# 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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### Selling blocks of time slots

Given $n$ time slots that $k$ people want to buy. Person $i$ has a value $h(i,j)\geq 0$ for each time slot $j$. Each person can only buy one consecutive block of time slots, which could be empty. ...
616 views

### How does variance in task completion time affect makespan?

Let's say that we have a large collection of tasks $\tau_1, \tau_2, ..., \tau_n$ and a collection of identical (in terms of performance) processors $\rho_1, \rho_2, ..., \rho_m$ which operate ...
5k views

### Getting parallel items in dependency resolution

I have implemented a topological sort based on the Wikipedia article which I'm using for dependency resolution, but it returns a linear list. What kind of algorithm can I use to find the independent ...
480 views

### Is this special case of a scheduling problem solvable in linear time?

Alice, a student, has a lot of homework over the next weeks. Each item of homework takes her exactly one day. Each item also has a deadline, and a negative impact on her grades (assume a real number,...
517 views

### Job scheduling with a bottleneck problem

Given $n$ jobs $J_1,J_2,...,J_n$, each job requires $T_i > 0, T_i \in N$ time to complete. Each job must be pre-processed and post-processed by a single machine M that can handle only 1 job at a ...
282 views

### Ordering elements so that some elements don't come between others

Given an integer $n$ and set of triplets of distinct integers $$S \subseteq \{(i, j, k) \mid 1\le i,j,k \le n, i \neq j, j \neq k, i \neq k\},$$ find an algorithm which either finds a permutation $\pi$...
596 views

### Find out whose turn it is to buy the croissants

A team has decided that every morning someone should bring croissants for everybody. It shouldn't be the same person every time, so there should be a system to determine whose turn it is next. The ...
287 views

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### Correctness proof for greedy algorithm based on ratio

I've an issue stated as follows: We have 10000 jobs to do, each with some length $l_i$ and weight (importance) $w_i$. Our goal is to arrange the schedule of doing these jobs (in other words, ...
251 views

### Does a greedy task selection algorithm find a c-approximate solution?

I was told this question may be better suited here. A scheduling problem can be stated as: Given a set $\{(s_i,f_i)\}_{1\le i\le n}\}$ of tasks identified by their start and end times, choose ...
60 views

### CPU scheduling Decisions

Operating System - CPU scheduling Decisions The question above talks about why CPU scheduling does not take place when ready to running. But I wonder why CPU scheduling does not take place when new ...
94 views

### Lower bound on competitive ratio of $m$-machine scheduling

Given a sequence of positive reals $a_1, a_2, \dots, a_n$ and an integer $m$, for each $j$ assign $a_j$ to a machine $i$, $1< i < m$, so as to minimize the maximum, over $i$, of the sum of all ...
1k views

### Time quantum assignment to processes

In a book I am reading it is stated that an input/output intensive process should receive a higher time quantum whereas a computing intensive process on the other hand should receive a lower one. Here ...
608 views

### A variant of job assignment (scheduling) problem with variable time span

The problem is a scheduling problem with n jobs and k machines. Each job i can be started at any time, but its duration is not exactly known except a time span interval. For example, a job may take ...
277 views

### Minimize the total execution time of jobs executed by 3 processors in sequence

There are 3 processors: $P_1$, $P_2$, $P_3$. $P_1$ can execute only one job while the other two can execute any number of jobs in parallel. Each job consists of 3 parts, and each part is processed by ...
87 views

### A task-scheduling problem as a matroid (CLRS book)

I don't understand very well section 16.5 of the 3rd edition of the famous Introduction to Algorithms book, known as CLRS. It defines the problem of scheduling unit-...
161 views

### Students in classroom problem - Flow in network

I have room, which is opened some days in week, in different hours each day. I have multiple students, each has time some days in week, in different hours. Each student have to visit the room ...
120 views

### Scheduling a tournament with variable game lengths

I want to solve the following scheduling problem: We have $N$ resources and $\binom{N}{2}$ tasks, such that every task requires exactly two resources and every pair of resources is required by exactly ...
125 views

### Offline scheduling fully determined arbitrary jobs in multiprocessor setting

Let $\mathcal{J} = \{J_1,...,J_n\}$ be a set of jobs with each $J_i = [a_i,r_i,d_i]$ where the job becomes available at its arrival time $a_i$, requires $r_i$ execution time and needs to be finished ...
47 views

### I'ld like a better algorithm for scheduling tutors to fill a set of shifts

My problem is as follows: I have a set of shifts at various locations that need to be filled by tutors. A simple example would be basic math in room A on M, W, F from 9-11am and Sa from 12-3 pm. ...
48 views

### Scheduling is NP-Hard via vertex cover

Are there any existing proofs involving a reduction of the single machine scheduling problem (in any of its forms really) from vertex cover in order to prove its NP-hardness? Particularly looking for ...
747 views

I want to write a scheduling algorithm for the following scenario: There is a set of tasks to complete, each one with a due date, difficulty (easy, normal, hard) and progress on the task. The idea is ...