NDLI: Self-Stabilizing Symmetry Breaking in Constant Space

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Mayer, Alain Ostrovsky, Rafail Ofek, Yoram Yung, Moti
Copyright Year	2002
Abstract	We investigate the problem of self-stabilizing round-robin token management on a bidirectional ring of identical processors. Each processor is an asynchronous probabilistic finite state (i.e., constant space) machine which sends and receives constant-size messages and whose state transition is triggered by the receipt of a message. We also show that this problem is equivalent to symmetry breaking (i.e., leader election).Wejustify and suggest a two-layer (hardware and software) solution to the token management problem: The subproblem of reducing an arbitrary but nonzero number of tokens (in an otherwise arbitrary initial system state) to exactly one token (and a legal system state) is solved in hardware and takes only small polynomial time. The detection of a complete lack of tokens (communication deadlock) is done by a software clock. In high-speed networks the hardware layer can be implemented using fast universal switches (i.e., finite state machines) independent of the size of the network. We note that randomization is essential, since Dijkstra showed that for arbitrary rings the subproblem does not have a deterministic solution (regardless of the computational power of the identical processors). The use of the software layer (deadlock detection) in our solution is minimized.
Starting Page	1571
Ending Page	1595
Page Count	25
File Format	PDF
ISSN	00975397
DOI	10.1137/S0097539798285997
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	5
Volume Number	31
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2002-01-01
Access Restriction	Subscribed
Subject Keyword	media access protocols Network protocols self-stabilization distributed algorithms Distributed systems self-stabilizing protocols token ring protocols Analysis of algorithms Distributed algorithms
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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