The black-white bakery algorithm and related bounded-space, adaptive, local-spinning and FIFO algorithms

Abstract

A mutual exclusion algorithm is presented that has four desired properties: (1) it satisfies FIFO fairness, (2) it satisfies localspinning, (3) it is adaptive, and (4) it uses finite number of bounded size atomic registers. No previously published algorithm satisfies all these properties. In fact, it is the first algorithm (using only atomic registers) which satisfies both FIFO and local-spinning, and it is the first bounded space algorithm which satisfies both FIFO and adaptivity. All the algorithms presented are based on Lamport's famous Bakery algorithm [27], which satisfies FIFO, but uses unbounded size registers (and does not satisfy local-spinning and is not adaptive). Using only one additional shared bit, we bound the amount of space required by the Bakery algorithm by coloring the tickets taken in the Bakery algorithm. The resulting Black-White Bakery algorithm preserves the simplicity and elegance of the original algorithm, satisfies FIFO and uses finite number of bounded size registers. Then, in a sequence of steps (which preserve simplicity and elegance) we modify the new algorithm so that it is also adaptive to point contention and satisfies local-spinning.