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Alignment is an important sequence comparison measure. Algorithms that compute alignments have a wide range of applications, namely in bioinformatic tools. Alignments can be computed as maximum scoring paths in Alignment DAGs. In this paper we study the properties of matrices that contain alignment scores between a string and all the sub-strings of another string. We focus on the fact that these matrices have the Monge property and are sparse in some sense. Related studies were recentlydoi:10.1016/j.tcs.2011.12.068 fatcat:xklelti2o5a3rdlzzgy5v2bk4m