Related papers: Min-Sum Set Cover on Parallel Machines
Given a natural number $k\ge 2$, we consider the $k$-submodular cover problem ($k$-SC). The objective is to find a minimum cost subset of a ground set $\mathcal{X}$ subject to the value of a $k$-submodular utility function being at least a…
A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…
In the classic maximum coverage problem, we are given subsets $T_1, \dots, T_m$ of a universe $[n]$ along with an integer $k$ and the objective is to find a subset $S \subseteq [m]$ of size $k$ that maximizes $C(S) := |\cup_{i \in S} T_i|$.…
We study policies aiming to minimize the weighted sum of completion times of jobs in the context of coordination mechanisms for selfish scheduling problems. Our goal is to design local policies that achieve a good price of anarchy in the…
We consider a basic problem of preemptive scheduling of $n$ non-simultaneously released jobs on a group of $m$ unrelated parallel machines so as to minimize maximum job completion time, the makespan. In the scheduling literature, the…
We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…
In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…
This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing…
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…
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…
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…
We consider the problem of minimizing the total processing time of tardy jobs on a single machine. This is a classical scheduling problem, first considered by [Lawler and Moore 1969], that also generalizes the Subset Sum problem. Recently,…
We study the scheduling of jobs on a single parallel-batching machine with non-identical job sizes and incompatible job families. Jobs from the same family have the same processing time and can be loaded into a batch, as long as the batch…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
We consider the problem of scheduling jobs with equal lengths on uniform parallel batch machines with non-identical capacities where each job can only be processed on a specified subset of machines called its processing set. For the case of…
Machine scheduling problems involving conflict jobs can be seen as a constrained version of the classical scheduling problem, in which some jobs are conflict in the sense that they cannot be proceeded simultaneously on different machines.…
The "Subset Sum problem" is a very well-known NP-complete problem. In this work, a top-k variation of the "Subset Sum problem" is considered. This problem has wide application in recommendation systems, where instead of k best objects the k…
This paper mainly focuses on a resource leveling variant of a two-processor scheduling problem. The latter problem is to schedule a set of dependent UET jobs on two identical processors with minimum makespan. It is known to be…
Scheduling with testing is a recent online problem within the framework of explorable uncertainty motivated by environments where some preliminary action can influence the duration of a task. Jobs have an unknown processing time that can be…
We consider a parallel system of $m$ identical machines prone to unpredictable crashes and restarts, trying to cope with the continuous arrival of tasks to be executed. Tasks have different computational requirements (i.e., processing time…