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Questions tagged [matching]

A matching (aka Independent Edge Set) in a simple graph is the set of pairwise non-adjacent edges i.e. no two edges have common vertex.

A matching (aka Independent Edge Set) in a simple graph is the set of pairwise non-adjacent edges i.e. no two edges have common vertex. The related concepts are maximal matching, maximum matching, perfect or complete matching and near-perfect matching.

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Find a minimum-weight perfect b-matching, where b is even

How would one find a minimum-weight perfect b-matching of a general graph, where the number of edges incident on each vertex is a positive even number not greater than b? A minimum-weight perfect b-matching of a graph G is a subgraph M of minimal…
Dmitry Kamenetsky
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Best algorithm to generate matchmaking pairs

I am trying to come up with a matchmaking algorithm based on player ratings for my game, and I am pretty sure the algorithm I have is not the best (or maybe doesn't even work), but have no idea how to improve it. Suppose that I have 5 players,…
Mantracker
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Is a matching $M$ maximum iff the graph doesn't have an augmenting path wrt $M$?

Berge's theorem: a matching $M$ is maximum if and only if the graph doesn't have an augmenting path with respect to $M$. I don't understand this theorem. For instance the following matching is maximum but has an augmenting path, doesn't it? The…
Revolucion for Monica
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Maximal Matching of nodes that fall into four categories

Nodes have values. Node n's value is denoted n.val. Two or more nodes can have the same value. A node n is a category 0 node or more simply a '0' node iff n.val % 4 == 0. A node n is a 1 node iff n.val % 4 == 1. A node n is a 2 node iff n.val % 4…
josfervi
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Similarity of two monochromatic shapes

I need to find out to what extent two shapes are similar. I mean I've got two vectors of points - and just that, no shadows, color or whatever - simplest case. Two triangles are the perfect example. Of course this has to work regardless of what the…
kboom
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Finding preferences for G-S algorithm (Algorithm Design Chapter 1 exercise 7)

I'm working on Algorithm Design (Kleinberg-Tardos) Chapter 1 exercise 7: Some of your friends are working for CluNet, a builder of large communication networks, and they are looking at algorithms for switching in a particular type of input/output…
Brady Dean
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Blossom Algorithm

I have noticed that in the blossom algorithm, we need to find the blossom while finding the augmenting path. What will happen if I just know there is a blossom in a graph and the contracted graph has an augmenting path. Will the original graph not…
Bajru
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String matching problem needed some explanation

This is a question from CLRS book. (Chapter 32, string matching, the question is the problem for the whole chapter, it's in the end of the chapter) Let $y^i$ denote the concatenation of string y with itself $i$ times. For example, $(ab)^{3}$ =…
amV
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Prove that any tree contains a matching of size |InternalNodes|/2

How can i prove that any tree contains a matching of size |InternalNodes|/2? Thanks in advance
user108220
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Find a minimum-weight perfect 2-matching

How would one find a minimum-weight perfect 2-matching of a general graph? Is it possible to use standard matching techniques like Blossom V? A minimum-weight perfect 2-matching of a graph G is a subgraph M of minimal total edge weight, such that…
Dmitry Kamenetsky
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information about matching algorithms?

I have been searching for matching algorithms similar to the Gale Shapley, or stable marriage algorithm, but with no luck. The question is if there are other algorithms that are similar to the GS and used for the assignation of persons or items…
Layla
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Is the maximum matching problem trivial when the graph is complete?

I have a quick question. The maximum matching problem is an easy problem but not a trivial one. I was wondering that if the bipartite graph was complete, is it a trivial problem? I think we can just select an arbitrary edge $\{u,v\}$ and remove the…
Brika
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How do I show that the matching polytope of $K_{2n}$ is a linear projection of the perfect matching polytope of $K_n$?

Of course a matching polytope is the convex hull of edges in a matching and similarly for a perfect matching polytope.
user173185
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Problem with understanding two sided Matching Algorithm: maximium cardinality

I am trying to understand the maximum cardinality problem in the context of stable matching algorithm. I am reading the following article at the link: A Two-Sided Matching Decision Model Based on Uncertain Preference Sequences The article says…
user2994783
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Pattern Matching Variant Problem

Given string P with length n, and a function A on P [n] --> [n] that does the following: For every 1 <= k <= n A on P [k] = { the maximum index i such that P[1...i] = P[k...k+i-1] Write an algorithm that's optimal as possible that given string P…
AndyBrondy7
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