# 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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1 vote
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### Find an assignment discarding a subset of possible assignments

We have a $N \times N$ cost matrix where the cost denotes the amount incurred for assigning a worker to a task. The number of possible assignments is $N!$. Let us call this set of all possible ...
41 views

### Number of matchings in a bipartite graph having missing edges

Suppose we have a bipartite graph with $N$ vertices on either side. In the full bipartite graph, the number of edges is $N^2$ and the number of possible matchings (i.e. assignments) is $N!$. Now ...
1 vote
93 views

### High-multiplicity maximum-weight matching

There are $n$ people and $m$ jobs. We would like to assign at most one job to each person. For each person,job pair, there is a positive value determining the fitness of this person to that job. The ...
132 views

### Best balanced assignment

I'm at a problem I don't know better to name it... maybe it's already a well known problem? It seems quite simple: There are objects and labels in a n:m relation. (Each of the n objects may be ...
1 vote
100 views

### Preference based assignment problem to maximize utility

I am studying an optimization problem which can be recast as an LP I have described below. I wish to understand the structure of optimizers of the original problem by studying the optimizers of the LP....
27 views

### How an assignment problem is solved using greedy heuristic algorithm

Consider small instance of GAP involving 5 items and 2 resources with capacities 5 and 12 respectively. If we have cost matrix Cij and also consumption matrix bij with jobs vs resources, how can we ...
48 views

### Assignment problem with maximal partitioning

Recently I came across a problem I don't get may hands on: Given p binary positions. Let s be the number of "set-bits" (1 < s < p * 2^(p-1) - 1). I need the maximal set of assigments ...
42 views

### Assignment problem - One task per agent, with restriction

I have $k$ agents and 2 tasks. Each agent is to be assigned to one task. Thus, agent $i$ must choose between tasks 1 and 2, which have costs $c_i$ and $b_i$ and flow $p_1(c_i)$ and $p_2(b_i)$, ...
1 vote
145 views

### Algorithm for a modified worker-task assignment problem with groups of tasks and substitutability between tasks within groups

I'm looking for an algorithm to solve a modified version of the assignment problem. It differs from the standard assignment problem in that the modified version has groups of tasks instead of just ...
1 vote
59 views

### A kind of generalised assignment problem where we minimise error relative to a goal "weight"/"value" - how to solve it?

I apologize if I did not use the terminology entirely correctly in the title. This problem seems to me quite similar to an assignment problem and likely something that occurs in real life in business. ...
1 vote
35 views

### Assign items from inventory to people maxmizing the number of satisfied people

We have a set of people, and each person has a list of wished items (not unique, they could want multiple copies of each item). We have an inventory of items that we want to assign to the people. We ...
1 vote
264 views

### fastest algorithm for rectangular linear assignment problem

I want to optimally assign $m$ jobs equally to $n$ workers, where $m>n$. Assume $m = an$ for some integer $a$, so that each worker must get exactly $a$ jobs. (The rectangular linear assignment ...
1 vote
61 views

1 vote
51 views

### Is n-dimentional assignment problem for points NP-hard?

We have $n$ sets of $k$ points in $\mathbb R^d$ and we are trying to partition them to $k$ clusters of $n$ points such that from each set every point is mapped to a different cluster and the sum of ...
1 vote
58 views

### Algorithms for alignment of posets

I have been looking for a while but I cannot find an algorithm for a particular generalisation of sequence alignment. I have two posets $(A, <)$ and $(B, <)$ and a similarity score $s(a, b)$ for ...
1 vote
43 views

### Find approximate 'best' matching pairs by calculating the fewest possible weights

My specific problem is as follows: Given two list of texts (in the order of 5 to 50 items) Find best matching pairs with their corresponding matching score (weight) Where each item can only be ...
1 vote
26 views

### Predicate variant of Assignment Problem

Given two equally sized sets, $P$ of Boolean predicates and $E$, I want to decide if there exists a bijective function $f: P \rightarrow E$, such that \begin{align} \forall p \in P \; p(f(p)) \end{...
1 vote
44 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 ...
31 views

### 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 ...
669 views

1 vote
94 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 ...