Related papers: On bin packing with clustering and bin packing wit…
We improve the lower bound on the asymptotic competitive ratio of any online algorithm for bin packing to above 1.54278. We demonstrate for the first time the advantage of branching and the applicability of full adaptivity in the design of…
Consider the classical Bin Packing problem with $d$ different item sizes $s_i$ and amounts of items $a_i.$ The support of a Bin Packing solution is the number of differently filled bins. In this work, we show that the lower bound on the…
In package-handling facilities, boxes of varying sizes are used to ship products. Improperly sized boxes with box dimensions much larger than the product dimensions create wastage and unduly increase the shipping costs. Since it is…
This paper focuses on exact approaches for the Colored Bin Packing Problem (CBPP), a generalization of the classical one-dimensional Bin Packing Problem in which each item has, in addition to its length, a color, and no two items of the…
We consider the offline sorting buffer problem. The input is a sequence of items of different types. All items must be processed one by one by a server. The server is equipped with a random-access buffer of limited capacity which can be…
We revisit the online Unit Clustering and Unit Covering problems in higher dimensions: Given a set of $n$ points in a metric space, that arrive one by one, Unit Clustering asks to partition the points into the minimum number of clusters…
We consider the {\em clustering with diversity} problem: given a set of colored points in a metric space, partition them into clusters such that each cluster has at least $\ell$ points, all of which have distinct colors. We give a…
We study an extension of the classical Bin Packing Problem, where each item consumes the bin capacity during a given time window that depends on the item itself. The problem asks for finding the minimum number of bins to pack all the items…
Motivated by distribution problems arising in the supply chain of Haleon, we investigate a discrete optimization problem that we call the "container delivery scheduling problem". The problem models a supplier dispatching ordered products…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
The optimal binning is the optimal discretization of a variable into bins given a discrete or continuous numeric target. We present a rigorous and extensible mathematical programming formulation for solving the optimal binning problem for a…
We consider the problem of online min-cost perfect matching with concave delays. We begin with the single location variant. Specifically, requests arrive in an online fashion at a single location. The algorithm must then choose between…
Bin packing problem examines the minimum number of identical bins needed to pack a set of items of various weights. This problem arises in various areas of the artificial intelligence demanding derivation of the exact solutions in the…
Fast and high quality document clustering is an important task in organizing information, search engine results obtaining from user query, enhancing web crawling and information retrieval. With the large amount of data available and with a…
At modern warehouses, mobile robots transport packages and drop them into collection bins/chutes based on shipping destinations grouped by, e.g., the ZIP code. System throughput, measured as the number of packages sorted per unit of time,…
Developing technology and changing lifestyles have made online grocery delivery applications an indispensable part of urban life. Since the beginning of the COVID-19 pandemic, the demand for such applications has dramatically increased,…
Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum…
Following an orginal idea by Kn\"odel, an online bin-packing problem is considered where the the large items arrive in double-packs. The dual problem where the small items arrive in double-packs is also considered. The enumerations have a…
$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…
This paper considers the problem of evaluating clusterings of very large populations of items. Given two clusterings, namely a Baseline clustering and an Experiment clustering, the tasks are twofold: 1) characterize their differences, and…