Related papers: Improved Online Square-into-Square Packing
We give an $O(\log\log k)$-competitive randomized online algorithm for reordering buffer management, where $k$ is the buffer size. Our bound matches the lower bound of Adamaszek et al. (STOC 2011). Our algorithm has two stages which are…
The problem of packing equal circles in a circle is a classic and famous packing problem, which is well-studied in academia and has a variety of applications in industry. This problem is computationally challenging, and researchers mainly…
Online algorithm is a well-known computational model. We introduce quantum online algorithms and investigate them with respect to a competitive ratio in two points of view: space complexity and advice complexity. We start with exploring a…
We propose a Deep Reinforcement Learning (Deep RL) algorithm for solving the online 3D bin packing problem for an arbitrary number of bins and any bin size. The focus is on producing decisions that can be physically implemented by a robotic…
In the (1-dimensional) bin packing problem, we are asked to pack all the given items into bins, each of capacity one, so that the number of non-empty bins is minimized. Zhu~[Chaos, Solitons \& Fractals 2016] proposed an approximation…
Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains…
We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…
In the paper, we consider the problem of searching for the Largest empty rectangle in a 2D map, and the one-dimensional version of the problem is the problem of searching for the largest empty segment. We present a quantum algorithm for the…
This work studies online scheduling algorithms for buffer management, develops new algorithms, and analyzes their performances. Packets arrive at a release time r, with a non-negative weight w and an integer deadline d. At each time step,…
In this paper, we explicitly study the online vertex cover problem, which is a natural generalization of the well-studied ski-rental problem. In the online vertex cover problem, we are required to maintain a monotone vertex cover in a graph…
In this paper, we propose an efficient clustering technique to solve the problem of clustering in the presence of obstacles. The proposed algorithm divides the spatial area into rectangular cells. Each cell is associated with statistical…
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 online knapsack problem is a classic online resource allocation problem in networking and operations research. Its basic version studies how to pack online arriving items of different sizes and values into a capacity-limited knapsack.…
We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…
In the Two-Bar Charts Packing Problem (2-BCPP), it is required to pack the bar charts (BCs) consisting of two bars into the horizontal unit-height strip of minimal length. The bars may move vertically within the strip, but it is forbidden…
In this paper we improve the approximation ratio for the problem of scheduling packets on line networks with bounded buffers, where the aim is that of maximizing the throughput. Each node in the network has a local buffer of bounded size…
In this paper we present a theoretical analysis of the deterministic on-line {\em Sum of Squares} algorithm ($SS$) for bin packing introduced and studied experimentally in \cite{CJK99}, along with several new variants. $SS$ is applicable to…
We consider a Two-Bar Charts Packing Problem (2-BCPP), in which it is necessary to pack two-bar charts (2-BCs) in a unit-height strip of minimum length. The problem is a generalization of the Bin Packing Problem (BPP). Earlier, we proposed…
A polyomino is a polygonal region with axis parallel edges and corners of integral coordinates, which may have holes. In this paper, we consider planar tiling and packing problems with polyomino pieces and a polyomino container $P$. We give…
We consider a variant of online convex optimization in which both the instances (input vectors) and the comparator (weight vector) are unconstrained. We exploit a natural scale invariance symmetry in our unconstrained setting: the…