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The Makespan Scheduling problem is an extensively studied NP-hard problem, and its simplest version looks for an allocation approach for a set of jobs with deterministic processing times to two identical machines such that the makespan is…
We consider a single machine scheduling problem that seeks to minimize a generalized cost function: given a subset of jobs we must order them so as to minimize $\sum f_j(C_j)$, where $C_j$ is the completion time of job $j$ and $f_j$ is a…
We study ordinal makespan scheduling on small numbers of identical machines, with respect to two parallel solutions. In ordinal scheduling, it is known that jobs are sorted by non-increasing sizes, but the specific sizes are not known in…
We study the restricted case of Scheduling on Unrelated Parallel Machines. In this problem, we are given a set of jobs $J$ with processing times $p_j$ and each job may be scheduled only on some subset of machines $S_j \subseteq M$. The goal…
Makespan minimization on parallel identical machines is a classical and intensively studied problem in scheduling, and a classic example for online algorithm analysis with Graham's famous list scheduling algorithm dating back to the 1960s.…
Consider the many shared resource scheduling problem where jobs have to be scheduled on identical parallel machines with the goal of minimizing the makespan. However, each job needs exactly one additional shared resource in order to be…
We consider a natural generalization of scheduling $n$ jobs on $m$ parallel machines so as to minimize the makespan. In our extension the set of jobs is partitioned into several classes and a machine requires a setup whenever it switches…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
The Map-Reduce computing framework rose to prominence with datasets of such size that dozens of machines on a single cluster were needed for individual jobs. As datasets approach the exabyte scale, a single job may need distributed…
We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of $2$ and $\min\{m-k+1,…
We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that…
We consider the classic problem of scheduling jobs with precedence constraints on a set of identical machines to minimize the makespan objective function. Understanding the exact approximability of the problem when the number of machines is…
We consider a scheduling problem of strategic agents representing jobs of different weights. Each agent has to decide on one of a finite set of identical machines to get their job processed. In contrast to the common and exclusive focus on…
We consider hypergraphs on vertices $P\cup R$ where each hyperedge contains exactly one vertex in $P$. Our goal is to select a matching that covers all of $P$, but we allow each selected hyperedge to drop all but an $(1/\alpha)$-fraction of…
We study approximation algorithms for the problem of minimizing the makespan on a set of machines with uncertainty on the processing times of jobs. In the model we consider, which goes back to~\cite{BertsimasS03}, once the schedule is…
Makespan minimization on unrelated machines is a classic problem in approximation algorithms. No polynomial time $(2-\delta)$-approximation algorithm is known for the problem for constant $\delta> 0$. This is true even for certain special…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
We study a fair resource scheduling problem, where a set of interval jobs are to be allocated to heterogeneous machines controlled by agents. Each job is associated with release time, deadline, and processing time such that it can be…
Assigning jobs onto identical machines with the objective to minimize the maximal load is one of the most basic problems in combinatorial optimization. Motivated by product planing and data placement, we study a natural extension called…
In many fundamental combinatorial optimization problems, a feasible solution induces some real cost vectors as an intermediate result, and the optimization objective is a certain function of the vectors. For example, in the problem of…