Spanning tree construction for nameless networks

Abstract

Two types of distributed fully asynchronous probabilistic algorithms are given in the present paper which elect a leader and find a spanning tree in arbitrary anonymous networks of processes. Our algorithms are simpler than in [11] and slightly improve on those in [9,11] with respect to communication complexity. So far, the present algorithms are very likely to be the first fully and precisely specified distributed communication protocols for nameless networks. They are basically patterned upon the spanning tree algorithm designed in [7,8], and motivated by the previous works proposed in [9,11].

For the case where no bound is known on the network size, we give a message terminating algorithm with error probability ε which requires O(m loglog(nr)+n log n) messages on the average, each of size O(log r+log log n), where n and m are the number of nodes and links in the network, and r=1/ε. In the case where some bounds are known on n (N<n ≤ KN, with K ≥ 1), we give a process terminating algorithm, with error probability ε, with O(m+n log n) messages of size O(log n) in the worst case. In either case, the (virtual) time complexity is O(D × log log (nr)). In the particular case where the exact value of n is known, a variant of the preceding algorithm process terminates and always succeeds in O(m+n log n) messages of size O(log n).

Supported in part by C ³ (COPARADIS Group)