Long Tours and Short Superstrings (Preliminary Version)
نویسندگان
چکیده
This paper considers weight-maximizing variants of the classical symmetric and asymmetric travelingsalesman problems. Like their weight-minimizing counterparts, these variants are M A X SNP-hard. We present the first nontrivial approximation algorithms for these problems. Our algorithm for directed graphs finds a tour whose weight is a t least Q M 0.603 times the weight of a maximum-weight tour, and our algorithm for undirected graphs finds a tour whose weight is at least M 0.714 times optimal. These bounds compare favorably with the f and 5 bounds that can be obtained for undirected and directed graphs, respectively, b y simply deleting the minimum-weight edge from each cycle of a maximum-weight cycle cover. Our algorithm for directed graphs can be used to improve several recent approxamation results for the shortestsuperstring problem.
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