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How a Problem About Pigeons Powers Complexity Theory
When pigeons outnumber pigeonholes, some birds must double up. This obvious statement — and its inverse — have deep connections to many areas of math and computer science. The post How a Problem About Pigeons Powers Complexity Theory first appeared on Quanta Magazine
They say a bird in the hand is worth two in the bush, but for computer scientists, two birds in a hole are better still. That’s because those cohabiting birds are the protagonists of a deceptively simple mathematical theorem called the pigeonhole principle. It’s easy to sum up in one short sentence: If six pigeons nestle into five pigeonholes, at least two of them must share a hole.
