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We study the approximation hardness of the Shortest Superstring, the MaximalCompression and the Maximum Asymmetric Traveling Salesperson (MAX-ATSP)problem. We introduce a new reduction method that produces strongly restrictedinstances of the Shortest Superstring problem, in which the maximal orbit sizeis eight (with no character appearing more than eight times) and all givenstrings having length four. Based on this reduction method, we are able toimprove the best up to now known approximation lower bound for the ShortestSuperstring problem and the Maximal Compression problem by an order ofmagnitude. The results imply also an improved approximation lower bound for theMAX-ATSP problem.

Improved Lower Bounds for the Shortest Superstring and Related Problems