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The multiple alignment problem is then reduced to to subsequent alignment steps of individual sequences to a growing multiple alignment graph.
The more recent IsoRankN uses a different method of spectral clustering on the multiple alignment graph to compute a global alignment of multiple PPI networks.
The assembler builds this multiple alignment graph using an adjustable greedy algorithm of taking a 'query' read, finding the pairwise overlaps to it, constructing a multiple alignment of those overlaps, then choosing a subsequent 'query' read from the overlapped reads that are only partially aligned so far (thereby extending the multiple alignment).
Following the construction of the multiple alignment graph, a series of 'detangling' algorithms are used to simplify the complex regions of the graph, such as overly collapsed regions shorter than the length of the reads (i.e., parts of reads that happened to be near-identical to each other by chance, and so produced overlaps that collapsed into a single multiple alignment region).
If any pairwise overlap alignments conflict with the current multiple alignment graph, corrective algorithms use the conflicting alignments to either ignore the new pairwise overlap (if the graph is more consistent) or to correct the constructed multiple alignment (if the new pairwise overlap identifies a misalignment in the graph).
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As a summary of graph comparisons, we have reviewed an array of methods from early single-feature, distance-based algorithms to the most current multiple network alignment graphs.
The pairwise alignments used to define segments in the anchor graph have already been filtered for orthology (using delta-filter as described in Section 2.1) but inconsistencies between pairwise alignments arising from repeats and duplications can produce paths in the alignment graph with multiple segments from the same genome.
A HAL graph, therefore, decomposes a multiple alignment into a set of pairwise alignments, which are represented as breakpoint graphs.
As a result, connected components in the alignment graph may contain multiple segments from a single genome.
This merging step must yield a directed acyclic graph for the next (multiple) alignment step.
A multiple alignment can then be derived from the graph using an efficient heaviest common subsequence algorithm (Jacobson and Vo, 1992).
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