15. The method of claim 14 , further including considering potential transitions to (i,j) that involve consolidation and combine four cells in the partial alignment, wherein the potential transitions further include antecedent cell (i−2, j−1), representing potential consolidation of elements i−1 and i−2 from the query sequence, and antecedent cell (i−1, j−2), representing potential consolidation of elements j−1 and j−2 from the target sequence; wherein scoring of the potential transitions involving consolidation selects or combines attributes of consolidated elements, and scores transitions both from an antecedent cell into the cells representing the consolidated elements and from the cells representing the consolidated elements into cell (i,j), corresponding to partial alignment of four cells, two of which represent consolidated elements.
14. A method of aligning elements in a query sequence and to elements in a target sequence, wherein the elements represent at least one attribute representing a physical characteristic, the method including: representing potential element-to-element partial alignments between the query and target sequences in an m-by-n cell data structure, such that cell (i,j) represents potential alignment of query element i with target element j; forward propagating the attributes, for scoring purposes, from cells included in partial alignments into cells chosen to have a deleted element; processing the cells in the data structure in an order that processes a particular cell after antecedent cells have been processed to have a recorded selected transition and cumulative score; choosing, cell-by-cell, whether element pair (i,j) of the query and target sequences should belong to a partial alignment or whether one element in the element pair (i,j) should be deleted, including scoring cumulative scores of potential transitions between antecedent cells and the cell (i,j), wherein scoring a cumulative score of potential inclusion of the element pair (i,j) in the partial alignment includes adding a match score to previously scored cell (i−1,j−1), wherein calculating the match score includes using the attributes or propagated attributes of cell (i−1,j−1) and the attributes of cell (i,j), applying a transition measure to calculate query and target transition values, then comparing the query and target transition values to determine the match score; scoring cumulative scores of the potential deletions from the query or target sequence includes subtracting a deletion penalty from a previously scored antecedent cell, either cell (i−1,j) for deletion of element i from the query sequence or cell (i,j−1) for deletion of element j from the target sequence; selecting among the cumulative scores of the potential transitions and recording at least one selected transition and the cumulative score of the selected transition; and backtracking through the cumulative scores and the selected transitions, beginning with one or more high scores at one end of the query or target sequences to an opposite end and determining a total alignment, taking into account deletions, between the elements of the query and target sequences, and reporting for further processing at least the total alignment between the elements of the query and target sequences.