  Lineage tracing, the joint segmentation and tracking of living cells as they
move and divide in a sequence of light microscopy images, is a challenging
task. Jug et al. have proposed a mathematical abstraction of this task, the
moral lineage tracing problem (MLTP), whose feasible solutions define both a
segmentation of every image and a lineage forest of cells. Their branch-and-cut
algorithm, however, is prone to many cuts and slow convergence for large
instances. To address this problem, we make three contributions: (i) we devise
the first efficient primal feasible local search algorithms for the MLTP, (ii)
we improve the branch-and-cut algorithm by separating tighter cutting planes
and by incorporating our primal algorithms, (iii) we show in experiments that
our algorithms find accurate solutions on the problem instances of Jug et al.
and scale to larger instances, leveraging moral lineage tracing to practical
significance.
