Chaining score contributions from anchors seem to be capped by the anchor length, but the paper doesn't explain why

[adamnovak]

In the Minimap2 paper in section 2.1.1, the chaining score contribution from going from one anchor (j) to the next (i) is supposed to be given by:

α(j,i)=min{min{yi−yj,xi−xj},wi} is the number of matching bases between the two anchors

In other words, take minimum distance between the tail ends of the two anchors in the read or in the reference, and then the minimum of that and the length of the destination anchor. That indeed seems to be what is implemented in the code:

minimap2/lchain.c

Lines 124 to 126 in ce03fbc

	dg = dr < dq? dr : dq;
	q_span = aj->y>>32&0xff;
	sc = q_span < dg? q_span : dg;

But why is the length of the destination anchor min'd in here, given what this is described as representing? Is this quantity really the "number of matching bases between the two anchors"? Or is it really intended to be something like the additional matching bases in anchor i that do not overlap matching bases in anchor j?

[lh3]

Is this quantity really the "number of matching bases between the two anchors"? Or is it really intended to be something like the additional matching bases in anchor i that do not overlap matching bases in anchor j?

This seems the same to me?

[adamnovak]

I'm thinking of the anchors as objects that occupy space in the read and the reference. For simplicity, consider the case of all matches. If there were zero bases "between" two anchors, the last base involved in the first anchor would immediately precede the first base involved in the second anchor. If there is some space between them it would look like this:

ACGTACGTACGTGATGA (Read)
JJJJJ (Anchor j = (0, 0, 5))
            IIIII (Anchor i = (12, 12, 5))
     ||||||| (7 matching bases between boundaries)
ACGTACGTACGTGATGA (Ref)

But given the 3-tuple anchor representation it could also be natural to think of anchors as point objects, with an associated w width but not actually occupying that space. But that also doesn't seem to describe what's being computed.

ACGTACGTACGTGATGA (Read)
J (Anchor j = (0, 0, 5))
            I (Anchor i = (12, 12, 5))
|||||||||||| (12 matching bases between start points)
ACGTACGTACGTGATGA (Ref)

Either way we still get:

α(j,i)=min{min{yi−yj,xi−xj},wi}
= min{min{12 - 5, 12 - 5}, 5}
= min{min{7, 7}, 5}
= min{7, 5}
= 5

The wi cap is hit and restricts the result.

Or have I missed a step where we ensured that the number of (potentially) matching bases between two anchors can't exceed the anchor width?