Abstract
We present an O ( n 3 ) -time approximation algorithm for the maximum traveling salesman problem whose approximation ratio is asymptotically 61 81 , where n is the number of vertices in the input complete edge-weighted (undirected) graph. We also present an O ( n 3 ) -time approximation algorithm for the metric case of the problem whose approximation ratio is asymptotically 17 20 . Both algorithms improve on the previous bests.
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