An essential task in comparative genomics is to decompose two or more genomes into synteny blocks that are segments of chromosomes with similar contents. Given a set of d genomic maps each containing the same n markers without duplicates, the problem MAXIMAL STRIP RECOVERY (MSR) aims at finding a decomposition of the genomic maps into synteny blocks (strips) of the maximum total length ', by deleting the minimum number k = n' of markers which are likely noise and ambiguities. In this paper, we present a collection of new or improved FPT and approximation algorithms for MSR and its variants. Our main results include a 2O(d ')poly(nd) time FPT algorithm for -gap-MSR-d, a 2:36kpoly(nd) time FPT algorithm for both CMSR-d and -gap-CMSR-d, and a (d+1:5)-approximation algorithm for both CMSR-d and -gap-CMSR-d.