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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.

For questions about the assignment problem in combinatorial optimization, not for problems that you've been set as a homework assignment.

124 questions
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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 function $c(i,j)$. We need to find an assignment so…
Patrick Schmidt
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8
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4 answers

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-flow algorithm. Flow networks are quite handy…
Patrick Schmidt
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7
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2 answers

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 all assignments and then checking if they are…
Gilfoyle
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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 needs to be assigned to exactly $m$ or $m+1$…
Nitzan Shaked
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5
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1 answer

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
Arie
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1 answer

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 variants. However, if $n$ is large, $O(n^3)$ may not…
Nathaniel Bubis
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Simple Task-Assignment Problem

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 the general assignment formulation in Wikipedia,…
bettersayhello
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2 answers

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 coordinates to the destination ones so that the total…
eawer
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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 $x_{ij}$ equals one if object $j$ is assigned to $i$, $0$…
deb2014
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1 answer

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 using the pegs given, satisfying the following…
user75291
4
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2 answers

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 assign agent to perform exactly one task $j$…
ELEC
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4
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2 answers

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 person has a different availability (ex. ABDE,…
louie mcconnell
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Stable marriage problem with only one side having preferences

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 through a series of proposals, we end up with a stable…
Vishaal Kalwani
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4
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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 rooms (rooms can have different sizes, ranging…
leller
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2 answers

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 these people, I want to check if it is a diverse…
user2038833
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