Related papers: Hardness of SetCover Reoptimization
We present new approximation schemes for bin packing based on the following two approaches: (1) partitioning the given problem into mostly identical sub-problems of constant size and then construct a solution by combining the solutions of…
Parallel machine scheduling has been extensively studied in the past decades, with applications ranging from production planning to job processing in large computing clusters. In this work we study some of these fundamental optimization…
Adaptive loss function formulation is an active area of research and has gained a great deal of popularity in recent years, following the success of deep learning. However, existing frameworks of adaptive loss functions often suffer from…
Model compression has gained a lot of attention due to its ability to reduce hardware resource requirements significantly while maintaining accuracy of DNNs. Model compression is especially useful for memory-intensive recurrent neural…
We consider the following geometric optimization problem: Given $ n $ axis-aligned rectangles in the plane, the goal is to find a set of horizontal segments of minimum total length such that each rectangle is stabbed. A segment stabs a…
We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…
In this paper, we prove that it is W[2]-hard to approximate k-SetCover within any constant ratio. Our proof is built upon the recently developed threshold graph composition technique. We propose a strong notion of threshold graphs and use a…
In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…
Quantization is one of the core components in lossy image compression. For neural image compression, end-to-end optimization requires differentiable approximations of quantization, which can generally be grouped into three categories:…
Partial Set Cover (PSC) is a generalization of the well-studied Set Cover problem (SC). In PSC the input consists of an integer $k$ and a set system $(U,S)$ where $U$ is a finite set, and $S \subseteq 2^U$ is a collection of subsets of $U$.…
We carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the {\sc Test Cover} problem we are given a set $[n]=\{1,...,n\}$ of items together…
Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the…
This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface,…
Several algorithms with an approximation guarantee of $O(\log n)$ are known for the Set Cover problem, where $n$ is the number of elements. We study a generalization of the Set Cover problem, called the Partition Set Cover problem. Here,…
We study set selection problems where the weights are uncertain. Instead of its exact weight, only an uncertainty interval containing its true weight is available for each element. In some cases, some solutions are universally optimal;…
We study a geometric hitting-set problem in which the input consists of a set $P$ of weighted points and a family $S=H\cup V$ of axis-parallel segments in the plane. The goal is to select a minimum-weight subset of $P$ that hits every…
In this paper, we study a method for finding robust solutions to multiobjective optimization problems under uncertainty. We follow the set-based minmax approach for handling the uncertainties which leads to a certain set optimization…
We consider the SUBSET SUM problem and its important variants in this paper. In the SUBSET SUM problem, a (multi-)set $X$ of $n$ positive numbers and a target number $t$ are given, and the task is to find a subset of $X$ with the maximal…
We consider a natural variant of the well-known Feedback Vertex Set problem, namely the problem of deleting a small subset of vertices or edges to a full binary tree. This version of the problem is motivated by real-world scenarios that are…
State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…