Parameterized complexity analysis in

Many computational problems in biology involve par-ameters/or which a small range of values cover important applications. We argue that for many problems in this setting, parameterized computational complexity rather than NF'-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(na)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