bipartite matching

USAGE SUMMARY

The phrase "bipartite matching" is correct and usable in written English. You can use it in contexts related to graph theory, computer science, and optimization problems. For example, "The algorithm efficiently finds a bipartite matching in the given graph." Alternative expressions include "two-sided matching" and "pairing in bipartite graphs."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

We demonstrate the close connection between the two problems by presenting a log space reduction from perfect bipartite matching to subtree isomorphism.

University of California, Berkeley

Figure 2 Weighted bipartite matching.

EURASIP Journal on Wireless Communications and Networking

Figure 5 Asymmetric bipartite matching with resource reallocation.

EURASIP Journal on Wireless Communications and Networking

Constraint (i) ensures the data chunk assignment as a bipartite matching.

EURASIP Journal on Wireless Communications and Networking

We then compute the maximum weight bipartite matching.

Bioinformatics

Values of similarity between conditions are used to compute the 1 1 maximum weight bipartite matching.

Database : the journal of biological databases and curation

AnnSim is defined as a 1 1 maximum weight bipartite matching.

Database : the journal of biological databases and curation

On the basis of this graph, we can compute a straightforward maximum-edge-weighted bipartite matching.

Algorithms for Molecular Biology

First of all, we introduce the concept of bipartite graph and maximum weight bipartite matching.

BioMed Research International

For every object of the type AlgebraicRule, a new AssignmentRule object is generated by means of the preceding bipartite matching.

BMC Systems Biology

Similarly to previous tree alignment and edit distance algorithms [ 26- 28], the algorithm presented here makes use of min-cost bipartite matching algorithms as subroutines.

Algorithms for Molecular Biology

Expert writing Tips

Best practice

When discussing "bipartite matching", clearly define the two distinct sets being matched to avoid ambiguity. For instance, specify whether you're matching workers to tasks or customers to services.

Common error

Avoid using "bipartite matching" interchangeably with general graph matching. Bipartite matching specifically applies to graphs where nodes can be divided into two disjoint sets, and edges only connect nodes from different sets.

Linguistic Context

The phrase "bipartite matching" functions as a noun phrase, typically used to describe a specific type of matching problem within graph theory and computer science. As Ludwig AI confirms, it's widely recognized and used in various academic and scientific contexts.

Expression frequency: Very common

Frequent in

Science

68%

Academia

30%

Formal & Business

1%

Less common in

News & Media

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "bipartite matching" is a grammatically sound noun phrase primarily used within scientific and academic domains. Ludwig AI analysis indicates its purpose is to define and categorize problems, with a strong prevalence in science-related contexts. The phrase maintains a formal register, and while very common in specific fields, it is less so in general or informal communication. When employing this term, clarity in defining the sets being matched is crucial to avoid ambiguity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

two-sided matching

Emphasizes the two distinct sets being matched, similar to bipartite structure.

stable matching

Focuses on the stability of the pairings, a common goal in matching problems.

assignment problem

Highlights the assignment of elements from one set to another.

maximum cardinality matching

Specifies the goal of maximizing the number of matched pairs.

perfect matching

Indicates a complete matching where all elements are paired.

graph matching

Broadly refers to matching problems in graphs, including bipartite graphs.

edge cover

Related concept in graph theory where edges 'cover' vertices.

maximum weight matching

Focuses on maximizing the total weight of the matched edges.

optimal assignment

Highlights the optimality of the matching or assignment.

combinatorial optimization

Broader term for finding the best solution from a finite set of possibilities, including matching problems.

FAQs

How is "bipartite matching" used in computer science?

"Bipartite matching" is a fundamental concept used in various algorithms and optimization problems, such as resource allocation, scheduling, and network flow. It involves finding the maximum number of independent edges in a bipartite graph.

What are some practical applications of "bipartite matching"?

Practical applications include assigning jobs to workers, matching organ donors to recipients, and routing data packets in networks. It is also used in image processing and data mining tasks.

What is the difference between "bipartite matching" and "maximum flow"?

"Bipartite matching" is often solved using maximum flow algorithms, but they are not the same. Bipartite matching is a specific type of problem, while maximum flow is a general algorithm that can be applied to various network problems, including bipartite matching.

What algorithms are commonly used to solve "bipartite matching" problems?

Common algorithms include the Hungarian algorithm, Ford-Fulkerson algorithm, and Hopcroft-Karp algorithm. The choice of algorithm depends on the size and structure of the bipartite graph.