  We propose a fast approximate solver for the combinatorial problem known as
tracking-by-assignment, which we apply to cell tracking. The latter plays a key
role in discovery in many life sciences, especially in cell and developmental
biology. So far, in the most general setting this problem was addressed by
off-the-shelf solvers like Gurobi, whose run time and memory requirements
rapidly grow with the size of the input. In contrast, for our method this
growth is nearly linear.
  Our contribution consists of a new (1) decomposable compact representation of
the problem; (2) dual block-coordinate ascent method for optimizing the
decomposition-based dual; and (3) primal heuristics that reconstructs a
feasible integer solution based on the dual information. Compared to solving
the problem with Gurobi, we observe an up to~60~times speed-up, while reducing
the memory footprint significantly. We demonstrate the efficacy of our method
on real-world tracking problems.
