# Questions tagged [scheduling]

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### Scheduling with Separation Constraint

There are $N$ types of jobs. For each $i$, we have to schedule $T/D_i$ jobs of type $i$ in $T$ timeslots. We know that $\sum_{i=1}^N 1/(D_i+1) = 1$. For each type $i$, the distance between two ...
69 views

### Optimal scheduling with delay constraints

Suppose you have $K$ servers numbered $\{1,2,...,K\}$. Playing server $i$ provides a value of $v_i > 0$. However, once you play server $i$, you are not allowed to play it for the next $n_i$ time-...
77 views

### Color shifting in a bipartite graph

Assume that we have a directed bipartite graph $G = \langle L\dot\cup R, E\rangle$. Where $E$ contains directed edges only from $L$ to $R$, that is, $E\subseteq L\times R$. Assume further that the ...
494 views

### Testing whether letters can be scheduled to achieve a word in a regular language

I fix a regular language $L$ on an alphabet $\Sigma$, and I consider the following problem that I call letter scheduling for $L$. Informally, the input gives me $n$ letters and an interval for each ...
68 views

### Series-parallel extension of a partial order respecting a given total order

Consider a partial order $P$, a series-parallel order $Q$ and a total order $R$, such that $P \subseteq Q \subseteq R$. Given $P$ and $R$, we are asked to find $Q$ of minimum length. An $O(n^3)$ ...
121 views

### Stacks serving interval storage requests

An interval storage request is represented by a tuple $(s,t,v)$ satisfying $s<t$, meaning that the value $v$ needs to be stored from time $s$ to time $t$. A stack serves the request $(s,t,v)$ in ...
62 views

### Complexity of Finding Optimal Synergistic Set Packings

Motivation: While developing tools for fast execution of machine learning workflows, we realized that many workflows require intermediate results -- sometimes we should cache these results, and ...
98 views

### Prove np-hard with reduction from scheduling resources [closed]

We have a system in which we have n number of process and m number of resources.The resources are boolean valued that is they can either have value 0 or 1(in brief suppose the resources as single way ...
179 views

### Who are active researchers in the scheduling theory? [closed]

I have an interest in a postdoc on scheduling problems but I cannot find many researchers who are actively involved in this. Any help?
43 views

### Equilvalence among two Scheduling problems

I have two problems for scheduling: Packets arrive at a router. Router schedules them i.e. router determines which one will go out first and which one last. Here, the problem is which packet to send ...
74 views

### What does the contention-free communication assumption really mean in the context of DAG scheduling?

In many papers about DAG (directed-acyclic graph) scheduling in distributed systems, the authors make the assumption that the communication between the processors of the system where the DAG is ...
440 views

### Proving NP-hardness of scheduling problem (total weighted completion time)

Consider the problem $P \mid \mid \sum w_j C_j$. I want to prove that this problem is (strongly) NP-hard by reducing from $3$-Partition, but I am not really sure how to do this. Just to be precise, ...
94 views

### Minimum size counter-example in a 2-machine scheduling problem proof

I'm confused about something in the main proof in this paper (sorry that it's behind a paywall, but I assume many people on here have access to such things through their university and my posting the ...
245 views

### Scheduling to maximize idle time

In the context of scheduling maintenance jobs on arcs of a flow network I came across the problem to schedule jobs, indexed by $j$, and given by triples $(r_j,d_j,p_j)$ of (integer) release time, due ...
217 views

### Job scheduling: minimizing number of reads

Consider the following scheduling problem: input: set of computations $C = \{c_1, ..., c_n\}$ set of computing nodes $P = \{p_1, ..., p_n\}$ Dependency graph $D$ between jobs (DAG) $(c_i,c_j)$ ...
97 views

### Are there any approaches to the following scheduling problem?

Consider the following problem: we are given $K$ tasks $\langle n_1, n_2, ..., n_K \rangle$. Every task $n_i$ is qualified with two parameters: The time it takes to be completed ($t_i$) and, The ...
2k views

### Existing benchmarks for scheduling problems?

Which benchmarks exist to evaluate the performance of algorithms for Job-Shop or Flow-shop scheduling problems?
176 views

### Minimize makespan on identical machines when jobs are vectors

Given are $n$ $d$-dimensional vectors and $m$ machines where $d$ need not be fixed. The objective is to minimize the makespan i.e., assign the vectors to machines such that the maximum of the ...
207 views

### Optimization of class schedule

I am creating a scheduling program that I need to either optimize or prove that what I have is already optimal. I have n groups, all of which need to do some activity a in time slot t. A person can ...
96 views

### Minimize the time when guard observes more than one event (for fixed number of guards)

Consider the following optimization problem: given a finite set $S$ of intervals on the line and a number $k$. We need to colour this set in $k$ colours so that the measure of the set of points, which ...