The Black-White Bakery Algorithm and Related Bounded-Space, Adaptive, Local-Spinning and FIFO Algorithms

Abstract

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.

Tournaments for mutual exclusion: verification and concurrent complexity

“…The Bakery algorithms of Lamport [Lam74] and Taubenfeld [Tau04] have throughput factors linear in N , and individual delay quadratic in N , see [Hes16a]. The algorithm of Lycklama-Hadzilacos [LH91] and all its variants have throughput factors quadratic in N , and individual delay cubic in N , see [Hes15].…”

Nonatomic dual bakery algorithm with bounded tokens

“…N − 1], and N safe shared bits. Taubenfeld's algorithm [33] uses N atomic variables with values in [0 . .…”

“…2, we introduce the dual bakery algorithm with atomic variables as a variation of the bakery algorithms of Lamport [20] and Taubenfeld [33]. We minimize the vulnerable information and prepare the ground for spreading it over different variables.…”

“…The downside is that these shared variables hold integer tokens that can become arbitrarily large. Several modifications to the bakery algorithm have been proposed to bound these tokens [2,15,16,32,33,35,38]. All these modifications, however, require some atomic shared variables.…”

An arbitration algorithm for multiport memory systems

“…This algorithm has a practical limitation that the token numbers can grow unboundedly, if always some processor is in need of using the shared memory. There are many recent attempts to bound the token values [3] and all these attempts require exclusive access to the shared variables (memory words). Therefore, they cannot be used in multiport memory systems.…”