Related papers: Online Circle and Sphere Packing
We show an asymptotic 2/3-competitive strategy for the bin covering problem using O(b+log n) bits of advice, where b is the number of bits used to encode a rational value and n is the length of the input sequence.
We study a generalization of the advice complexity model of online computation in which the advice is provided by an untrusted source. Our objective is to quantify the impact of untrusted advice so as to design and analyze online algorithms…
Balanced circular bin packing problems consist in positioning a given number of weighted circles in order to minimize the radius of a circular container while satisfying equilibrium constraints. These problems are NP-hard, highly…
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…
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to…
In \emph{Online Sorting}, an array of $n$ initially empty cells is given. At each time step $t$, an element $x_t \in [0,1]$ arrives and must be placed irrevocably into an empty cell without any knowledge of future arrivals. We aim to…
Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. When these systems are confined their structural properties…
In the conventional cloud service model, computing resources are allocated for tenants on a pay-per-use basis. However, the performance of applications that communicate inside this network is unpredictable because network resources are not…
We study the online facility assignment problem on regular polygons, where all sides are of equal length. The influence of specific geometric settings has remained mostly unexplored, even though classical online facility assignment problems…
We study a wholesale supply chain ordering problem. In this problem, the supplier has an initial stock, and faces an unpredictable stream of incoming orders, making real-time decisions on whether to accept or reject each order. What makes…
The problem of packing unequal circles into a circular container stands as a classic and challenging optimization problem in computational geometry. This study introduces a suite of innovative and efficient methods to tackle this problem.…
We study the packing of a large number of congruent and non--overlapping circles inside a regular polygon. We have devised efficient algorithms that allow one to generate configurations of $N$ densely packed circles inside a regular polygon…
In online unit clustering, points of a metric space arriving one by one must be partitioned into clusters of diameter at most 1, where the cost is the number of clusters. This paper gives linear upper and lower bounds on the advice…
We examine packing of $n$ congruent spheres in a cube when $n$ is close but less than the number of spheres in a regular cubic close-packed (ccp) arrangement of $\lceil p^{3}/2\rceil$ spheres. For this family of packings, the previous…
We present an algorithm for computing upper bounds for the Online Bin Stretching Problem with a small number of bins and the resulting upper bounds for 4, 5 and 6 bins. This both demonstrates the possibility of using computer search for…
This paper presents theoretical and practical results for the bin packing problem with scenarios, a generalization of the classical bin packing problem which considers the presence of uncertain scenarios, of which only one is realized. For…
We address the NP-hard problem of finding a non-overlapping dense packing pattern for n Unequal Circle items in a two-dimensional Square Container (PUC-SC) such that the size of the container is minimized. Based on our previous work on an…
Online algorithms that allow a small amount of migration or recourse have been intensively studied in the last years. They are essential in the design of competitive algorithms for dynamic problems, where objects can also depart from the…
Motivated by bursty bandwidth allocation and by the allocation of virtual machines to servers in the cloud, we consider the online problem of packing items with random sizes into unit-capacity bins. Items arrive sequentially, but upon…
We provide a tight result for a fundamental problem arising from packing squares into a circular container: The critical density of packing squares into a disk is $\delta=\frac{8}{5\pi}\approx 0.509$. This implies that any set of (not…