The Held-Karp algorithm solves the travelling salesman problem exactly using dynamic programming, computing the shortest path that visits every subset of cities ending at each possible city, building up from small subsets to the full set of cities so each larger subproblem reuses previously computed smaller ones. It runs in O(n squared times 2 to the power n) time, exponential but a substantial improvement over the O(n factorial) time of brute force enumeration of all possible routes. Michael Held and Richard Karp published the algorithm in 1962, and it remains the standard method for computing exact travelling salesman solutions on modestly sized instances.
Facts
Time Complexity
Time Complexity (category)Exponential Time -- O(2^n) 1 Classification
Design Technique Credited ToMichael Held and Richard Karp (1962), independently Richard Bellman 2 Connections
Credited To
Source Wikipedia: Held-Karp algorithm
Source Wikipedia: Held-Karp algorithm
In Field
Source Wikipedia: Held-Karp algorithm
Invented By
Richard Karp co-developed this dynamic programming algorithm for the traveling salesman problem with Michael Held, published in 1962.
Source Wikipedia: Richard M. Karp
Uses Design Technique
Sources
1. Held-Karp Algorithm (Wikipedia)
Wikipedia infobox: time complexity exponential
exponential
Lead section
The Held-Karp algorithm, also called the Bellman-Held-Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to the starting point.
View the Source2. Wikipedia: Held-Karp algorithm
Lead section, history
proposed in 1962 independently by Bellman and by Held and Karp
entity record, description (design-technique)
The Held-Karp algorithm solves the travelling salesman problem exactly using dynamic programming, computing the shortest path that visits every subset of cities ending at each possible city, building up from small subsets to the full set of cities so each larger subproblem reuses previously computed smaller ones.
In Field: Algorithms and Complexity Theory, Lead sentence
Held-Karp algorithm, also called the Bellman-Held-Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a
Credited To: Richard M. Karp, Lead
The Held-Karp algorithm, also called the Bellman-Held-Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to the starting point.
Credited To: Richard E. Bellman, Lead
The Held-Karp algorithm, also called the Bellman-Held-Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to the starting point.
In Group: Traveling Salesman Tour Algorithms, Lead
The Held-Karp algorithm, also called the Bellman-Held-Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to the starting point.
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