News Excerpt:

An unsolved problem in computer science simply called the P (Polynomial time) versus NP (Nondeterministic Polynomial time) problem, could hold the key to many modern-day problems.

What is the P versus NP problem?

• The P versus NP problem is one of the most famous unsolved questions in computer science and mathematics. 
• It essentially asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.
• Before delving into complex layers of P vs NP, you must understand what P and NP stand for:
• P (Polynomial time) comprises a class of problems that algorithms can solve quickly, within polynomial time.
• NP (Nondeterministic Polynomial time) includes problems whose solutions can be verified quickly, also within polynomial time.

What if P = NP?

• If P does equal NP, it would mean that the ability to check the correctness of a solution is essentially as good as knowing the method of getting to the solution. 
• If P is not equal to NP, it would mean that there are problems for which no quick solution exists, whereas this does not impede the ability to verify a solution quickly.

Implications for healthcare:

• The P vs NP question is a problem in mathematics and computer science, but that does not mean it will be confined there. 
• Antibiotic resistance is a significant global health concern. 
  • If P equals NP, we may have a way to quickly analyse bacterial genomes and predict their resistance patterns, helping doctors prescribe the most effective antibiotics. 
  • This would improve patient outcomes and help combat antibiotic resistance, including new antibiotics discoveries for emerging diseases.

• Cancer treatment:
• If P equals NP, we may have an opportunity to swiftly identify the optimal treatment for each individual cancer patient and potentially save many lives.
• Insurance companies grapple with NP problems when they have to determine premiums and packages based on considering numerous variables like age, health status, lifestyle, and medical history. 
• The P vs NP problem could help these companies optimise their decision-making and pave the way to fairer and more accurate premiums and conditions. 
• Government spending on healthcare can also be utilised with minimal leakage while programmes like Ayushman Bharat can contribute more effectively to achieving universal health coverage.
• By solving these complex problems more efficiently, we could potentially dramatically reduce resource constraints and improve health outcomes.

Other fields that can potentially benefit from P vs NP problem:

• These fields include logistics, finance, and even climate modelling, all of which could experience paradigm shifts if the P vs NP problem is solved in favour of the P = NP outcome.

Drawbacks of P being equal to NP:

• One potential drawback of P being equal to NP if ever that outcome comes to pass, lies in the realm of cryptography. 
• Many encryption schemes and algorithms rely on problems that are currently hard to solve, believed to be in the set of ‘NP’, not ‘P’ problems. 
• These schemes protect secrets by hiding them behind a problem that is very hard to solve but easy to verify. 
• If P equals NP, these problems will become easy to solve, rendering these encryption schemes vulnerable to attacks and compromising digital security.