Questions tagged [assignment-problem]
For questions about the assignment problem in combinatorial optimization, NOT for problems that you've been set as a homework assignment.
82
questions
4
votes
1answer
99 views
Minimizing total distance traveled by points in points cloud transformation
I have a point cloud of size n (in the example on picture n = 5). The starting coordinates are in green, destination coordinates are in red. What I need is to move the points from the starting ...
4
votes
1answer
65 views
Maximum flow on a tripartite graph
I have to solve an assignment problem between $\{1,\dots, N\}$ agents and $\{1,\dots, M\}$ objects, which comes to maximize :
\begin{equation}
\sum_{ij}\beta_{ij}x_{ij}
\end{equation}
where $x_{ij}$ ...
2
votes
1answer
67 views
Assignment problem or something else?
My primary goal with this question is to identify the type of problem I have so I know what solution to pursue. I think it's either an instance of the assignment problem or the fair item allocation ...
0
votes
0answers
23 views
Algorithm for dual sided matching problem
Is the an algorithm that would help solve this problem:
Teams are swapping members.
Each team has preferences for members it 'wants' from other teams.
Each member has preferences for the teams its ...
4
votes
0answers
67 views
Assign n people to m rooms of different sizes, such that noone is alone
I'm looking for an efficient way to assign n people to m rooms in a very specific way.
INPUT:
The program receives two sets of people (set of males and set of females), as well as a set of available ...
3
votes
1answer
61 views
Assignment Problem — finding the $k$ agents with the best assignment
I have a question that I have been thinking about. Suppose we have $n$ agents, $m$ tasks, a cost matrix with $M_{ij}$ being the cost of agent $i$ performing task $j$, and are given a value $k \leq n$. ...
3
votes
0answers
42 views
Assignment problem with symmetric matrix
I came across a problem which I think can be reduced to the assignment problem/Hungarian algorithm.
We have matrix $A$ and matrix $B$ which are both $n\times n$ symmetric matrices. We can rearrange $...
0
votes
1answer
27 views
Grouping n points into groups of size m with objective to have least traveling distance in each group
Assumptions:
There are "n" jobs which are distributed over the city.
Company has "k" available workers.
Each worker can do "x" jobs per day.
"x" is dependent to the worker skills and the distance ...
2
votes
0answers
39 views
Explain this Graph Matching solved in Linear Time
I'm interested in a better explanation about the paper Computing Optimal Assignments in Linear Time for Approximate Graph Matching.
The graph edit distance is approximated by assignments in linear ...
3
votes
1answer
22 views
Choosing which workers (limited number) to use in a binary assignment problem?
First of all, I am not completely sure whether this problem belong to the category of assignment problems so feel free to correct me in this case.
The problem:
We are given a set of $m$ workers $A = ...
0
votes
0answers
9 views
How to assign people to categories based on some voting rules?
Say in an election there are predefined categories users can be assigned to. Of the people who are assigned to a certain category, other users can vote for them. To compute the results, the following ...
1
vote
1answer
128 views
How to cover given entries in a matrix with minimum number of rows and columns?
We have a matrix of 0 and 1. We want to cover all the 1's. We can cover a raw or a column with a plate. We want to use the minimum number of plates.
example
0 0 1 0
0 1 0 1
0 0 1 0
0 0 1 0
...
0
votes
0answers
89 views
Is this variation of the assignment problem NP-hard, and does it have a name?
I’m trying to solve a problem very similar to the assignment problem, with a few twists.
The problem has a certain amount of workers, and a certain amount of tasks - workers is always >= tasks. Each ...
1
vote
1answer
25 views
Problem class of assigning N persons to N tasks, zero costs with prefs
I am looking for the general problem class / computational complexity / algorithms for the following problem:
N tasks must be accomplished by N persons. 1 task to be done by exactly 1 person and vice ...
0
votes
0answers
48 views
What is the most efficient way to solve a workshop scheduling problem?
I am trying to design an algorithm to solve a workshop scheduling problem.
The problem is as follows:
I have to schedule a workshop consisting of a finite number of time slots, and a finite number of ...
1
vote
1answer
24 views
Algorithm to assign producers to consumers with respect to connections
I am trying to analyze supply chains in a game and have come across this problem:
First, an informal description: I have producers and consumers. Each producer produces a certain amount of goods, ...
1
vote
0answers
23 views
Optimal matching of individuals in vehicles
I am looking for an algorithm to find the optimal matching/allocation of n individuals in m identical vehicles. The aim is to create groups of individuals who will share these vehicles. Groups' size ...
1
vote
1answer
51 views
find separate pairs of points with minimal total distance
I am looking for suitable algorithm how to solve the following problem.
For finite set $S \subset \mathbb{R}$ ($|S| = N_{S}$) we need to find its disjunctive separation $S = A \cup B$ ($A \cap B = \...
2
votes
0answers
137 views
Sub-optimal and fast solutions to assignment problem
I am looking for a fast solution to the assignment problem for large cost matrices (5000x5000 or larger). The Hungarian algorithm is $O^3$, which is impractical for any moderately large problem.
Are ...
1
vote
1answer
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 ...
0
votes
1answer
125 views
Difference between stable marriage problem and assignment problem
What is the difference between the stable marriage problem and an assignment problem? Both refer to a matching problem in general but what is their specific difference?
I can see clear differences in ...
1
vote
0answers
46 views
Task assignment problem with capabilities and time restrictions
I have the following optimalization problem. I use the notations below because maybe it would be easier to understand that way, but I'm not good at conventions – I'm not sure if I'm using it all the ...
1
vote
0answers
70 views
Hungarian algorithm to search over all matching?
I am working on the following problem-
"Finding the matching among all possible matching such that the sum of edge weight is minimum in the matching."
Please note that I like to search over all ...
4
votes
1answer
396 views
Maximizing the sum of selected elements in a matrix
I’m trying to find an efficient algorithm for the following optimization problem:
Given a matrix $A$ with elements $a_{ij}$ and dimension $k$, select exactly $n$ elements from $A$ ($n<k$) such ...
1
vote
2answers
337 views
How to solve this very complicated assignment problem
A set of m items need to be placed into n stacks, where m > n. Each stack has z positions. An item has different widths when placed into different positions in a stack. The width of an item depends ...
3
votes
1answer
107 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 ...
0
votes
1answer
106 views
Efficient traffic allocation
Users can be assigned to one experiment on my site. I have an API that developers use to trigger logic for each experiment. They call ExperimentEngine.run() to trigger the code logic for the ...
0
votes
2answers
106 views
Reduction from an assignment problem to an independent set problem: NP-hard
The problem I have is as follows:
I have a complete bipartite graph $G=(V \cup C,E)$ as input, where $|V|=1, |C|=n, |E|=n$
The interpretation is that the node of $V$ is a vehicle, the $n$ nodes of C ...
2
votes
1answer
379 views
Bipartite Perfect Matching “Assignment Problem” - finding an assignment of a particular weight
The assignment problem is to find the minimum weight perfect matching in a weighted bipartite graph. This problem can be solved using the Hungarian algorithm in polynomial time. It is also possible to ...
2
votes
0answers
79 views
How to sum vectors to maximize magnitude? [duplicate]
There are $n$ vectors, represented as $(d_x, d_y)$ pairs. Someone stands at point $(0, 0)$ of infinite euclidean grid. For every vector he can either move by $d_x$ in $x$ axis and $d_y$ in $y$ axis or ...
3
votes
1answer
70 views
affinity based static load balancing
I am trying to find a good model the following problem:
Given a collection of work packets x, y, z, ..., and a collection of worker nodes ...
3
votes
1answer
643 views
Assignment Problem - multiple tasks, but only one chosen based on their preference (cost)
I've looked at Hungarian algorithm and Knapsack problems and neither quite hit the nail on the head. I've been trying to best rephrase my question while searching for answers and haven't got anywhere.
...
1
vote
0answers
419 views
Optimal Preference Matching
I'm trying to find an algorithm that finds an optimal matching between $A$ and $B$, where each element $a$ of $A$ provides a preference order $\prec_a$ over $B$. I will notate the index of an element $...
1
vote
1answer
561 views
Matching with One-sided Preferences
I'm dealing with a slight variation on a classic matching problem on sets $A$ and $B$), where:
Set $A$ has an incomplete set of preferences (not all of $B$ is included)
Set $B$ has no preferences ...
3
votes
2answers
106 views
Algorithm for arranging elements into different sized buckets
I have a set of items. For each item, there is a list of buyers I can sell it to and a corresponding price they will pay me. For example:
...
4
votes
1answer
203 views
How do solve assignment of one interval to another?
Is there an efficient algorithm for the following problem?
Input: Set of holes and pegs. Each hole/peg is an interval $[\ell,u]$ with integer endpoints.
Question: Can all the holes be filled ...
1
vote
0answers
65 views
Assignment problem for compute mininum weight cycle cover?
I've read in multiple articles and books that the computation of a cycle cover
for a given graph is possible in polynomial time, since this problem can be
viewed as the assignment problem, which is a ...
0
votes
1answer
3k views
Is there a greedy algorithm to solve the assignment problem?
The assignment problem is defined as:
There are n people who need to be assigned to n jobs, one person per job. The cost that would accrue if the ith person is assigned to the jth job is a known ...
0
votes
1answer
343 views
Given a list of students and their courses, place them in specific classes
I could use some help coming up with the best way to solve this problem. I've been curious as to how something like this would work, as the worst case seems way too bad.
Problem
Given a group of ...
4
votes
2answers
135 views
Discrete assignment problem with penalties
I came across a problem were you have to plan an optimal assignment pattern. Let's say you have $j=1,\ldots,n$ tasks during $i=1,\ldots,m$ time periods.
It's an single agent problem where we have to ...
3
votes
2answers
352 views
Optimality in multi-agent multi-target path finding
Suppose I have a regular rectangular weighted grid with multiple agents and obstacles. Agents cannot be in grid sites that contain obstacles, and for simplicity assume multiple agents can be in the ...
1
vote
2answers
186 views
Selecting best crew combination that meets requirements of a variety of jobs
I am developing an application, which performs combinatorial function as described below. Could anyone point out a suitable algorithm (or direction)?
== Basic scheme: ==
There are fixed amount of ...
0
votes
0answers
753 views
Minimum cost perfect matching (Using General graph
This is a continuation of the problem described in this topic: Optimized algorithm to match entities together based on heuristics. I've come a little closer as to what might be the best solution.
I'...
5
votes
1answer
430 views
Heuristic algorithms for the dense assignment problem
Given a dense assignment problem ($n$ tasks assigned to $n$ workers, where each worker can do any one of the tasks), I understand the best complexity is $O(n^3)$, using the Hungarian Algorithm or ...
1
vote
1answer
331 views
An algorithm to find the maximum profitable assignment
Given a set of workers $w_1,...,w_m$ and and a set of tasks $t_1,...,t_n$, and a $m\times n$ matrix $P$ s.t. $P(i,j)$ is the profit of assigning worker $i$ to task $j$. One worker can only be ...
0
votes
0answers
93 views
Job Scheduling: Two Resources, Defined Job Length, Defined Earliest Start
Problem
I stumbled over the following job scheduling problem.
There are two resources, for simplicity I call them ...
CPU_RAM (MAX_CPU_RAM specifies what is available in total)
GPU_RAM (MAX_GPU_RAM ...
1
vote
1answer
249 views
How can I assign cooks to customers?
I haven't done much algorithm writing till now. I have a specific scenario and I am wondering which approach shall I take.
Scenario:
Let us suppose that
we have 4 guys (A,B,C,D)
We want to ...
7
votes
2answers
101 views
CNF form of variable assignment problem
There are n variables $x_1$, $x_2$,..., $x_n$ and each one of them takes values from 1 to k (k>= n) and all are distinct. How can I represent this in the CNF form? (I tried the trivial way of trying ...
2
votes
1answer
588 views
Polynomial time solution for bipartite matching
Inspired by this StackOverflow question, I am wondering if there is an efficient algorithm for the following problem:
Assume $n$ items and $n$ boxes, with all boxes numbered numerically and all ...
4
votes
2answers
276 views
Working Optimization Algorithm
This is my basic setup: I have five time slots (A, B, C, D, E; each day has these five time slots) over 60 days that all need to be filled with n people each (n must remain a variable). However, each ...
