Algorithms Improvement

For large computing problems, 43 percent of algorithm families had year-on-year improvements that were equal to or larger than the much-touted gains from Moore’s Law. In 14 percent of problems, the improvement to performance from algorithms vastly outpaced those that have come from improved hardware. The gains from algorithm improvement were particularly large for big-data problems, so the importance of those advancements has grown in recent decades.

The single biggest change that the authors observed came when an algorithm family transitioned from exponential to polynomial complexity. The amount of effort it takes to solve an exponential problem is like a person trying to guess a combination on a lock. If you only have a single 10-digit dial, the task is easy. With four dials like a bicycle lock, it’s hard enough that no one steals your bike, but still conceivable that you could try every combination. With 50, it’s almost impossible — it would take too many steps. Problems that have exponential complexity are like that for computers: As they get bigger they quickly outpace the ability of the computer to handle them. Finding a polynomial algorithm often solves that, making it possible to tackle problems in a way that no amount of hardware improvement can.