Related papers: Min-Sum Set Cover on Parallel Machines
We study the problem of minimizing total completion time on parallel machines subject to varying processing capacity. In this paper, we develop an approximation scheme for the problem under the data stream model where the input data is…
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 $[0,T)$,…
In this paper, we study a class of set cover problems that satisfy a special property which we call the {\em small neighborhood cover} property. This class encompasses several well-studied problems including vertex cover, interval cover,…
We investigate deterministic non-preemptive online scheduling with delayed commitment for total completion time minimization on parallel identical machines. In this problem, jobs arrive one-by-one and their processing times are revealed…
We study the \textit{min-sum uniform coverage} problem for a swarm of $n$ mobile robots on a given finite line segment and on a circle having finite positive radius, where the circle is given as an input. The robots must coordinate their…
In a classical covering problem, we are given a set of requests that we need to satisfy (fully or partially), by buying a subset of items at minimum cost. For example, in the k-MST problem we want to find the cheapest tree spanning at least…
In this paper, we consider an NP-hard problem of scheduling a set of jobs of equal processing time on two machines, given a partial precedence order on the set of jobs, with an objective to minimize the makespan. An approximation algorithm…
We consider the problem of scheduling multiprocessor jobs to minimize the total completion time under the given energy budget. Each multiprocessor job requires more than one processor at the same moment of time. Processors may operate at…
We study the classic problem of minimizing the expected total completion time of jobs on $m$ identical machines in the setting where the sizes of the jobs are stochastic. Specifically, the size of each job is a random variable whose…
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…
We consider non-preemptive scheduling of MapReduce jobs with multiple tasks in the practical scenario where each job requires several map-reduce rounds. We seek to minimize the average weighted completion time and consider scheduling on…
Motivated by applications in energy-efficient scheduling in data centers, Khuller, Li, and Saha introduced the {\em machine activation} problem as a generalization of the classical optimization problems of set cover and load balancing on…
Sorting is one of the fundamental problems in computer science. Playing a role in many processes, it has a lower complexity bound imposed by $\mathcal{O}(n\log{n})$ when executing on a sequential machine. This limit can be brought down to…
In this work, we study the computational (parameterized) complexity of $P \mid r_j, p_j=p \mid \sum_j w_j U_j$. Here, we are given $m$ identical parallel machines and $n$ jobs with equal processing time, each characterized by a release…
We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…
Over the past few years, self-attention is shining in the field of deep learning, especially in the domain of natural language processing(NLP). Its impressive effectiveness, along with ubiquitous implementations, have aroused our interest…
In this work we revisit the elementary scheduling problem $1||\sum p_j U_j$. The goal is to select, among $n$ jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence…
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…
We consider the offline sorting buffer problem. The input is a sequence of items of different types. All items must be processed one by one by a server. The server is equipped with a random-access buffer of limited capacity which can be…
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…