# Questions tagged [scheduling]

Questions about the optimisation problem of ordering a set of tasks so that some objective function (e.g. makespan) is minimised. The set of constraints is crucial; in particular, there is a large body of research covering online variants. Use the process-scheduling tag for questions specifically about scheduling in operating systems.

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### Unconditionally fair, weakly fair, and strongly fair scheduling

I am trying to understand the difference between weakly fair and strongly fair scheduling. For example, what scheduling policy would ensure that a process delayed at its first await statement will ...
131 views

### Hardness of a scheduling/assignment problem

I am trying to prove the hardness of the following problem. This problem is from google hashcode, qualification-round, 2020. Hier is a brief description of the problem. Given a list or libraries and ...
28 views

### Scheduling jobs on a single machine - minimising the weighted sum of completion times

Consider the following problem: there are $n$ jobs $\{1,...,n\}$, each has a processing time, $p_i$, a weight $w_i$, and an arriving time $r_i$. The goal is to minimise the weighted sum of completion ...
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### Can't Understand the formula for processing speed of each job

I am trying to understand the formula for processing speed of each job. I got the formula from the following link: Fair Online Scheduling for Selfish Jobs on Heterogeneous Machines The other ...
43 views

### Algorithm to enumerate all complete schedulings of finals tests?

I'm creating an app that receives some map between finals and the respective periods during which they are held and a student's required finals. I was wondering if there was an algorithm to enumerate ...
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### Schedule management optimizer

I had this idea of program tohelp me in my everyday life. We both work and don't live in the same city. I was wondering how to make a program that calculate, depending on the work scheduleand the ...
29 views

### Tournament Scheduling Problem

I am trying to design an algorithm to compute the solution to this problem. Given a list of n tournaments with a name, start_date, end_date, latitude and longitude, find the list of p tournaments in ...
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### Criteria based estimation of a task's due date

Basically we have a ticket system, each day we get multiple tickets with different categorization (Question,Change,Error) and importance (High,Mid,Low) for different customers (A,B,C). My job is to ...
48 views

I'm currently studying for an exam which includes operating systems. I'm solving the exams from previous years and I'm stuck on a particular question: "One of the advantages of preemptive scheduling ...
17 views

### How do programs like Apache Airflow/ Luigi determine shortest path and how does that relate to graph theory?

I am looking for a simple layman's term explanation on how do programs like Apache Airflow or Luigi (or any Task/ETL schedulers) determine the shortest path to complete a certain task and make it ...
25 views

### Upper bound on the average number of overlaps for an interval within a set of intervals

Let $\mathcal{I}$ be a set of intervals with cardinality $L$, where each interval $I_i \in \mathcal{I}$ is of the form $[a_i, b_i]$ and $a_i, b_i$ are pairwise distinct non-negative integers bounded ...
171 views

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### Difference between greedy and work conserving scheduler for DAG

For both schedulers I have found the definition, that no processor stays idle, if there is more work it can do. However, I found two different upper bounds on the computation time of $T$. For the ...
132 views

### Scheduling algorithm to minimize the number of late jobs

There are $n$ (non-recurring) jobs where each job $i$ has an arrival time $a_i$ and a duration $t_i$. All the jobs share a deadline length $d$ (deadline for each job is $a_i + d$). The problem is to ...
29 views

### How to justify using available code (in different language) for comparing algorithms [closed]

I have proposed an algorithm for a scheduling problem in a submitting paper. In the revision, the reviewer asked us to compare with another algorithm in the literature. Our algorithm is in MATLAB, and ...
3k views

### How to calculate average waiting time for round robin cpu scheduling?

I have tried to calculate average waiting time for the below details there are two answers I'm getting using two methods I'm not understanding which one is correct? The time quantum is 2 This is the ...
45 views

### Interval scheduling with shared resources between steps

I'm working on a (real life!) scenario that involves scheduling workers on an assembly line. Let's say it involves steps a -> b -> c -> d -> e, and each ...
314 views

### Algorithm for scheduling unit time tasks with arrival times and deadlines

Suppose we have $n$ tasks to order over $n$ days. Each tasks takes 1 day to be completed. Each task has a start date when the task becomes available and a deadline when the task must be delivered. ...
67 views

### Calculating minimum processing time for many recipes and tools

I originally asked this question on StackOverflow but a comment was made to the effect that my problem pertains to Job Shop Scheduling and that it was more of a comp sci problem than a programming ...
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### How can I develop a pseudo-polynomial time algorithm for a non-integer problem?

I have an scheduling probelm with a set of jobs $J$, with a ''non-integer'' parameter $\beta_j$, i.e. the parameter is a real number and $\beta_j \leqslant 0.5, \exists j \in J$. Since the problem ...
193 views

### Calculate makespan of job shop solution?

I have a job shop problem with n jobs and m machines, a job shop means that not all jobs have to go through every machine. A job shop problem can be written as such : ...
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### Finding an optimal machine assigning

I have $m$ machines and $n$ jobs. Each machine has a load capacity. Each job can be only handled by either one or two machine, and each job takes some time to finish. After it finished, new jobs can ...
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### Job shop scheduling variant with non-sequential process plans

As the title says, I am looking for a variant of the job shop scheduling problem which allows for non-sequential process plans. For example, I might have a job whose task-order constraints look like ...
91 views

### Response time of scheduling a DAG where each vertex is a task

Suppose I have a directed acyclic graph where each vertex $v$ represents a task with a certain execution time and the edges represent precendence constraints between the tasks. I.e. task $v_i$ has to ...
239 views

### Implementing a job-scheduling problem with multiple dependencies and variable tasks (time frames) using dynamic programming

I'm writing a "Chores Scheduler" in Python. It has to be implemented using dynamic programming and has to take in two types of chores, as below: Regular chores with a start time and end time (a real-...
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### A scheduling problem on an oriented graph with multiple constraints

The problem is the following : Data An oriented graph $(V, E)$ : to be understood as a set of partially ordered tasks A map $d: V -> \mathbb{N}$ : to be understood a function mapping tasks to a ...
101 views

### Approximation ratio of greedy algorithm for makespan

In the course notes for Stanford MS&E-319: https://web.stanford.edu/class/msande319/lec1.pdf Lemma 5 is given as: The approximation factor of the modified greedy [scheduling] algorithm is 4/3. ...
89 views

### Can a schedule be conflict serializable but not serializable?

A schedule is called conflict serializable if it can be transformed into a serial schedule by swapping non-conflicting operations. Then, My question is: Can a schedule be conflict serializable but ...
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### $n$ machines, $n$ types of jobs with $q_j$ jobs, minimizing the cost

I have this problem A ﬁrm has $q_j$ jobs of type $j$, where $1 \leq j \leq n$. It also has $[n] = {1,2,...n}$ machines. Machine $i$ can service any job of type $j$ where $j ≤ i$. The cost of ...
67 views

### Matching schedules between users and providers

I have a problem I've been dealing for the past few days, and I'm pretty stuck. Each user has a schedule for a given week, such as ...
122 views

### Round-Robin fashion exercise

In my Operating Systems class I have an exercise to sketch out how a round-robin algorithm would apply to a specific scenario, which is the following: Now the correction that I was provided with by ...
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### Proccess scheduling arrival time

If I have a set of processes, let's say 9 and I know the burst time and the waiting time for SJF algorithm and also know that processes arrive in groups of 3 processes at M1 moment, M2 moment, M3 ...
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### Disk Scheduling for a Fragmented Hard-Drive

Recently In class I have been learning about simple disk scheduling algorithms such as FCFS, STTF, LOOK, LOOK-SCAN etc. From my understanding these algorithms schedule I/O requests depending on which ...
106 views

### How to generate an instance for an NP_hard proof, where each element has two inputs?

I want to prove the NP-hardness of an scheduling problem. The problem seems to be NP-hard in the ordinary sense, so I am trying with the Partition Problem, precisely the Equal Cardinality Partition (...
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### Variant of interval scheduling (multiple machines with given availability)

I am looking for an algorithm to solve the following variant of interval scheduling : schedule some tasks on multiple machines, which are only available during a given interval of time. Two tasks ...