Abstract
Two natural polynomial-time approximation algorithms for the shortest common supersequence (SCS) of k strings are analysed from the point of view of worst-case performance guarantee. Both algorithms behave badly in the worst case, whether the underlying alphabet is unbounded or of fixed size. For a Tournament style algorithm proposed by Timkovskii, we show that the length of the SCS found is between k/4 and (3k + 2)/8 times the length of the optimal in the worst case. The corresponding bounds proved for the obvious Greedy algorithm are (4k + 17)/27 and (k−1)/e. Even for a binary alphabet, no constant performance guarantee is possible for either algorithm, in contrast with the guarantee of 2 provided by a trivial algorithm in that case.
Supported by a postgraduate research studentship from the Science and Engineering Research Council
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© 1993 Springer-Verlag Berlin Heidelberg
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Irving, R.W., Fraser, C.B. (1993). On the worst-case behaviour of some approximation algorithms for the shortest common supersequence of k strings. In: Apostolico, A., Crochemore, M., Galil, Z., Manber, U. (eds) Combinatorial Pattern Matching. CPM 1993. Lecture Notes in Computer Science, vol 684. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029797
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DOI: https://doi.org/10.1007/BFb0029797
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