Space and time efficient self-stabilizing and l-exclusion in tree networks

We propose a very efficient self-stabilizing l-exclusion algorithm in rooted tree networks. The l-exclusion problem is a generalization of the mutual exclusion problem-we allow l (l⩾1) processors, instead of 1, to use a shared resource. The algorithm is semi-uniform and its space requirement is (l+3)Δ_r states (or [log((l+3)Δ_r)] bits) for the root r, 3Δ_p states (or [log(3Δ_p)] bits) for an internal processor p, and 2 states (or 1 bit) for a leaf processor, where Δ _p is the degree of processor p. Our algorithm is unique in the sense that this is the first l-exclusion algorithm on trees, whose space requirement is independent of the size of the network for any processor and is independent of l for all processors except the root