Abstract
For the traveling salesman problem (TSP) on n nodes, we show that a tour which is better than ω((n/2)!) alternative tours can be identified in O(n 3) time. Also we provide another algorithm of complexity O n 3) which is guaranteed to produce a solution which is better than ω(n/(k+1))!(k!) n/(k+1) alternative tours, whenever k is fixed. Further we show that by using an O(n 4) algorithm, a TSP tour which dominates ω((n/2)!n) alternative tours can be identified. We also suggest an O(n 5) algorithm with improved domination number.