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# Questions tagged [bipartite-matching]

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28 questions with no upvoted or accepted answers
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### Complexity of removing edges to eliminate a perfect matching

Suppose $G$ is a bipartite graph which has a perfect matching. I want to find the fewest number of edges to delete from $G$ so that a perfect matching no longer exists. What is the complexity of this ...
738 views

### Faster maximum weight matching algorithm in bipartite graph

I need to do a maximum weight matching in bipartite graphs rather than maximum weight perfect matching (which means that there is no need to match all the nodes). The nodes each side are both (at ...
321 views

699 views

### How can we add back edges in Ford - Fulkerson algorithm?

I was going through the Ford-Fulkerson(FF) algorithm. The given graph is directed and there is an edge from A to B with capacity y. Now sending a flow of x units (x < y) from A to B is equivalent ...
317 views

### Min-weight bipartite matching in Christofides' algorithm

Content: The Christofides algorithm finds a minimum spanning tree, then finds all the odd degree vertices, and adds extra edges using a minimum weight bipartite matching on those odd vertices to make ...
1 vote
175 views

### Graph in which greedy algorithm for maximum matching is a 2-approximation

Here is a greedy algorithm for maximum bipartite matching: Iteratively select an edge that is not incident to previously selected edges. This algorithm returns a 2-approximation, and runs in linear ...
1 vote
71 views

### Hardness result for online matching

Currently studying the following paper: "Fair Allocation in Online Markets" - Gollapudi and Panigrahi 2014 In which they present Theorem 2 as a hardness result for online maxmin matchings (...
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
42 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
45 views

### bipartite d regular expender explicit construction

I am looking for an explicit (and simple) construction of a d regular bi bipartite graph which is an expander. I searched the web and didn't find any sufficient answer. The only explicit graph I did ...
1 vote
84 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 ...
1 vote
80 views

### Finding maximum bipartite matching

I read an article https://www.geeksforgeeks.org/maximum-bipartite-matching/ to solve the maximum bipartite problem. In this article, two solutions are given. In the first solution, they have ...
1 vote
90 views

### Stable matching of producers, consumers and objects

Has the following version of the stable matching problem been studied? There are $k$ types of objects. There are $n$ producers, each of whom can produce a single object of any type, and has a ...
1 vote
54 views

### How to maximize the number of buyers in a shop?

There is a shop which consists of N items and there are M buyers. Each buyer wants to buy a specific set of items. However, the cost of all transactions is same irrespective of the number of items ...
53 views

### Budgeted min cost max flow in bipartite where the flows must also be a matching set

I'm trying to find a problem description that is roughly akin to a budgeted min-cost max-weight bipartite matching where the capacities are greater than 1. Imagine a max-flow problem on a graph that ...
49 views

### Is there a reduction from 2sat to bpm?

Given a 2SAT instance can we convert into bipartite perfect matching in parsimonious reduction?
48 views

### Problem with understanding Multi-party security circuit for secure stable matching

I am reading the following paper: MPCircuits: Optimized Circuit Generation for Secure Multi-Party Computation Paper Link I have following question: We have two groups shown in the circuit. Why we ...
62 views

### Maximum Matching for Line Graphs

I tried to study the maximum matching for a line-graph , i.e , $L(G)$ of a graph , $G(V,E)$ , from here : https://www.sciencedirect.com/science/article/pii/S0012365X97001039 But could not understand ...
68 views

### How to solve this problem using the Maximum matching algorithm for general graph?

For any general graph G(V,E) , the maximum matching can be calculated in O(√V.|E|) time using the following algorithm : https://www.researchgate.net/publication/...