BOUNDS ON THE STEP AND NAMESPACE COMPLEXITY OF RENAMING

Hagit Attiya, Armando Castaneda, Maurice Herlihy, Ami Paz

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)1-32
Number of pages32
JournalSIAM Journal on Computing
Volume48
Issue number1
DOIs
StatePublished - 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

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