Related papers: Verified Approximation Algorithms
Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on…
This paper presents pragmatic solutions for verifying complex mathematical algorithms implemented in hardware in an efficient and effective manner. Maximizing leverage of a known-answer-test strategy, based on predefined data scenarios…
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm…
We investigate {\em multidimensional covering mechanism-design} problems, wherein there are $m$ items that need to be covered and $n$ agents who provide covering objects, with each agent $i$ having a private cost for the covering objects he…
Designing and analyzing algorithms with provable performance guarantees enables efficient optimization problem solving in different application domains, e.g.\ communication networks, transportation, economics, and manufacturing. Despite the…
We consider several extensions of the fractional bin packing problem, a relaxation of the traditional bin packing problem where the objects may be split across multiple bins. In these extensions, we introduce load-balancing constraints…
In the recent paper \cite{BDT10} we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a "good and fast" packing or…
Optimal packing of objects in containers is a critical problem in various real-life and industrial applications. This paper investigates the two-dimensional packing of convex polygons without rotations, where only translations are allowed.…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
We propose a novel proof technique that can be applied to attack a broad class of problems in computational complexity, when switching the order of universal and existential quantifiers is helpful. Our approach combines the standard min-max…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
Finding a minimum vertex cover in a network is a fundamental NP-complete graph problem. One way to deal with its computational hardness, is to trade the qualitative performance of an algorithm (allowing non-optimal outputs) for an improved…
In this paper we show that the problem of identifying an edge $(i,j)$ in a graph $G$ such that there exists an optimal vertex cover $S$ of $G$ containing exactly one of the nodes $i$ and $j$ is NP-hard. Such an edge is called a weak edge.…
An important area of combinatorial optimization is the study of packing and covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering. Those problems have been studied extensively from the viewpoint of approximation…
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and…
Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class. In this paper, we first investigate some organizations of…
In this paper we will be concerned with a class of packing and covering problems which includes Vertex Cover and Independent Set. Typically, one can write an LP relaxation and then round the solution. In this paper, we explain why the…
We study the approximability of the NP-complete \textsc{Maximum Minimal Feedback Vertex Set} problem. Informally, this natural problem seems to lie in an intermediate space between two more well-studied problems of this type:…
We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement…
The efficiency of modern optimization methods, coupled with increasing computational resources, has led to the possibility of real-time optimization algorithms acting in safety critical roles. There is a considerable body of mathematical…