Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Feedback arc set: Applications, Algorithms & Hardness

In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at least one edge out of every cycle in the graph. Removing these edges from the graph breaks all of the cycles, producing an acyclic subgraph of the given graph, often called a directed acyclic graph. A…

Language: English [EN]
Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.
100%
More settings
100% 100% 100% 100% 100%

Feedback arc set topic overview

The analysis highlights Applications, Algorithms and Hardness as prominent areas in the source structure around Feedback arc set.

Related topics
91
Source areas
5
Connected nodes
96
Extracted relationships
72
Concept neighborhoods
38
Bridge connections
96

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Algorithms · 32 topics
Overview · 24 topics
Applications · 18 topics
Hardness · 12 topics
Theory · 5 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Applications

Algorithms

Hardness

Theory

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

How Feedback arc set connects Entity context

The extracted context around Feedback arc set shows recurring relationship patterns in the source. For example, Feedback arc set → Although, APX, APX-hard, As, Beyond, By, If, Karp, Lawler, NP, NP-hard, The, This Another extracted example is Feedback arc set → Alternatively, Among, Applications, Finding, In, Kemeny, Many, Reversing, Several, The, This, Young. Use these groups to spot repeated connection types before inspecting the individual relationships.

Feedback arc set

Top relations

related to Inapproximability · 13
Feedback arc set → Although, APX, APX-hard, As, Beyond, By, If, Karp, Lawler, NP, NP-hard, The, This
has application · 12
Feedback arc set → Alternatively, Among, Applications, Finding, In, Kemeny, Many, Reversing, Several, The, This, Young
related to NP-hardness · 12
Feedback arc set → But, Eugene Lawler, In, It, Karp, Karp's, NP-complete, NP-completeness, Richard, Some NP-complete, This, Thus
related to Theory · 12
Feedback arc set → Conversely, Every, For, Hamiltonian, In, It, More, Omega, The, The Hamiltonian, Therefore, This
related to Restricted inputs · 8
Feedback arc set → Although, Every, In, It, Planar, The, These, This
related to Exact · 7
Feedback arc set → Because, Held, In, Karp, On, One, Searching
related to Equivalences · 5
Feedback arc set → Here, However, In, The, These
related to Approximate · 3
Feedback arc set → Determining, The, This

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

feedback arc set graph edges problem displaystyle minimum directed acyclic time graphs vertices maximum approximation one size algorithm vertex subgraph

Feedback arc set relationships Subject–Predicate–Object triples

TTTA extracted 72 structured relationships around Feedback arc set. Examples in this analysis include Feedback arc set → has application → Several and Feedback arc set → has application → Reversing. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Feedback arc sethas applicationSeveral0.60section
Feedback arc sethas applicationReversing0.60section
Feedback arc sethas applicationApplications0.60section
Feedback arc sethas applicationIn0.60section
Feedback arc sethas applicationFinding0.60section
Feedback arc sethas applicationAmong0.60section
Feedback arc sethas applicationMany0.60section
Feedback arc sethas applicationThe0.60section
Feedback arc sethas applicationAlternatively0.60section
Feedback arc sethas applicationKemeny0.60section
Feedback arc sethas applicationYoung0.60section
Feedback arc sethas applicationThis0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Feedback arc set bring nearby vocabulary together. In this analysis, examples include Arc, Feedback and Set. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Feedback arc set
    • Arc
    • Feedback
    • Set
    • Minimum
    • Graph
    • Problem
    • Edges
    • Directed
    • Displaystyle
    • Acyclic
    • Vertices
    • Sets
  • feedback arc set
    • Arc
    • Feedback
    • Set
    • Minimum
    • Graph
    • Problem
    • Edges
    • Directed
    • Displaystyle
    • Acyclic
    • Sets
    • Vertices
  • graph theory
    • Directed
    • Set
    • Edges
    • Displaystyle
    • Minimum
    • Vertex
    • Vertices
    • Size
    • Every
    • Graphs
    • One
    • Acyclic
  • graph algorithms
    • Directed
    • Set
    • Edges
    • Displaystyle
    • Minimum
    • Vertex
    • Vertices
    • Size
    • Every
    • Graphs
    • Edge
    • Used
  • directed graph
    • Directed
    • Graph
    • Set
    • Graphs
    • Edges
    • Displaystyle
    • Feedback
    • Minimum
    • Vertices
    • Vertex
    • Acyclic
    • Edge
  • directed acyclic graph
    • Subgraph
    • Directed
    • Graph
    • Maximum
    • Set
    • Graphs
    • Edges
    • Displaystyle
    • Feedback
    • Minimum
    • Vertices
    • Approximation
  • graph drawing
    • Directed
    • Set
    • Edges
    • Displaystyle
    • Minimum
    • Vertex
    • Vertices
    • Size
    • Every
    • Graphs
    • One
    • Acyclic
  • approximation ratio
    • Ratio
    • Algorithm
    • Subgraph
    • Maximum
    • Polynomial
    • Time
    • Subgraphs
    • Displaystyle
    • Problem
    • Set
    • Minimum
    • Arc

Connections between topic areas Semantic bridges

For Feedback arc set, one of the stronger structural bridges in this analysis connects Feedback arc set with Algorithms. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Feedback arc set — Algorithms · splits 64 ⟂ 33
Feedback arc set — Overview · splits 72 ⟂ 25
Feedback arc set — Applications · splits 78 ⟂ 19
Feedback arc set — Hardness · splits 84 ⟂ 13
Feedback arc set — Theory · splits 91 ⟂ 6

Map overview Semantic statistics

Feedback arc set

Nodes97
Edges96
Triples72
Avg. degree1.98
Density0.020619
Components1

Source & methodology

TTTA analyzes the structure around Feedback arc set to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Applications, Algorithms & Hardness, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Feedback arc set · EN edition · Analysis: TopicsToTalkAbout

For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.