In comparing genomic maps, it is often difficult to distinguish mapping errors and incorrectly resolved paralogies from genuine rearrangements of the genomes. A solution to this can be formulated directly as a Maximum Weight Independent Set (MWIS) search, where strips of markers syntenic on both genomes are the vertices, and conflicting strips are joined by edges, in order to extract the ensemble of compatible strips that accounts for the largest proportion of the data. This technique is computationally hard, however, and for the available maps on cereal genomes, for example, seems infeasible. To overcome this, we introduce biologically meaningful constraints on the strips, not only reducing the number of vertices for the MWIS analysis, but also provoking a decomposition of the graph into more tractable components. We introduce improvements to existing MWIS algorithms that greatly improve running time, especially when the strip conflicts define an interval graph structure. This, t...