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This paper presents a new technique for deterministic length reduction. This technique improves the running time of the algorithm presented in \cite{LR07} for performing fast convolution in sparse data. While the regular fast convolution of…

数据结构与算法 · 计算机科学 2008-02-04 Amihood Amir , Klim Efremenko , Oren Kapah , Ely Porat , Amir Rothschild

We study stochastic combinatorial optimization problems where the objective is to minimize the expected maximum load (a.k.a.\ the makespan). In this framework, we have a set of $n$ tasks and $m$ resources, where each task $j$ uses some…

数据结构与算法 · 计算机科学 2021-06-25 Anupam Gupta , Amit Kumar , Viswanath Nagarajan , Xiangkun Shen

We consider the online resource minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible schedule on a minimum number of machines. We rigorously study this…

数据结构与算法 · 计算机科学 2015-12-09 Lin Chen , Nicole Megow , Kevin Schewior

Consider a problem in which $n$ jobs that are classified into $k$ types arrive over time at their release times and are to be scheduled on a single machine so as to minimize the maximum flow time. The machine requires a setup taking $s$…

数据结构与算法 · 计算机科学 2017-09-19 Alexander Mäcker , Manuel Malatyali , Friedhelm Meyer auf der Heide , Sören Riechers

We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…

计算几何 · 计算机科学 2015-05-12 Jian Li , Haitao Wang , Bowei Zhang , Ningye Zhang

The Restricted Assignment Problem is a prominent special case of Scheduling on Parallel Unrelated Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the non-constructive bound on its…

数据结构与算法 · 计算机科学 2019-08-21 Klaus Jansen , Lars Rohwedder

In the last decade remarkable progress has been made in development of suitable proof techniques for analysing randomised search heuristics. The theoretical investigation of these algorithms on classes of functions is essential to the…

神经与进化计算 · 计算机科学 2020-10-22 Frank Neumann , Mojgan Pourhassan , Carsten Witt

We study classical deadline-based preemptive scheduling of tasks in a computing environment equipped with both dynamic speed scaling and sleep state capabilities: Each task is specified by a release time, a deadline and a processing volume,…

数据结构与算法 · 计算机科学 2014-07-04 Antonios Antoniadis , Chien-Chung Huang , Sebastian Ott

We study a classical iterative algorithm for balancing matrices in the $L_\infty$ norm via a scaling transformation. This algorithm, which goes back to Osborne and Parlett \& Reinsch in the 1960s, is implemented as a standard preconditioner…

数据结构与算法 · 计算机科学 2015-06-16 Leonard J. Schulman , Alistair Sinclair

Parameterizing by the largest processing time $p_{max}$ and the number of different job processing times $d$, we propose a proximity technique for High-Multiplicity Scheduling on Uniform Machines for the objectives Makespan Minimization…

数据结构与算法 · 计算机科学 2024-09-24 Hauke Brinkop , David Fischer , Klaus Jansen

Several classic problems in graph processing and computational geometry are solved via incremental algorithms, which split computation into a series of small tasks acting on shared state, which gets updated progressively. While the…

数据结构与算法 · 计算机科学 2020-03-24 Dan Alistarh , Nikita Koval , Giorgi Nadiradze

We consider energy-efficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power $s^{\alpha}$ when running at speed $s$, for $\alpha>1$. A scheduling algorithm needs to…

数据结构与算法 · 计算机科学 2014-10-14 Hongyang Sun , Yuxiong He , Wen-Jing Hsu , Rui Fan

We study the fundamental scheduling problem $1\|\sum p_jU_j$. Given a set of $n$ jobs with processing times $p_j$ and deadlines $d_j$, the problem is to select a subset of jobs such that the total processing time is maximized without…

数据结构与算法 · 计算机科学 2024-02-29 Mihail Stoian

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)…

数据结构与算法 · 计算机科学 2026-02-16 Alexander Lindermayr , Guido Schäfer , Jens Schlöter , Leen Stougie

A moldable job is a job that can be executed on an arbitrary number of processors, and whose processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing…

数据结构与算法 · 计算机科学 2018-01-09 Klaus Jansen , Felix Land

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…

数据结构与算法 · 计算机科学 2022-10-05 Max A. Deppert , Klaus Jansen , Marten Maack , Simon Pukrop , Malin Rau

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…

数据结构与算法 · 计算机科学 2022-12-08 Eric Balkanski , Tingting Ou , Clifford Stein , Hao-Ting Wei

He and Yuan's prediction-correction framework [SIAM J. Numer. Anal. 50: 700-709, 2012] is able to provide convergent algorithms for solving separable convex optimization problems at a rate of $O(1/t)$ ($t$ represents iteration times) in…

最优化与控制 · 数学 2024-02-06 Tao Zhang , Yong Xia , Shiru Li

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…

数据结构与算法 · 计算机科学 2022-08-30 Anupam Gupta , Benjamin Moseley , Rudy Zhou

We study a difficult problem of how to schedule complex workflows with precedence constraints under a limited budget in the cloud environment. We first formulate the scheduling problem as an integer programming problem, which can be…

分布式、并行与集群计算 · 计算机科学 2019-03-05 Hang Zhang , Xiaoying Zheng , Ye Xia , Mingqi Li