Abstract
The M(n)-renaming task requires n + 1 processes, each starting with a unique input name (from an arbitrary large range), to coordinate the choice of new output names from a range of size M(n). It is known that 2n-renaming can be solved if and only if n + 1 is not a prime power. However, the previous proof of solvability was not constructive, involving a complex approximation theorem, and so it did not yield a concrete upper bound on the complexity of the resulting protocol. Here, we present the first upper bound on the step complexity of 2n-renaming, whenever it is solvable, i.e., when n + 1 is not a prime power. The paper also presents the first lower bound on the output namespace, showing that if n + 1 is not a prime power and n is a prime power, then 2n is a tight bound on the output namespace for n + 1 processes.
Original language | English |
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Pages (from-to) | 1-32 |
Number of pages | 32 |
Journal | SIAM Journal on Computing |
Volume | 48 |
Issue number | 1 |
DOIs | |
State | Published - 2019 |
Keywords
- combinatorial topology
- distributed systems
- renaming
- shared memory systems
- symmetry breaking
- wait-free computation
All Science Journal Classification (ASJC) codes
- General Computer Science
- General Mathematics