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Makespan scheduling on identical machines is one of the most basic and fundamental packing problems studied in the discrete optimization literature. It asks for an assignment of $n$ jobs to a set of $m$ identical machines that minimizes the…
We develop a framework for obtaining polynomial time approximation schemes (PTAS) for a class of stochastic dynamic programs. Using our framework, we obtain the first PTAS for the following stochastic combinatorial optimization problems:…
Many combinatorial optimisation problems can be modelled as valued constraint satisfaction problems. In this paper, we present a polynomial-time algorithm solving the valued constraint satisfaction problem for a fixed number of variables…
This research addresses the multiprocessor scheduling problem of hard real-time systems, and it especially focuses on optimal and global schedulers when practical constraints are taken into account. First, we propose an improvement of the…
Independent set is a fundamental problem in combinatorial optimization. While in general graphs the problem is essentially inapproximable, for many important graph classes there are approximation algorithms known in the offline setting.…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…
Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in…
Dominating Set is a well-known combinatorial optimization problem which finds application in computational biology or mobile communication. Because of its $\mathrm{NP}$-hardness, one often turns to heuristics for good solutions. Many such…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
In this paper, we consider the problem of choosing a minimum cost set of resources for executing a specified set of jobs. Each input job is an interval, determined by its start-time and end-time. Each resource is also an interval determined…
We present a dynamic programming algorithm for selecting a representative subset of size $k$ from a given set with $n$ points such that the Riesz $s$-energy is near minimized. While NP-hard in general dimensions, the one-dimensional case…
Weakly hard real-time systems can, to some degree, tolerate deadline misses, but their schedulability still needs to be analyzed to ensure their quality of service. Such analysis usually occurs at early design stages to provide…
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…
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…
We study scheduling problems motivated by recently developed techniques for microprocessor thermal management at the operating systems level. The general scenario can be described as follows. The microprocessor's temperature is controlled…
The emergence of Big Data has enabled new research perspectives in the discrete choice community. While the techniques to estimate Machine Learning models on a massive amount of data are well established, these have not yet been fully…
Healthcare systems are facing serious challenges in balancing their human resources to cope with volatile service demand, while at the same time providing necessary job satisfaction to the healthcare workers. We propose in this paper a…
Optimization is an important module of modern machine learning applications. Tremendous efforts have been made to accelerate optimization algorithms. A common formulation is achieving a lower loss at a given time. This enables a…
In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different…
Real-time end-to-end task scheduling in networked control systems (NCSs) requires the joint consideration of both network and computing resources to guarantee the desired quality of service (QoS). This paper introduces a new model for…