Related papers: Improved Lower Bounds for Online Hypercube and Rec…
We first give an improved lower bound for the deterministic online simulation of tapes or pushdown stores by queues. Then we inspect some proofs in a classical work on queue machines in the area of Formal Languages and outline why a main…
In a recent paper, Brusco, K\"ohn and Steinley [Ann. Oper. Res. 206:611-626 (2013)] conjecture that the 2 bins special case of the one-dimensional minimax bin-packing problem with bin size constraints might be solvable in polynomial time.…
A frequently studied performance measure in online optimization is competitive analysis. It corresponds to the worst-case ratio, over all possible inputs of an algorithm, between the performance of the algorithm and the optimal offline…
Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and…
Object packing by autonomous robots is an im-portant challenge in warehouses and logistics industry. Most conventional data-driven packing planning approaches focus on regular cuboid packing, which are usually heuristic and limit the…
We use computational experiments to find the rectangles of minimum area into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. Most of the packings found have…
Consider a storage area where arriving items are stored temporarily in bounded capacity stacks until their departure. We look into the problem of deciding where to put an arriving item with the objective of minimizing the maximum number of…
We explore a novel theoretical model for studying the performance of distributed storage management systems where the data-centers have limited capacities (as compared to storage space requested by the users). Prior schemes such as…
We study the following problem, introduced by Chung et al. in 2006. We are given, online or offline, a set of coloured items of different sizes, and wish to pack them into bins of equal size so that we use few bins in total (at most…
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…
An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemer\'edi proved that any on-line algorithm could be forced to use…
As e-commerce expands, delivering real-time personalized recommendations from vast catalogs poses a critical challenge for retail platforms. Maximizing revenue requires careful consideration of both individual customer characteristics and…
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…
We consider the online vector packing problem in which we have a $d$ dimensional knapsack and items $u$ with weight vectors $\mathbf{w}_u \in \mathbb{R}_+^d$ arrive online in an arbitrary order. Upon the arrival of an item, the algorithm…
We explore approximation algorithms for the $d$-dimensional geometric bin packing problem ($d$BP). Caprara (MOR 2008) gave a harmonic-based algorithm for $d$BP having an asymptotic approximation ratio (AAR) of $T_{\infty}^{d-1}$ (where…
Recent progress in the field of robotic manipulation has generated interest in fully automatic object packing in warehouses. This paper proposes a formulation of the packing problem that is tailored to the automated warehousing domain.…
Optimization problems is one of the most challenging applications of quantum computers, as well as one of the most relevants. As a consequence, it has attracted huge efforts to obtain a speedup over classical algorithms using quantum…
We explore the fundamental limits of distributed balls-into-bins algorithms. We present an adaptive symmetric algorithm that achieves a bin load of two in log* n+O(1) communication rounds using O(n) messages in total. Larger bin loads can…
In recent years, the throughput requirements of e-commerce fulfillment warehouses have seen a steep increase. This has resulted in various automation solutions being developed for item picking and movement. In this paper, we address the…
With the rapid development of digital information, the data volume generated by humans and machines is growing exponentially. Along with this trend, machine learning algorithms have been formed and evolved continuously to discover new…