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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…
We study classic scheduling problems on uniformly related machines. Efficient polynomial time approximation schemes (EPTAS's) are fast and practical approximation schemes. New methods and techniques are essential in developing such improved…
In approximating solutions of nonstationary problems, various approaches are used to compute the solution at a new time level from a number of simpler (sub-)problems. Among these approaches are splitting methods. Standard splitting schemes…
A bilevel program is an optimization problem whose constraints involve another optimization problem. This paper studies bilevel polynomial programs (BPPs), i.e., all the functions are polynomials. We reformulate BPPs equivalently as…
In theory, hierarchies of semidefinite programming (SDP) relaxations based on sum of squares (SOS) polynomials have been shown to provide arbitrarily close approximations for a general polynomial optimization problem (POP). However, due to…
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for…
Current state-of-the-art solvers for mixed-integer programming (MIP) problems are designed to perform well on a wide range of problems. However, for many real-world use cases, problem instances come from a narrow distribution. This has…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted…
We investigate the scheduling of $n$ jobs divided into $c$ classes on $m$ identical parallel machines. For every class there is a setup time which is required whenever a machine switches from the processing of one class to another class.…
The well-known sequentially lifted cover inequality is widely employed in solving mixed integer programs. However, it is still an open question whether a sequentially lifted cover inequality can be computed in polynomial time for a given…
In this work, we systematically examine the application of spatio-temporal splitting heuristics to the Multi-Robot Motion Planning (MRMP) problem in a graph-theoretic setting: a problem known to be NP-hard to optimally solve. Following the…
This report considers a sporadic real-time task system with $n$ sporadic tasks on a uniprocessor platform, in which the lowest-priority task is a segmented self-suspension task and the other higher-priority tasks are ordinary sporadic…
Project scheduling in manufacturing environments often requires flexibility in terms of the selection and the exact length of alternative production activities. Moreover, the simultaneous scheduling of multiple lots is mandatory in many…
Vertex Subset Problems (VSPs) are a class of combinatorial optimization problems on graphs where the goal is to find a subset of vertices satisfying a predefined condition. Two prominent approaches for solving VSPs are dynamic programming…
In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are…
The facilitated simple exclusion process (FEP) is a one-dimensional exclusion process with a dynamical constraint. We establish bounds on the mixing time of the FEP on the segment, with closed boundaries, and the circle. The FEP on these…
This paper considers a recoverable robust single-machine scheduling problem under polyhedral uncertainty with the objective of minimising the total flow time. In this setting, a decision-maker must determine a first-stage schedule subject…
Modern vertical take-off and landing vehicles (VTOLs) could significantly affect the future of mobility. The broad range of their application fields encompasses urban air mobility, transportation and logistics as well as reconnaissance and…
We analyze a class of high performance, low decoding-data-flow error-correcting codes suitable for high bit-rate optical-fiber communication systems. A spatially-coupled split-component ensemble is defined, generalizing from the most…