Abstract
AbstractThe Travelling Salesman's Problem is to find a Hamilton path (or circuit) which has minimum total weight W*, in a graph (or digraph) with a non‐negative weight on each edge. The Greedy Travelling Salesman's Problem is “How much larger than W* can the total weight G* of the solution obtained by the Greedy Algorithm be?”. Using the theory of independence systems, it is shown that G*‐W* may be as large as f(n,M,W*) where n is the number of vertices and M is the maximum edge‐weight. The function f is determined for the several variations of the Travelling Salesman's Problem and the bound is shown to be best possible in each case.
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