Gaps in XPARAL

Currently version 2.0 of XPARAL supports 6 gap types, in the future there will probably be fewer. This increased variety arose from an inability to parameterize log(N) as a cost function of gap length because it violates the rules of convex functions. There are three alternatives that do work; replacing Log(1) with Log(1.5), having gap length cost be Log(N)+1, or having gap length cost be Log(N+1). Currently the latter two of these options are available in XPARAL. The first of the three fixes is prone to hanging due to rounding error. Also,similar extensions were made to the square root case to maintain consistency and study their effects.

An illustration of the cover decomposition with each of the gap types is shown below. Note that in each picture the black polygon is the same alignment.

GapCost(N) = Gap Init + N
Affine

GapCost(N) = Gap Init + Log(N) + 1
 Convex

GapCost(N) = Gap Init + Log(N+1)
 Convex

GapCost(N) = Gap Init + Root(N)
 Convex

GapCost(N) = Gap Init + Root(N) + 1
 Convex

GapCost(N) = Gap Init + Root(N+1)
 Convex

Kristian Stevens
Last modified: Mon Oct 12 19:13:21 PDT 1998