Medical diagnosis and treatment is NP-complete

Abstract

ABSTRACT There is great interest in the pursuit of process-driven, algorithmic allocation of health-care resources, including computer-aided medical diagnosis and treatment (MDT). Little is understood regarding the computational complexity of MDT; however, and if determined, how relevant the complexity would be to automating MDT. We approach analysing the computational complexity of MDT in several ways: (1) proving that MDT is computationally intractable (NP-complete, NPC) by reducing the travelling salesperson (TSP) and set-cover (SETCOVER) problems to MDT, (2) showing, in contrast, an example of MDT in tractable form, and (3) showing that, leaving aside TSP and SETCOVER, there are computationally efficient, heuristic-driven search methods based on human diagnostician methods. Calculations show that the sparseness of actual symptom-treatments sets in the space of all possible sets is astronomical (e.g., 10−204,678). While the computational complexity of MDT is interesting theoretically, pragmatically uncovering actual human cognitive practices of MDT will accelerate the development of artificial intelligence to assist and eventually replace physicians.