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© Oxford University Press

Parameterized complexity analysis in computational biology

H.L. Bodlaender , R.G. Downey , M.R. Fellows 1, M.T. Hallett and H.T. Wareham

1To whom correspondence and requests for reprints should be sent computer Science Departement, Utrecht University, P.O. Box 80 089. 3508 TB. Utrecht, the Netherlands Mathematics Department, Victoria University. P.O. Box 600, Wellington, New Zealand Computer Science Department, University of Victoria, Victoria, British Columbia, V8W 3Pe, Canada Computer Science Department, University of Victoria, victoria, British Columbia, V8W 3P6, Canada Computer Science Department. University of Victoria, Victoria, British Columbia, V8W 3Pe, canada

Many computational problems in biology involve par–ameters for which a small range of values cover important applications. We argue that for many problems in this setting, parameterized computational complexity rather than NP-completeness is the appropriate tool for studying apparent intractability. At issue in the theory of parameter–ized complexity is whether a problem can be solved in time O(n{alpha})for each fixed parameter value, where a is a constant independent of the parameter. In addition to surveying this complexity framework, we describe a new result for the Longest Common Subsequence problem. In particular, we show that the problem is hard for W[t] for all I when parameterized by the number of strings and the size of the alphabet. Lower bounds on the complexity of this basic combinatorial problem imply lower bounds on more general sequence alignment and consensus discovery problems. We also describe a number of open problems pertaining to the parameterized complexity of problems in computational biology where small parameter values are important

Received on June 20, 1994; accepted on October 7, 1994

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