The present invention provides methods for reducing the complexity of a nucleic acid sample to interrogate a collection of target sequences. Complexity reduction can be accomplished by fragmenting the nucleic acid sample with a restriction enzyme that has at least one variable position in the recognition sequence. In some aspects adaptors that ligate to some but not all possible overhangs generated by digestion are ligated to the fragments. This selective adaptor ligation allows for selective amplification of a subset of the fragments using primers complementary to the adaptor sequence. In another aspect primers that are complementary to a subset of the fragments after adaptor ligation are used for amplification. Amplified fragments may be analyzed to genotype polymorphisms by hybridization to an array of probes that are complementary to target sequences that will be amplified.