Cautionary Tales of Inapproximability

Modeling biology as classical problems in computer science allows researchers to leverage the wealth of theoretical advancements in this field. Despite countless studies presenting heuristics that report improvement on specific benchmarking data, there has been comparatively little focus on exploring the theoretical bounds on the performance of practical (polynomial-time) algorithms. Conversely, theoretical studies tend to overstate the generalizability of their conclusions to physical biological processes. In this article we provide a fresh perspective on the concepts of NP-hardness and inapproximability in the computational biology domain, using popular sequence assembly and alignment (mapping) algorithms as illustrative examples. These algorithms exemplify how computer science theory can both (a) lead to substantial improvement in practical performance and (b) highlight areas ripe for future innovation. Importantly, we discuss caveats that seemingly allow the performance of heuristics to exceed their provable bounds.