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

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

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