Message terminating algorithms for anonymous rings of unknown size

We consider a ring of an unknown number of anonymous processors. We focus on message terminating algorithms, i.e., algorithms that terminate when no more messages are present in the system but the processors may lack the ability to detect this situation. This paper addresses the design of deterministic and probabilistic algorithms that message terminate with the correct result. For this model we show: (i) A deterministic ring orientation algorithm that employs symmetry breaking link markings and requires O(n log² n) bits for communication and O(n) time. A probabilistic Las-Vegas version of this algorithm (that requires no link markings) has the same average communication and time complexities, (ii) A probabilistic Las-Vegas algorithm for partitioning an even size ring into pairs that requires O(n log n) communication bits and time, (iii) The impossibility of computing (via a Las-Vegas algorithm) most functions (the class of nonsymmetric functions) including: leader election, XOR and finding the ring size. The same technique can be applied to prove the impossibility of partitioning an odd size ring into a maximal number of pairs.