Synchronization Algorithms on Oriented Chains

We present a spaceand time-optimal self-stabilizing algorithm, SSDS, for a given synchronization problem on asynchronous oriented chains. SSDS is uniform and works under the unfair distributed daemon. From SSDS we derive solutions for the local mutual exclusion and distributed sorting. Algorithm SSDS can also be used to obtain optimal space solutions for other problems such as broadcasting, leader election, and mutual exclusion. 1 Motivation and Background Distributed algorithms aim to reduce the amount of communication among the nodes in the system (the number of messages exchanged for messagepassing or the number of memory accesses – reading or writing into variables – for shared-memory model), while keeping a relative low memory requirement per node and a low time complexity. Fault-tolerance is the ability of an algorithm to withstand transient faults (still perform its function), where by a fault we mean that the variables of some nodes are changed to some arbitrary values by some external action. Self-stabilization is the strongest case of fault-tolerance: An algorithm is self-stabilizing when, “regardless of Contact author. Applied Research Laboratory, The Pennsylvania State University, PA 16802, USA. Email: [email protected]. School of Computer Science, University of Nevada, Las Vegas, NV 89154, USA. Email: [email protected]. School of Computer Science, University of Nevada, Las Vegas, NV 89154, USA. Email: [email protected].