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.
Questions tagged [scheduling]
285 questions
27
votes
2 answers
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.
Is there a polynomial-time algorithm to compute the…
user11550
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18
votes
1 answer
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 paths?
Masse
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16
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2 answers
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 completely in parallel. For scenarios of interest, we may…
Patrick87
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12
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3 answers
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, bonus points for only assuming comparability),…
Matthias
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11
votes
2 answers
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 time and both phases require 1 unit of time. After…
Vor
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10
votes
2 answers
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 $\pi$ of the set $\{1, 2, \dots, n\}$ such…
Patrick87
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10
votes
1 answer
2D interval scheduling problem
Suppose I give you $n$ axis-aligned rectangles with a specified width, height, and x-position (of the left edge) $\{(w_i, h_i, x_i) \mid i \in \{0, \ldots, n - 1\}\}$, as well as a bound $(y_\mathrm{min}, y_\mathrm{max})$ on the valid y-positions.…
taktoa
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9
votes
3 answers
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 purpose of this question is to determine an…
Gilles 'SO- stop being evil'
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8
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Can Santa be both fair and efficient?
As the net-evergreen The Physics of Santa establishes, it is physically impossible for Santa to get a gift to every kid on the planet. Route planning won't help much there, but can a good planning algorithm at least make sure that every kid gets a…
Raphael
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8
votes
1 answer
Weighted interval scheduling with m-machines
I am looking for some advice and direction on solving the weighted interval scheduling problem with $m$-machines to plan some experimental "wet lab" procedures.
The problem is very similar to the standard weighted interval scheduling problem…
tomnl
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8
votes
6 answers
What is the average turnaround time?
For the following jobs:
The average wait time would be using a FCFS algorithm:
(6-6)+(7-2)+(11-5)+(17-5)+(14-1) -> 0+5+6+10+13 -> 34/5 = 7 (6.8)
What would the average turnaround time be?
Sheldon
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8
votes
4 answers
Find non-overlapping scheduled jobs with maximum cost
Given a set of n jobs with [start time, end time, cost] find a subset so that no 2 jobs overlap and the cost is maximum.
Now I'm not sure if a greedy algorithm will do the trick. That is, sort by cost and always take the next job that doesn't…
user1531186
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7
votes
0 answers
Finding a rainbow independent set in a circle
Inside the interval $[0,1]$, there are $n^2$ intervals of $n$ different colors: $n$ intervals of each color. The intervals of each color are pairwise-disjoint. A rainbow independent set is a set of $n$ pairwise-disjoint intervals, one of each…
Erel Segal-Halevi
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7
votes
1 answer
Analyzing load balancing schemes to minimize overall execution time
Suppose that a certain parallel application uses a master-slave design to process a large number of workloads. Each workload takes some number of cycles to complete; the number of cycles any given workload will take is given by a known random…
Patrick87
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7
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Classification of job shop scheduling problems
I'm writing a program (using genetic algorithms) that finds sort-of-optimal scheduling plan for a factory.
The factory has several types of machines (say, locksmith, miller, welding)
There are few machines of each type. (say, 3 locksmiths, 2…
Martin Janiczek
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