# 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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### Assignment problem for multiple days

I have a problem that can be reduced to an assignment problem. (In a previous question i found out how to do that.) Which means we have a set $A$ of agents and a set $T$ of tasks as well as a cost ...
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### XOR-like behavior in flow networks

XOR is not the correct name, but I am looking for some kind of exclusive behavior. I am currently solving a set of different (assignment) problems by modeling flow networks and running a min-cost-max-...
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### 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 ...
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### A variant of the Assignment Problem

In my variant of the assignment problem I have a set $A$ of agents and a set (of possibly different cardinality) $T$ of tasks. Each agent needs to be assigned exactly $n$ or $n+1$ tasks, and each task ...
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### 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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### 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 ...
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I have this simple 'assignment' problem: We have a set of agents $A = \{a_1, a_2, \dotso, a_n\}$ and set of tasks $T= \{t_1, t_2, \dotso, t_m\}$. Note that $m$ is not necessarily equal to $n$. Unlike ...
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### 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 $x_{ij}$ ...
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 ...
317 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 ...
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### Stable marriage problem with only one side having preferences [duplicate]

I was wondering about a variation on the Stable Marriage Problem. Initially, we have two sets of entities, usually males and females, and they have preference lists ranking the other group, and ...
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### 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 ...
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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### 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 with no cost

I have a problem that I was able to conceptualize as following: Problem We have a set of n people. And m subsets representing their ethnicity like White, Hispanic, Asian etc. Given any combination of ...
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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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### 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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### Choice of algorithm for hierarchical clustering for minimizing network communication costs

Suppose I have a large distributed task running on a cluster system where part of the workload is compute bound and part depends on network performance. Data transfer is not completely homogeneous ...
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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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### What makes an MILP problem solvable?

Knapsack problems, Assignment problems can all be expressed as (MILP) mixed integer linear programs. MILP is NP-complete. But Knapsack problem is solvable in pseudo-polynomial time using dynamic ...
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### Hungarian Assignment Algorithm Implementation

I want to implement the "vertex similarity" algorithm described in the paper Graph Isomorphism Detection Using Vertex Similarity Measure. The algorithm is as follows: ...