows the plants to grow in optimal conditions, so that…
One of the oldest and most intriguing problems in the handling of materials is how a collection of solid grains packs together. While granular packing is normally determined by how grains are poured or shaken, we find that a systematic and…
In this paper, we study the problem of learning one-dimensional Gaussian mixture models (GMMs) with a specific focus on estimating both the model order and the mixing distribution from independent and identically distributed (i.i.d.)…
We study the Colored Bin Packing Problem: we are given a set of items where each item has a weight and color. We must pack the items in bins of uniform capacity such that no two items of the same color may be adjacent within in a bin. The…
The Best-Worst Method (BWM) is a well-known Multi-Criteria Decision-Making (MCDM) method. This article deals with the multiplicative model of BWM. We first formulate an optimization model that is equivalent to the existing multiplicative…
Mixing grains with different properties is a remarkably challenging process, relevant to many industrial applications. Rotating drums have been used extensively as model systems to study granular media flow and mixing and segregation.…
The Coin Change problem, also known as the Change-Making problem, is a well-studied combinatorial optimization problem, which involves minimizing the number of coins needed to make a specific change amount using a given set of coin…
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…
The weighted $3$-Set Packing problem is defined as follows: As input, we are given a collection $\mathcal{S}$ of sets, each of cardinality at most $3$ and equipped with a positive weight. The task is to find a disjoint sub-collection of…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
Order picking and order packing entail retrieving items from storage and packaging them according to customer requests. These activities have always been the main concerns of the companies in reducing warehouse management costs. This paper…
We consider several extensions of the fractional bin packing problem, a relaxation of the traditional bin packing problem where the objects may be split across multiple bins. In these extensions, we introduce load-balancing constraints…
Important pricing problems in centralized matching markets -- such as carpooling, food delivery and freight shipping platforms -- often exhibit a bi-level structure. At the upper level, the platform sets prices for heterogeneous demand…
We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and…
Finding a low-weight multiple (LWPM) of a given polynomial is very useful in the cryptanalysis of stream ciphers and arithmetic in finite fields. There is no known deterministic polynomial time complexity algorithm for solving this problem,…
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…
Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…