Related papers: Approximating the Geometric Knapsack Problem in Ne…
We present fully dynamic approximation algorithms for the Maximum Independent Set problem on several types of geometric objects: intervals on the real line, arbitrary axis-aligned squares in the plane and axis-aligned $d$-dimensional…
The stochastic knapsack problem is the stochastic variant of the classical knapsack problem in which the algorithm designer is given a a knapsack with a given capacity and a collection of items where each item is associated with a profit…
We study the generalized multidimensional bin packing problem (GVBP) that generalizes both geometric packing and vector packing. Here, we are given $n$ rectangular items where the $i^{\textrm{th}}$ item has width $w(i)$, height $h(i)$, and…
Efficiently computing accurate representations of high-dimensional data is essential for data analysis and unsupervised learning. Dendrograms, also known as ultrametrics, are widely used representations that preserve hierarchical…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
In the stochastic knapsack problem, we are given a knapsack of size B, and a set of jobs whose sizes and rewards are drawn from a known probability distribution. However, we know the actual size and reward only when the job completes. How…
We study pseudo-polynomial time algorithms for the fundamental \emph{0-1 Knapsack} problem. In terms of $n$ and $w_{\max}$, previous algorithms for 0-1 Knapsack have cubic time complexities: $O(n^2w_{\max})$ (Bellman 1957), $O(nw_{\max}^2)$…
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…
This work proposes an efficient parallel algorithm for non-monotone submodular maximization under a knapsack constraint problem over the ground set of size $n$. Our algorithm improves the best approximation factor of the existing parallel…
In the bottleneck multiple knapsack problem, we are given a set of items and a set of knapsacks, where each item has a profit and a weight, and each knapsack has a capacity. Our goal is to assign items to knapsacks so as to maximize the…
We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the…
Multidimensional packing problems generalize the classical packing problems such as Bin Packing, Multiprocessor Scheduling by allowing the jobs to be $d$-dimensional vectors. While the approximability of the scalar problems is well…
We give new sublinear and parallel algorithms for the extensively studied problem of approximating n-variable r-CSPs (constraint satisfaction problems with constraints of arity r up to an additive error. The running time of our algorithms…
In the Maximum Independent Set of Hyperrectangles problem, we are given a set of $n$ (possibly overlapping) $d$-dimensional axis-aligned hyperrectangles, and the goal is to find a subset of non-overlapping hyperrectangles of maximum…
In this paper we consider the discounted 0-1 knapsack problem (DKP), which is an extension of the classical knapsack problem where a set of items is decomposed into groups of three items. At most one item can be chosen from each group and…
We investigate the classic Knapsack problem and propose a fully polynomial-time approximation scheme (FPTAS) that runs in $\widetilde{O}(n + (1/\varepsilon)^2)$ time. This improves upon the $\widetilde{O}(n + (1/\varepsilon)^{11/5})$-time…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
In this paper, we investigate the parametric knapsack problem, in which the item profits are affine functions depending on a real-valued parameter. The aim is to provide a solution for all values of the parameter. It is well-known that any…