# A computer science conundrum that could transform healthcare

In the 17th century, a Dutch draper named Anton van Leeuwenhoek used a small handmade microscope to peer into a world previously invisible to the human eye. This is how he discovered micro-organisms and the field of microbiology was born. It offered solutions to healthcare challenges that had previously seemed intractable.

Today we face a new set of complex health care problems that appear more intractable than others, due to their inherent complexity and the constraints they threaten to impose on resources.

#### P vs NP

Coincidentally, an unsolved problem in computer science, simply called the P versus NP problem, could hold the key to these modern-day conundrums. While it may sound like a cryptic puzzle reserved for computer scientists, its implications extend beyond algorithms and data structures and ripple through several fields, including healthcare. But what exactly is this puzzle, and how can its solution unlock a new era in medical science?

Let’s start with a simple arithmetic example. Suppose you are asked to multiply 17 by 19. Over time you arrive at the answer: 323. This is a ‘P’ problem: you can solve it fairly quickly. (‘P’ stands for polynomial time.) Suppose you are presented with 323 and asked to identify the two prime numbers you multiplied to get this. In this case you will have to take the trial and error route until you arrive at 17 and 19. This is a ‘NP’ problem: it takes longer to solve, but once you have the solution you can quickly verify it. (‘NP’ here is non-deterministic polynomial time.)

Healthcare has complex problems. Consider scheduling in a hospital: assigning doctors and nurses to shifts, booking operating rooms for operations, and organizing patient appointments. It is a complex puzzle that requires taking into account several factors – availability of staff, urgency of medical cases, etc. – and possible changes such as emergencies and cancellations.

The P versus NP question is this: Could there be a shortcut to solving ‘NP’ problems as quickly as ‘P’ problems? Because the implication is that if P equals NP, we could quickly find the optimal solution to these scheduling problems, which would significantly improve patient care.

The implications of solving this issue are deep and far-reaching, including for healthcare.

#### Implications for healthcare

The P versus NP question is a problem in mathematics and computer science, but that doesn’t mean it will be limited to that. If an existing problem can be given a faithful mathematical representation and turns out to be an ‘NP’ problem, the appropriate shortcut can help by turning it into a ‘P’ problem.

For example, antibiotic resistance is a major global health problem. If P equals NP, we may have a way to quickly analyze bacterial genomes and predict their resistance patterns, allowing doctors to prescribe the most effective antibiotics. This would improve patient outcomes and help combat antibiotic resistance, including new antibiotic discoveries for emerging diseases. Of course, patient compliance will still matter.

Cancer is a complex disease with numerous mutations. Determining the best treatment plan is an NP problem because it requires consideration of all possible combinations of medications and therapies. If P equals NP, we may have the opportunity to quickly identify the optimal treatment for each individual cancer patient and potentially save many lives. The catch here is that we will still need a large amount of data.

Insurance companies struggle with NP issues when they must determine premiums and packages based on numerous variables such as age, health status, lifestyle and medical history. If there is a shortcut to solving the P versus NP problem, these companies can optimize their decision-making and pave the way for fairer and more accurate premiums and terms. Moreover, government expenditure on healthcare can also be leveraged with minimal leakage, while programs like Ayushman Bharath can contribute more effectively to achieving universal healthcare coverage.

By solving these complex problems more efficiently, we can potentially dramatically reduce limited resources and improve health outcomes.

#### Surprising sources of progress

Although the P versus NP problem is a subject of ongoing research in computer science, the consensus among most experts is that P is unlikely to equal NP, implying that some problems will remain very difficult to crack even if there are a solution is found. – will be easier to verify. But this has not stopped researchers from exploring this question, and in pursuing it they have uncovered improvements in algorithms and new approaches to dealing with complex problems.

Throughout history, there have been many examples of seemingly insurmountable problems being overcome through innovative thinking. For example, before the discovery of electricity, candle makers lit our world. Yet most of them may never have anticipated the revolutionary consequences of Thomas Edison’s light bulb, which brought light to more people and for longer hours.

Likewise, after inventing the calculus and extending the binomial theorem to negative integers and fractions, Isaac Newton greatly improved our understanding of the irrational number pi. The tech giant Apple has transformed our expectations of what to expect from a watch in ways that Swiss watchmakers may never have expected.

#### They won’t all be winners

That said, one potential downside of P equals NP, if that outcome ever comes to fruition, lies in the area of cryptography. Many encryption schemes and algorithms are based on problems that are currently difficult to solve, and are considered to belong to the set of ‘NP’ problems and not to the ‘P’ problems. That is, these plans protect secrets by hiding them behind a problem that is very difficult to solve, but easy to verify. If P equals NP, these problems will be easy to solve, leaving these encryption schemes vulnerable to attack and compromising digital security.

That said, healthcare is not the only beneficiary of this problem-solving. The barrier faced by the P versus NP problem includes any area where the solution to a problem is blocked by the availability of significant computational resources. These areas thus include logistics, finance, and even climate modeling, all of which could undergo paradigm shifts if the P versus NP problem is resolved in favor of the P=NP outcome.

The Clay Mathematics Institute in Colorado continues to offer a million dollars to anyone who can definitively solve the P versus NP problem. But for anyone who does, a million dollars will pale in comparison to the rewards they can receive by revolutionizing various human endeavors, potentially boosting human progress in unimaginable ways.

As we look to the future, let’s remember that problems that seem insurmountable today may not be so tomorrow. Just like with the candle makers, the watchmakers and even Anton van Leeuwenhoek, the solution often comes from where we least expect it. Today’s brightest minds grappling with the P versus NP problem may be on the verge of a breakthrough that could redefine healthcare as we know it.

*Dr. C. Aravinda is a public health physician and student at IIT Madras pursuing a bachelor’s degree in data science.*

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