Taubenfeld G. (2011) Tight Space Bounds for ℓ-Exclusion. In: Peleg D. (eds) Distributed Computing. DISC 2011. Lecture Notes in Computer Science, vol 6950. Springer, Berlin, Heidelberg
The simplest deadlock-free algorithm for mutual exclusion requires only one single-writer non-atomic bit per process [4,6,13]. This algorithm is known to be space optimal [5,6]. For over 20 years now it has remained an intriguing open problem whether a similar type of algorithm, which uses only one single-writer bit per process, exists also for ℓ-exclusion for some ℓ ≥ 2.
We resolve this longstanding open problem. For any ℓ and n, we provide a tight space bound on the number of single-writer bits required to solve ℓ-exclusion for n processes. It follows from our results that it is not possible to solve ℓ-exclusion with one single-writer bit per process, for any ℓ ≥ 2.
In an attempt to understand the inherent difference between the space complexity of mutual exclusion and that of ℓ-exclusion for ℓ ≥ 2, we define a weaker version of ℓ-exclusion in which the liveness property is relaxed, and show that, similarly to mutual exclusion, this weaker version can be solve using one single-writer non-atomic bit per process.
Mutual Exclusion ℓ-exclusion space complexity tight bounds