# Multi-fragment algorithm

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Class Approximation algorithm Graph ${\displaystyle \Theta (N^{2}\log N)}$

The multi-fragment (MF) algorithm is a heuristic or approximation algorithm for the travelling salesman problem (TSP) (and related problems). This algorithm is also sometimes called the "greedy algorithm" for the TSP.

The algorithm builds a tour for the traveling salesman one edge at a time and thus maintains multiple tour fragments, each of which is a simple path in the complete graph of cities. At each stage, the algorithm selects the edge of minimal cost that either creates a new fragment, extends one of the existing paths or creates a cycle of length equal to the number of cities.[1]

## References

1. ^ Johnson, David; A. McGeoch, Lyle (1997). "The Traveling Salesman Problem: A Case Study in Local Optimization". Local Search in Combinatorial Optimization. 1. CiteSeerX 10.1.1.92.1635.