Thursday, March 15, 2007

Dr. Karp and The TCS Lens

or How I learned to stop worrying and love complexity.

[ed. note: This note was prompted by Aaron Clauset's series of articles titled 'Unreasonable effectiveness' (the title itself a riff on Eugene Wigner's famous essay). Further inspiration came from reading the various summaries of Karp's 'algorithmic lens' idea.]

I believe in the gospel of St. Bernard. We are about to enter the age of the algorithm. The only question is: what kind of algorithm will it be ?

We're all familiar with the steps. Define the problem. Design an algorithm. Analyze the algorithm. Rinse and repeat, till we have a matching lower bound, or till we hit an even harder problem. Algorithms are designed from the top down, by a coffee-swilling researcher with a whiteboard, with the elegance of a swiss watch, or the clumsiness of a sledgehammer. Some of them are so beautiful they make you weep. Some are algorithms "in name only"; no one in their right minds would ever dream of implementing one of these beasts.

The algorithmic lens flips this on its head: complexity (and the solution) emerges from a set of simple rules. It's like Spore; set up the rules, start the game, and see what happens. The ingenuity here is not in the construction of a solution, but in the design of the rules. It's declarative, not procedural. It's bottom up, not top down. It's distributed, not centralized.

It has the flavor of (computational) complexity: I'll give you a resource; a guess, a random coin, a scratch pad, an AskJeeves clone. You tell me what I can do with how little. But it's still a lens. Why ? Things we're familiar with show up as distributed, bottom up, emergent constructions: A Voronoi diagram is a battle between equally (or unequally) matched forces. A Steiner tree is a soap bubble diagram. A clustering algorithm is a local "I'll go to my closest friend"; a regular language is the consequence of amnesiac entities bouncing around between states.

It's unsettling: we aren't the masters of our domain any more. We're not GOD, intelligently designing beautiful watches. We're just the rule-makers for a complex system. It's like being the parent of a young child !

What we can do is this: find out which rules yield cause what solutions to emerge. We study social networks, and watch complexity emerge from a set of simple pairwise interactions. In other words, the algorithm IS the social network. You can't get much more Web 2.0 than that...

If you've heard this before, it's because you have: things like the Ising model, phase transitions, statistical mechanics, Conway's Game of Life, Stephen Wolfram's New Kind of Science. So what makes these concepts so exciting now ?

Maybe it's all about scale. We preach that immense scale requires theoretical analysis; the N0 in the "for all n > N0" of O() notation is finally here. But maybe linear time algorithms, streaming algorithms, and small space sketching are all soon-to-be-futile attempts to stave off the inevitable horrible failure of programs to manage the complexity of the data we deal with. Suddenly, local algorithms that evolve continuing solutions look quite appealing, as well adaptive.

It's an exciting time to do algorithms, whether you're designing watches, or setting up an ecosystem.