Optimal scheduling

Interval scheduling

Interval scheduling is a class of problems in computer science, particularly in the area of algorithm design. The problems consider a set of tasks. Each task is represented by an interval describing the time in which it needs to be processed by some machine (or, equivalently, scheduled on some resource). For instance, task A might run from 2:00 to 5:00, task B might run from 4:00 to 10:00 and task C might run from 9:00 to 11:00. A subset of intervals is compatible if no two intervals overlap on the machine/resource. For example, the subset {A,C} is compatible, as is the subset {B}; but neither {A,B} nor {B,C} are compatible subsets, because the corresponding intervals within each subset overlap. The interval scheduling maximization problem (ISMP) is to find a largest compatible set, i.e., a set of non-overlapping intervals of maximum size. The goal here is to execute as many tasks as possible, that is, to maximize the throughput. It is equivalent to finding a maximum independent set in an interval graph. A generalization of the problem considers machines/resources. Here the goal is to find compatible subsets whose union is the largest. In an upgraded version of the problem, the intervals are partitioned into groups. A subset of intervals is compatible if no two intervals overlap, and moreover, no two intervals belong to the same group (i.e., the subset contains at most a single representative of each group). Each group of intervals corresponds to a single task, and represents several alternative intervals in which it can be executed. The group interval scheduling decision problem (GISDP) is to decide whether there exists a compatible set in which all groups are represented. The goal here is to execute a single representative task from each group. GISDPk is a restricted version of GISDP in which the number of intervals in each group is at most k. The group interval scheduling maximization problem (GISMP) is to find a largest compatible set - a set of non-overlapping representatives of maximum size. The goal here is to execute a representative task from as many groups as possible. GISMPk is a restricted version of GISMP in which the number of intervals in each group is at most k. This problem is often called JISPk, where J stands for Job. GISMP is the most general problem; the other two problems can be seen as special cases of it: * ISMP is the special case in which each task belongs to its own group (i.e. it is equal to GISMP1). * GISDP is the problem of deciding whether the maximum exactly equals the number of groups. All these problems can be generalized by adding a weight for each interval, representing the profit from executing the task in that interval. Then, the goal is to maximize the total weight. All these problems are special cases of single-machine scheduling, since they assume that all tasks must run on a single processor. Single-machine scheduling is a special case of optimal job scheduling. (Wikipedia).

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Introduction to Scheduling

This lesson introduces the topic of scheduling and define basic scheduling vocabulary. Site: http://mathispower4u.com

From playlist Scheduling

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Scheduling: The List Processing Algorithm Part 1

This lesson explains and provides an example of the list processing algorithm to make a schedule given a priority list. Site: http://mathispower4u.com

From playlist Scheduling

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Scheduling: The Decreasing Time Algorithm

This lesson explains how to use the decreasing time algorithm to create a priority list and then a schedule. Site: http://mathispower4u.com

From playlist Scheduling

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Process Scheduling

An animation showing the main features of a process scheduling system including the ready queue, blocked queue, high level scheduler and low level scheduler. It explains the principle of a round robin scheduling algorithm.

From playlist Operating Systems

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Into to the Mathematics of Scheduling

Terminology explained includes preference schedule, digraphs, tasks, arcs, processors, and timelines.

From playlist Discrete Math

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Scheduling: The List Processing Algorithm Part 2

This lesson explains and provides an example of the list processing algorithm to create a digraph and make a schedule. Site: http://mathispower4u.com

From playlist Scheduling

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From playlist Timers

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Thomas Rothvoß: Scheduling with Communication Delays via LP Hierarchies and Clustering

We consider the classic problem of scheduling jobs with precedence constraints on identical machines to minimize makespan, in the presence of communication delays. In this setting, denoted by P | prec,c | Cmax, if two dependent jobs are scheduled on different machines, then at least c unit

From playlist Workshop: Approximation and Relaxation

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From playlist Time Management

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From playlist Behavior | MCAT | Khan Academy

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From playlist SimBiology Tutorials for QSP, PBPK, and PK/PD Modeling and Analysis

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From playlist Psych 9B: Psych Fundamentals

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MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Ling Ren In this recitation, problems related to matrix multiplication and weighted interval scheduling are discussed. Chapters 00:00 Title slate 00:20 Recitation

From playlist MIT 6.046J Design and Analysis of Algorithms, Spring 2015

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From playlist How to Study

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Shark Attack! Thursday at Noon - Variable Ratio & Interval Schedules - Extra Credits

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Puzzle 2: The Best Time to Party

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From playlist MIT 6.S095 Programming for the Puzzled, January IAP 2018

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R6. Greedy Algorithms

MIT 6.046J Design and Analysis of Algorithms, Spring 2015 View the complete course: http://ocw.mit.edu/6-046JS15 Instructor: Amartya Shankha Biswas In this recitation, problems related to greedy algorithms are discussed. License: Creative Commons BY-NC-SA More information at http://ocw.m

From playlist MIT 6.046J Design and Analysis of Algorithms, Spring 2015

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Searching and Sorting Algorithms (part 4 of 4)

Introductory coverage of basic searching and sorting algorithms, as well as a rudimentary overview of Big-O algorithm analysis. Part of a larger series teaching programming at http://codeschool.org

From playlist Searching and Sorting Algorithms

Related pages

Interval graph | Linear programming relaxation | Single-machine scheduling | Independent set (graph theory) | Optimal job scheduling | Identical-machines scheduling | Intersection graph | Maximum disjoint set | 2-satisfiability | Charging argument | Job stream | Boolean satisfiability problem | Earliest deadline first scheduling | Algorithm | Greedy algorithm