Naming Anonymous Processes Using an Optimal Number of Test-and-Set Registers

Abstract

Anonymous distributed systems consist of processes without names to identify them, and the goal is to assign unique names to them using a distributed algorithm. Synchronous and asynchronous communication models are considered with eight different categories based on number of test-and-set (TAS) registers available and knowledge of number of processes. Processes can only communicate through shared read/write and TAS registers. In this paper, I have developed two deterministic algorithms and one randomized algorithm for naming anonymous processes in all variations of the problem model. Proof of correctness for each algorithm is presented along with the analysis. The developed algorithms are optimal in both shared memory size requirements and namespace size. The Counting and Global Counting algorithm have a time complexity of \(O(n^2)\) steps with a space complexity of O(1) and O(2) shared registers, while Segment Shuffling algorithm has a time complexity of \(\mathcal {O}(n \lceil \log {n} \rceil )\) steps with a space complexity of \(O(2 *\lceil \log {n} \rceil ))\) shared registers.