where $`\mathcal{C}`$, $`\mathcal{O}`$ and $`\mathcal{E}`$ are the sets of cycles, odd paths, and even paths in the constructed adjacency graph of $`S''`$ and $`T''`$, and $`d := |S|+|T|-(|S''|+|T''|)`$ is the number of deleted markers. Function $`f : 2\mathbb{N} \rightarrow \mathbb{R}`$ scores each cycle and path proportional to its length. Because short cycles and paths are indicators of similarity, whereas long cycles and paths suggest the opposite, Gecko3-DCJ uses a simple realization of $`f`$ that works well in general:

where $`\mathcal{C}`$, $`\mathcal{O}`$ and $`\mathcal{E}`$ are the sets of cycles, odd paths, and even paths in the constructed adjacency graph of $`S''`$ and $`T''`$, $`d := |S|+|T|-(|S''|+|T''|)`$ is the number of deleted markers and $`p`$ is the deletion penalty. Function $`f : 2\mathbb{N} \rightarrow \mathbb{R}`$ scores each cycle and path proportional to its length. Because short cycles and paths are indicators of similarity, whereas long cycles and paths suggest the opposite, Gecko3-DCJ uses a simple realization of $`f`$ that works well in general: