Space and Time Efficient Self-Stabilizing ℓ-Exclusion in Tree Networks

Abstract

We propose an efficient self-stabilizing ℓ-exclusion algorithm in rooted tree networks running under an unfair distributed daemon. The ℓ-exclusion problem is a generalization of the mutual exclusion problem—ℓ (ℓ⩾1) processors, instead of 1, are permitted to use a shared resource. The algorithm is semi-uniform and its space requirement is (ℓ+3)Δr states (or ⌈log((ℓ+3)Δr)⌉ bits) for the root r, 4(Δp−1) states (or ⌈2 log(Δp−1)⌉ bits) for an internal processor p, and 3 states (or 2 bits) for a leaf processor, where Δp is the degree of processor p. This is the first ℓ-exclusion algorithm on trees with the property that the space requirement is independent of the size of the network for any processor, and is independent of ℓ for all processors except the root. The stabilization time of the algorithm is only O(ℓ+h) rounds, where h is the height of the tree.