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The potential harms of algorithmic decisions have ignited algorithmic fairness as a central topic in computer science. One of the fundamental problems in computer science is Set Cover, which has numerous applications with societal impacts,…
Generalizing many well-known and natural scheduling problems, scheduling with job-specific cost functions has gained a lot of attention recently. In this setting, each job incurs a cost depending on its completion time, given by a private…
The minimum linear ordering problem (MLOP) generalizes well-known combinatorial optimization problems such as minimum linear arrangement and minimum sum set cover. MLOP seeks to minimize an aggregated cost $f(\cdot)$ due to an ordering…
We consider the machine covering problem for selfish related machines. For a constant number of machines, m, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a…
We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…
In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In…
We introduce a natural but seemingly yet unstudied generalization of the problem of scheduling jobs on a single machine so as to minimize the number of tardy jobs. Our generalization lies in simultaneously considering several instances of…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$,…
Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…
We investigate a single machine rescheduling problem that arises from an unexpected machine unavailability, after the given set of jobs has already been scheduled to minimize the total weighted completion time. Such a disruption is…
Apart from the principles and methodologies inherited from Economics and Game Theory, the studies in Algorithmic Mechanism Design typically employ the worst-case analysis and approximation schemes of Theoretical Computer Science. For…
The (Non-Preemptive) Throughput Maximization problem is a natural and fundamental scheduling problem. We are given $n$ jobs, where each job $j$ is characterized by a processing time and a time window, contained in a global interval $[0,T)$,…
This paper discusses the graph covering problem in which a set of edges in an edge- and node-weighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large…
We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$.…
This paper resolves a long-standing open question in bicriteria scheduling regarding the complexity of a single machine scheduling problem which combines the number of tardy jobs and the maximal tardiness criteria. We use the lexicographic…
Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set…
An optimal solution to the problem of scheduling real-time tasks on a set of identical processors is derived. The described approach is based on solving an equivalent uniprocessor real-time scheduling problem. Although there are other…
Time-dependent scheduling with linear deterioration involves determining when to execute jobs whose processing times degrade as their beginning is delayed. Each job i is associated with a release time r_i and a processing time function…
This paper addresses a new variant of the multi-trip single vehicle routing problem where the nodes are related to each other through AND-type precedence constraints. The problem aims at determining a sequence of trips to visit all the…