Related papers: An approximation notion between P and FPTAS
We study the budgeted versions of the well known matching and matroid intersection problems. While both problems admit a polynomial-time approximation scheme (PTAS) [Berger et al. (Math. Programming, 2011), Chekuri, Vondrak and Zenklusen…
In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
In this paper we study the classical scheduling problem of minimizing the total weighted completion time on a single machine with the constraint that one specific job must be scheduled at a specified position. We give dynamic programs with…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Recently, there has been increasing interest and progress in improvising the approximation algorithm for well-known NP-Complete problems, particularly the approximation algorithm for the Vertex-Cover problem. Here we have proposed a…
In this paper, we introduce a method for approximating the solution to inference and optimization tasks in uncertain and deterministic reasoning. Such tasks are in general intractable for exact algorithms because of the large number of…
Rational and neural network based approximations are efficient tools in modern approximation. These approaches are able to produce accurate approximations to nonsmooth and non-Lipschitz functions, including multivariate domain functions. In…
In this paper we consider single machine scheduling problems with additional non-renewable resource constraints. Examples for non-renewable resources include raw materials, energy, or money. Usually they have an initial stock and…
We consider scheduling on identical and unrelated parallel machines with job assignment restrictions. These problems are NP-hard and they do not admit polynomial time approximation algorithms with approximation ratios smaller than $1.5$…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods…
The minimization problem for propositional formulas is an important optimization problem in the second level of the polynomial hierarchy. In general, the problem is Sigma-2-complete under Turing reductions, but restricted versions are…
Assuming that P is not equal to NP, the worst-case run time of any algorithm solving an NP-complete problem must be super-polynomial. But what is the fastest run time we can get? Before one can even hope to approach this question, a more…
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…
Binary optimisation tasks are ubiquitous in areas ranging from logistics to cryptography. The exponential complexity of such problems means that the performance of traditional computational methods decreases rapidly with increasing problem…
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…
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…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…