The constrained greedy algorithm

For the symmetric TSP problem (STSP), the greedy algorithm is a preferred heuristic for constructing initial tours. However, the greedy heuristic can result in constructing a bad tour, or the worst tour. Therefore the greedy algorithm should be used with great care. In this paper, we present a greedy preprocessing algorithm used prior to STSP algorithms. The greedy preprocessing step is named the constrained greedy algorithm. The result of the preprocessing step is not a complete tour, and has sub-paths that have length less than or equal to a parameter L. Applying the preprocessing algorithm along with the STSP greedy algorithm results in competitive tours with Bentley's greedy, and Johnson-McGeoch greedy, for small and medium STSP problems.