Questions tagged [assignment-problem]

For questions about the [assignment problem](https://en.wikipedia.org/wiki/Assignment_problem) in combinatorial optimization, **not** for problems that you've been set as a homework assignment.

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1answer
33 views

Assign n people to m rooms of different sizes, such that noone is alone and people are in largest rooms possible

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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13 views

How to clear rows in Tetris? [closed]

I'm doing an java assignment on tetris and this little bit of code is giving me trouble. I can't seem to figure out why my code for clearing completed lines is not working. Can some one please help me ...
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1answer
50 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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38 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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1answer
22 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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38 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
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1answer
21 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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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 ...
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1answer
77 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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64 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
24 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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44 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
20 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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22 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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1answer
50 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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129 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
65 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
108 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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44 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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0answers
68 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
347 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
313 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
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1answer
102 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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1answer
104 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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2answers
100 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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1answer
351 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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71 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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1answer
69 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
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1answer
589 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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379 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
492 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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2answers
103 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
202 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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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 ...
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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 ...
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1answer
311 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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2answers
129 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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2answers
332 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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2answers
182 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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725 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'...
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1answer
406 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 ...
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1answer
325 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 ...
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90 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 ...
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1answer
248 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 ...
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2answers
93 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 ...
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1answer
571 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 ...
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2answers
269 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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2answers
1k views

How to match two sets of points based on the closeset distance?

I have a set of points (tiny triangles) $K=\{1,2,\ldots, k\}$ and a set points (tiny circles) $N=\{1,2,\ldots, n\}$ and a matrix of positive real values $\mathbf{D}=\left[d_{ij}\right]$ for all $i\in ...
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0answers
114 views

How to construct a network flow problem?

I have the optimization problem given below max $\sum_{i=1}^{N}\sum_{j=1}^{M} x_{ij}R_{ij}$ s.t $\quad 1)\quad \sum_{j=1}^{M} x_{ij}=1 \quad \forall i$ $\quad 2)\quad x_{ij} \in {0,1}$ $\quad ...
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2answers
207 views

Minimizing the overall cost over groups

I am trying to solve the problem of minimizing the overall cost over several groups. The schema of the data goes something like this: ...