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We give a deterministic, polynomial-time algorithm for approximately counting the number of {0,1}-solutions to any instance of the knapsack problem. On an instance of length n with total weight W and accuracy parameter eps, our algorithm…
We consider a special case of the ordinary NP-hard two-machine flow shop problem with the objective of determining simultaneously a minimal common due date and the minimal number of tardy jobs. In [S. S. Panwalkar, C. Koulamas, An O(n^2)…
In the Time-Windows Unsplittable Flow on a Path problem (twUFP) we are given a resource whose available amount changes over a given time interval (modeled as the edge-capacities of a given path $G$) and a collection of tasks. Each task is…
We provide faster strongly polynomial time algorithms solving maximum flow in structured $n$-node $m$-arc networks. Our results imply an $n^{\omega + o(1)}$-time strongly polynomial time algorithms for computing a maximum bipartite…
We consider the $\mathcal{NP}$-hard problem $\mathrm{P} \mathbf{\vert} \mathrm{pmtn, setup=s_i} \mathbf{\vert} \mathrm{C_{\max}}$, the problem of scheduling $n$ jobs, which are divided into $c$ classes, on $m$ identical parallel machines…
As a hybrid of the Parallel Two-stage Flowshop problem and the Multiple Knapsack problem, we investigate the scheduling of parallel two-stage flowshops under makespan constraint, which was motivated by applications in cloud computing and…
In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the…
We consider the problem of online preemptive scheduling on a single machine to minimize the total flow time. In clairvoyant scheduling, where job processing times are revealed upon arrival, the Shortest Remaining Processing Time (SRPT)…
Algorithms with predictions is a recent framework that has been used to overcome pessimistic worst-case bounds in incomplete information settings. In the context of scheduling, very recent work has leveraged machine-learned predictions to…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
We study the classical problem of minimizing the total weighted completion time on a fixed set of $m$ identical machines working in parallel, the $Pm||\sum w_jC_j$ problem in the standard three field notation for scheduling problems. This…
We consider the robust permutation flowshop problem under the budgeted uncertainty model, where at most a given number of job processing times may deviate on each machine. We show that solutions for this problem can be determined by solving…
We devise a polynomial-time approximation scheme for the classical geometric problem of finding an approximate short path amid weighted regions. In this problem, a triangulated region P comprising of n vertices, a positive weight associated…
Motivated by modern parallel computing applications, we consider the problem of scheduling parallel-task jobs with heterogeneous resource requirements in a cluster of machines. Each job consists of a set of tasks that can be processed in…
We introduce the notion of {\em fair cuts} as an approach to leverage approximate $(s,t)$-mincut (equivalently $(s,t)$-maxflow) algorithms in undirected graphs to obtain near-linear time approximation algorithms for several cut problems.…
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…
We consider a classical scheduling problem on $m$ identical machines. For an arbitrary constant $q>1$, the aim is to assign jobs to machines such that $\sum_{i=1}^m C_i^q$ is minimized, where $C_i$ is the total processing time of jobs…
Datacenter networks commonly facilitate the transmission of data in distributed computing frameworks through coflows, which are collections of parallel flows associated with a common task. Most of the existing research has concentrated on…
In the restricted assignment problem, the input consists of a set of machines and a set of jobs each with a processing time and a subset of eligible machines. The goal is to find an assignment of the jobs to the machines minimizing the…
Coflow is a recently proposed network abstraction for data-parallel computing applications. This paper considers scheduling coflows with precedence constraints in identical parallel networks, such as to minimize the total weighted…