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.

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How to find the optimal assignment using the Kuhn-Munkres algorithm?

I managed to get through the Wikipedia article until the last step and I have implemented an algorithm that can reach the optimum. Unfortunately the article does not say anything about how can I make ...
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32 views

Fair assignment of storage for multiple writers (load balance)

I'm trying to optimize a system with a better algorithm for allocating storage. The system has 'N' writer processes and 'M' disks. (N < 30, M < 10. N can change, M is constant). Any process can ...
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Hungarian method: seemingly different algorithms from different sources?

When I look online for examples of the Hungarian method for solving the min-weight assignment problem, for example here, it involves iterating on the cost matrix; subtracting entries from the rows and ...
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41 views

Algorithm for assigning people to groups

Given a list $L = [1, 2, .., n]$ and a list $C = [(L_i, L_j), ....]$ form a group of pairs $G = g_1, ..., g_{n/2}$ such that: every element of $L$ is assigned to exactly one group $g_k = (L_i, L_j) \...
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42 views

Randomized Assignment Problem

Given $x_1,...,x_n,y_1,...,y_n\in \mathbb{R}^d$ find a permutation matrix $P\in\mathbb{S}_d$ that minimizes $\sum_{ij}P_{ij}|x_i-y_j|$. This is an assignment problem and can be solved in $O(n^3+n^2d)$ ...
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Assignment Problem with Non assignable cell

I have question for you guys. In this question is there something else that I should do ? When i try to solve with the way that my professor thought , its unsolveable. What should i do to solve this ? ...
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21 views

Algorithm for this generalized assignment problem

I'm trying to find an algorithm for the following problem. There are $5$ computer files with capacity $18$, $23$, $12$, $125$, $45$ MB respectively and there are $4$ hard disks with capacity $25$, $...
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61 views

Special case of stable marriage

I have an instance of the stable marriage problem in which the first side $S_1$ has $n_1$ agents and the second side $S_2$ has $n_2$ agents with $n_2$ is very big in comparison to $n_1$. In addition, ...
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123 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 ...
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122 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 $x_{ij}$ ...
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1answer
92 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 ...
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35 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 ...
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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 ...
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117 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 $k \leq n$. ...
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68 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 $...
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33 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 ...
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42 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 ...
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23 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 = ...
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346 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 ...
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208 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 ...
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1answer
52 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 ...
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68 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 ...
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1answer
36 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, ...
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25 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 ...
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53 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 = \...
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183 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 ...
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1answer
85 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 ...
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1answer
216 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 ...
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71 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 ...
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75 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 ...
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1answer
641 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 ...
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2answers
387 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 ...
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138 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 ...
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122 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 ...
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125 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 ...
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468 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 ...
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107 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 ...
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73 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 ...
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1answer
849 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. ...
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491 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 $...
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1answer
809 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 ...
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115 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: ...
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1answer
207 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 ...
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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 ...
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1answer
4k 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 ...
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390 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 ...
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166 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 ...
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404 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 ...
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200 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 ...
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808 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'...