The classes of problems which are respectively known and…
![“The classes of problems which are respectively known and not known to have good algorithms are of great theoretical interest. [...] I conjecture that there is no good algorithm for the traveling salesman problem. My reasons are the same as for any mathematical conjecture: (1) It is a legitimate…” quote by Jack Edmonds](https://sms4smile.com/q/img-quotes/43a/jack-edmonds-61996_algorithms_the-classes-of-problems-which-are-respec_50487.jpg)
“The classes of problems which are respectively known and not known to have good algorithms are of great theoretical interest. [...] I conjecture that there is no good algorithm for the traveling salesman problem. My reasons are the same as for any mathematical conjecture: (1) It is a legitimate mathematical possibility, and (2) I do not know.”
About This Quote
This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.
The quote highlights the intrigue of classifying problems by algorithmic tractability and posits a conjecture about the inherent difficulty of the traveling salesman problem, emphasizing uncertainty as a legitimate basis for mathematical speculation.
In simple terms: It underscores the theoretical value of distinguishing solvable from intractable problems.
Key Takeaway
The TSP likely lacks a polynomial‑time solution.
Themes
computational complexity
algorithmic theory
NP‑hardness
conjecture
theoretical computer science
Mood
curiosity
skepticism
intellectual rigor
Type
theoretical statement
conjecture
observation
When to use this quote
- research on NP‑complete problems
- academic discussions on algorithm limits
- designing heuristics for TSP
- teaching complexity theory
- evaluating algorithm performance
Key Concepts
algorithmic tractability
complexity classes
hardness conjecture
mathematical uncertainty
Practical Applications
- guiding research priorities in optimization
- informing curriculum on computational complexity
Questions to Reflect On
- What evidence would shift this conjecture?
- How does uncertainty drive research in complexity?