Parallel and Sequential Approximations of Shortest Superstrings
نویسندگان
چکیده
Superstrings have many applications in data compression and genetics. However the decision version of the shortest superstring problem is NP-complete. In this paper we examine the complexity of approximating a shortest superstring. There are two basic measures of the approximations: the compression ratio and the approximation ratio. The well known and practical approximation algorithm is the sequential algorithm GREEDY. It approximates the shortest superstring with the compression ratio of 1 2 and with the approximation ratio of 4. Our main results are: (1) An NC algorithm which achieves the compression ratio of 1 4+" . (2) The proof that the algorithm GREEDY is not parallelizable, the computation of its output is P-complete. (3) An improved sequential algorithm: the approximation ratio is reduced to 2.83. Previously it was reduced by Teng and Yao from 3 to 2.89. (4) The design of an RNC algorithm with constant approximation ratio and an NC algorithm with logarithmic approximation ratio.
منابع مشابه
Sequential and Parallel Approximation of Shortest Superstrings
Superstrings have many applications in data compression and genetics. However, the decision version of the shortest superstring problem is N P-complete. In this paper we examine the complexity of approximating shortest superstrings. There are two basic measures of the approximations: the length factor and the compression factor. The well known and practical approximation algorithm is the sequen...
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