An Algorithm for the Traveling Salesman Problem (Classic Reprint) - Tapa dura

Sinopsis

Excerpt from An Algorithm for the Traveling Salesman Problem

Held and Karpta] have solved problems up to 13 cities by dynamic programming using an ibm 7090. A 13 city problem required 17 seconds. But such is the power of an exponential that, if their computation grows at the same rate as that of Gonzalez, a 20 city problem would require about 10 hours. Storage requirements, however, may become prohibitive before then. For larger problems than 13 cities, Held and Karp develop an approximation method which seems to work well but does not guarantee an optimal tour. Our concern here will be with methods that must eventually yield an optimal tour.

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