*Lance Fortnow*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175782
- eISBN:
- 9781400846610
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175782.003.0006
- Subject:
- Computer Science, Programming Languages

This chapter demonstrates several approaches for dealing with hard problems. These approaches include brute force, heuristics, and approximation. Typically, no single technique will suffice to handle ...
More

This chapter demonstrates several approaches for dealing with hard problems. These approaches include brute force, heuristics, and approximation. Typically, no single technique will suffice to handle the difficult NP problems one needs to solve. For moderate-sized problems one can search over all possible solutions with the very fast computers available today. One can use algorithms that might not work for every problem but do work for many of the problems one cares about. Other algorithms may not find the best possible solution but still a solution that's good enough. Other times one just cannot get a solution for an NP-complete problem. One has to try to solve a different problem or just give up.Less

This chapter demonstrates several approaches for dealing with hard problems. These approaches include brute force, heuristics, and approximation. Typically, no single technique will suffice to handle the difficult NP problems one needs to solve. For moderate-sized problems one can search over all possible solutions with the very fast computers available today. One can use algorithms that might not work for every problem but do work for many of the problems one cares about. Other algorithms may not find the best possible solution but still a solution that's good enough. Other times one just cannot get a solution for an NP-complete problem. One has to try to solve a different problem or just give up.

*Lance Fortnow*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175782
- eISBN:
- 9781400846610
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175782.003.0010
- Subject:
- Computer Science, Programming Languages

This chapter explores some of today's great challenges of computing. These challenges include parallel computation, dealing with big data, and the networking of everything. The chapter then argues ...
More

This chapter explores some of today's great challenges of computing. These challenges include parallel computation, dealing with big data, and the networking of everything. The chapter then argues that P versus NP goes well beyond a simple mathematical puzzle. The P versus NP problem is a way of thinking, a way to classify computational problems by their inherent difficulty. P versus NP also brings communities together. There are NP-complete problems in physics, biology, economics, and many other fields. Physicists and economists work on very different problems, but they share a commonality that can give great benefits from sharing tools and techniques. Tools developed to find the ground state of a physical system can help find equilibrium behavior in a complex economic environment. Ultimately, the inherent difficulty of NP problems leads to new technologies.Less

This chapter explores some of today's great challenges of computing. These challenges include parallel computation, dealing with big data, and the networking of everything. The chapter then argues that P versus NP goes well beyond a simple mathematical puzzle. The P versus NP problem is a way of thinking, a way to classify computational problems by their inherent difficulty. P versus NP also brings communities together. There are NP-complete problems in physics, biology, economics, and many other fields. Physicists and economists work on very different problems, but they share a commonality that can give great benefits from sharing tools and techniques. Tools developed to find the ground state of a physical system can help find equilibrium behavior in a complex economic environment. Ultimately, the inherent difficulty of NP problems leads to new technologies.