traveling salesman problem: meaning, definition, pronunciation and examples
Low (Academic/Technical)Formal, Technical
Quick answer
What does “traveling salesman problem” mean?
A fundamental optimization problem in mathematics and computer science: find the shortest possible route that visits each given set of points exactly once and returns to the origin point.
Audio
Pronunciation
Definition
Meaning and Definition
A fundamental optimization problem in mathematics and computer science: find the shortest possible route that visits each given set of points exactly once and returns to the origin point.
A classic NP-hard problem in combinatorial optimization, used as a benchmark for algorithmic efficiency. It models real-world logistics and routing challenges.
Dialectal Variation
British vs American Usage
Differences
Primarily spelling: British 'travelling salesman problem', American 'traveling salesman problem'. Concept and usage are identical.
Connotations
Identical technical connotations in both varieties.
Frequency
Equal technical frequency. Abbreviation 'TSP' is universal.
Grammar
How to Use “traveling salesman problem” in a Sentence
The TSP is [adjective: NP-hard, computationally intensive].Researchers [verb: study, solve, approximate] the TSP.An algorithm for the TSP.Vocabulary
Collocations
Examples
Examples of “traveling salesman problem” in a Sentence
verb
British English
- The team is researching how to efficiently solve the travelling salesman problem.
American English
- This new software aims to approximate the traveling salesman problem faster.
adjective
British English
- The travelling-salesman-problem formulation is crucial for their model.
American English
- They faced a classic traveling-salesman-problem scenario in logistics.
Usage
Meaning in Context
Business
Rarely used directly; underlying concept applies to logistics and delivery route planning.
Academic
Central concept in operations research, computer science, and applied mathematics.
Everyday
Virtually never used. Might be mentioned in popular science contexts.
Technical
Standard term for a specific class of optimization problems.
Vocabulary
Synonyms of “traveling salesman problem”
Neutral
Weak
Watch out
Common Mistakes When Using “traveling salesman problem”
- Using 'travelling salesman' problem' (incorrect apostrophe).
- Assuming it has a simple, quick solution.
- Using it as a general term for any difficult journey.
FAQ
Frequently Asked Questions
For the general case, no. It is NP-hard, meaning no known algorithm can solve all instances quickly as the number of points increases.
No, it has many practical applications in logistics, microchip manufacturing (circuit board drilling), DNA sequencing, and network planning.
It means the problem is at least as hard as the hardest problems in NP. In practice, it suggests that finding an optimal solution for large instances is computationally infeasible.
The TSP requires finding a Hamiltonian cycle (a cycle visiting each vertex once) with the minimum total edge weight. The Hamiltonian path problem simply asks if any such cycle/path exists, without considering weights.
A fundamental optimization problem in mathematics and computer science: find the shortest possible route that visits each given set of points exactly once and returns to the origin point.
Traveling salesman problem is usually formal, technical in register.
Traveling salesman problem: in British English it is pronounced /ˈtrævəlɪŋ ˈseɪlzmən ˌprɒbləm/, and in American English it is pronounced /ˈtrævəlɪŋ ˈseɪlzmən ˌprɑːbləm/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of a SALESMAN who must TRAVEL to all CITIES on his list in the shortest PATH. The first letters spell T-S-P-C-P.
Conceptual Metaphor
OPTIMIZATION IS A SHORTEST PATH. / COMPLEXITY IS A MAZE.
Practice
Quiz
What does the 'traveling salesman problem' primarily model?