相关论文: Several methods of analysis for cardinality constr…
We continue the study of two recently introduced bin packing type problems, called bin packing with clustering, and online bin packing with delays. A bin packing input consists of items of sizes not larger than 1, and the goal is to…
We analyze a recently introduced concept, called the price of clustering, for variants of bin packing called open-end bin packing problems (OEBP). Input items have sizes, and they also belong to a certain number of types. The new concept…
Cardinality constrained bin packing or bin packing with cardinality constraints is a basic bin packing problem. In the online version with the parameter k \geq 2, items having sizes in (0,1] associated with them are presented one by one to…
The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization…
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…
Bin packing with cardinality constraints is a bin packing problem where an upper bound k \geq 2 on the number of items packed into each bin is given, in addition to the standard constraint on the total size of items packed into a bin. We…
Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items,…
The problem considered is the splittable bin packing with cardinality constraint. It is a variant of the bin packing problem where items are allowed to be split into parts but the number of parts in each bin is at most a given upper bound.…
We develop new algorithmic methods with provable guarantees for feature selection in regard to categorical data clustering. While feature selection is one of the most common approaches to reduce dimensionality in practice, most of the known…
Traditionally, clustering algorithms focus on partitioning the data into groups of similar instances. The similarity objective, however, is not sufficient in applications where a fair-representation of the groups in terms of protected…
We consider the following generalization of the bin packing problem. We are given a set of items each of which is associated with a rational size in the interval [0,1], and a monotone non-decreasing non-negative cost function f defined over…
We consider the Bin Packing problem with a partition matroid constraint. The input is a set of items of sizes in $(0,1]$, and a partition matroid over the items. The goal is to pack all items in a minimum number of unit-size bins, such that…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…
We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size s_i \in [0,1] and a color c_i \in C, where C is a set…
We study here the semi-supervised $k$-clustering problem where information is available on whether pairs of objects are in the same or in different clusters. This information is either available with certainty or with a limited level of…
Bin Packing with Conflicts (BPC) are problems in which items with compatibility constraints must be packed in the least number of bins, not exceeding the capacity of the bins and ensuring that non-conflicting items are packed in each bin.…
We study the Min-Weighted Sum Bin Packing problem, a variant of the classical Bin Packing problem in which items have a weight, and each item induces a cost equal to its weight multiplied by the index of the bin in which it is packed. This…
The subset sum algorithm is a natural heuristic for the classical Bin Packing problem: In each iteration, the algorithm finds among the unpacked items, a maximum size set of items that fits into a new bin. More than 35 years after its first…
We study the problem of clustering a set of items based on bandit feedback. Each of the $n$ items is characterized by a feature vector, with a possibly large dimension $d$. The items are partitioned into two unknown groups such that items…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…