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Longest path problem: Science, Special classes of graphs & Parameterized complexity

In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges. In…

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Longest path problem topic overview

The analysis highlights Science, Special classes of graphs and Parameterized complexity as prominent areas in the source structure around Longest path problem.

Related topics
52
Source areas
6
Connected nodes
58
Extracted relationships
25
Concept neighborhoods
38
Bridge connections
58

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.

Special classes of graphs · 20 topics
Overview · 15 topics
Parameterized complexity · 7 topics
NP-hardness · 4 topics
Acyclic graphs · 3 topics
Approximation · 3 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

NP-hardness

Acyclic graphs

Approximation

Parameterized complexity

Special classes of graphs

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 Longest path problem connects Entity context

The extracted context around Longest path problem shows recurring relationship patterns in the source. For example, Longest path problem → Because, Hamiltonian, If, In, NP-complete, NP-hard, The, The NP-hardness, Therefore Another extracted example is Longest path problem → Björklund, For, Husfeldt, In, Khanna, NP, Omega, The. Use these groups to spot repeated connection types before inspecting the individual relationships.

Longest path problem

Top relations

related to NP-hardness · 9
Longest path problem → Because, Hamiltonian, If, In, NP-complete, NP-hard, The, The NP-hardness, Therefore
related to Approximation · 8
Longest path problem → Björklund, For, Husfeldt, In, Khanna, NP, Omega, The
related to Parameterized complexity · 6
Longest path problem → Apply, For, Let, Perform, The, Use
is a · 2
Longest path problem → problem of finding a simple path of maximum length in a given graph, same as the Travelling salesman path problem

Important terminology

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

Important terminology

path longest graphs problem length time graph displaystyle also algorithm polynomial vertices number simple paths acyclic known directed given solved

Longest path problem relationships Subject–Predicate–Object triples

TTTA extracted 25 structured relationships around Longest path problem. Examples in this analysis include Longest path problem → is a → problem of finding a simple path of maximum length in a given graph and Longest path problem → is a → same as the Travelling salesman path problem. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Longest path problemis aproblem of finding a simple path of maximum length in a given graph0.90text
Longest path problemis asame as the Travelling salesman path problem0.90text
Longest path problemrelated to ApproximationBjörklund0.60section
Longest path problemrelated to ApproximationHusfeldt0.60section
Longest path problemrelated to ApproximationKhanna0.60section
Longest path problemrelated to ApproximationThe0.60section
Longest path problemrelated to ApproximationOmega0.60section
Longest path problemrelated to ApproximationFor0.60section
Longest path problemrelated to ApproximationNP0.60section
Longest path problemrelated to ApproximationIn0.60section
Longest path problemrelated to NP-hardnessThe NP-hardness0.60section
Longest path problemrelated to NP-hardnessHamiltonian0.60section

Related concept clusters Concept neighborhoods

The concept neighborhoods around Longest path problem bring nearby vocabulary together. In this analysis, examples include Path, Problem and Length. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Longest path problem
    • Path
    • Problem
    • Length
    • Time
    • Also
    • Graphs
    • Dag
    • Vertex
    • Paths
    • Polynomial
    • Vertices
    • Algorithm
  • longest path problem
    • Path
    • Problem
    • Length
    • Time
    • Decision
    • Graphs
    • Parameterized
    • Also
    • Polynomial
    • Np-hard
    • Vertices
    • Dag
  • graph theory
    • Path
    • Acyclic
    • Paths
    • Also
    • Directed
    • Longest
    • Simple
    • Number
    • Vertices
    • Problem
    • Time
    • Critical
  • path
    • Problem
    • Time
    • Graphs
    • Vertices
    • Also
    • Algorithm
    • Dag
    • Weighted
    • Displaystyle
    • Acyclic
    • Vertex
    • Number
  • graph
    • Path
    • Acyclic
    • Paths
    • Also
    • Directed
    • Longest
    • Simple
    • Number
    • Vertices
    • Problem
    • Time
    • Critical
  • weighted graphs
    • Vertices
    • Time
    • Edges
    • Problem
    • Path
    • Polynomial
    • Also
    • Longest
    • Length
    • Algorithm
    • Dynamic
    • Graphs
  • shortest path problem
    • Problem
    • Time
    • Decision
    • Found
    • Graphs
    • Parameterized
    • Paths
    • Polynomial
    • Np-hard
    • Vertices
    • Np-complete
    • Also
  • directed acyclic graphs
    • Acyclic
    • Directed
    • Critical
    • Paths
    • Time
    • Graph
    • Problem
    • Results
    • Path
    • Polynomial
    • Also
    • Longest

Connections between topic areas Semantic bridges

For Longest path problem, one of the stronger structural bridges in this analysis connects Longest path problem with Special classes of graphs. 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
Longest path problem — Special classes of graphs · splits 38 ⟂ 21
Longest path problem — Overview · splits 43 ⟂ 16
Longest path problem — Parameterized complexity · splits 51 ⟂ 8
Longest path problem — NP-hardness · splits 54 ⟂ 5
Longest path problem — Acyclic graphs · splits 55 ⟂ 4
Longest path problem — Approximation · splits 55 ⟂ 4

Map overview Semantic statistics

Longest path problem

Nodes59
Edges58
Triples25
Avg. degree1.97
Density0.033898
Components1

Source & methodology

TTTA analyzes the structure around Longest path problem to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Science, Special classes of graphs & Parameterized complexity, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Longest path problem · EN edition · Analysis: TopicsToTalkAbout

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