Questions tagged [bipartite-matching]

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4
votes
2answers
6k views

The stable marriage algorithm with asymmetric arrays

I have a question about the stable marriage algorithm, for what I know it can only be used when I have arrays with the same number of elements for building the preference and the ranking matrices. ...
5
votes
2answers
466 views

Finding a subset in bipartite graph violating Hall's condition

We are given a bipartite graph of $n \leq 200$ vertices in both the first and the second partite set. Let $U$ be some set of vertices in the first set, and $V$ those vertices from the second that are ...
7
votes
1answer
4k views

How to find the maximum independent set of a directed graph?

I'm trying to solve this problem. Problem: Given $n$ positive integers, your task is to select a maximum number of integers so that there are no two numbers $a, b$ in which $a$ is divisible by $b$...
4
votes
3answers
2k views

Number of ways to fill a 2xN grid with M colors

This question was asked in the onsite regionals for ACM ICPC 2013 at Amritapuri. In short, the question asked to find the number of ways to fill a $ 2\times N$ grid with $M$ colors such that no two ...
4
votes
1answer
3k views

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 ...
4
votes
1answer
393 views

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 ...
5
votes
1answer
376 views

Decomposing a bipartite graph of maximal degree d to d matchings

I have tried for the last few days to prove that any bipartite graph of maximal degree d may be broken into (at most) d matchings. My main approach is to prove this inductively over the maximal ...
2
votes
1answer
575 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 ...
5
votes
3answers
1k views

Maximum number of matched vertexes in a one-to-many bipartite graph

I have a variant of bidding problem at hand. There are N bidders(~20) who bid for items from a pool of many items(~10K). Each bidder can bid many items. I want to maximize the number of bidders who ...
4
votes
1answer
637 views

Changing preference in Gale-Shapley algorithm?

Suppose, in the context of the classic marriage problem, two equal size groups of $n$ men and $n$ women are being matched, with the GS algorithm. If a man were to switch the order of a pair of women, ...
3
votes
1answer
2k views

Existence of bipartite perfect matching

Let $B = G(L, R, E)$ be a bipartite graph. I want to find out whether this graph has a perfect matching. One way to test whether this graph has a perfect matching is Hall's Marriage Theorem, but it is ...
1
vote
1answer
259 views

Weighted Matching with multiple assignments and min assignments

I need to do a weighted matching between two sets (say students and professors). The set of students is much larger than set of professors. So multiple students can be matched to professors. However, ...