# Fast, long-lived renaming improved and simplified

## Abstract

In the *long-lived M-renaming problem, N* processes repeatedly acquire and release *names* ranging over {0,..., M−1}, where *M < N*. It is assumed that at most *k* processes concurrently request or hold names. Efficient solutions to the long-lived renaming problem can be used to improve the performance of applications in which processes repeatedly perform computations whose time complexity depends on the size of the name space containing the processes that participate concurrently. In this paper, we consider wait-free solutions to the long-lived *M*-renaming problem that use only read and write instructions in an asynchronous, shared-memory multiprocessor. A solution to long-lived renaming is *fast* if the time complexity of acquiring and releasing a name once is independent of *N*. We present a new fast, long-lived (*k(k + 1)/2*)-renaming algorithm that significantly improves upon the time and space complexity of similar previous algorithms, while providing a much simpler solution. We also show for the first time that fast, long-lived (*2k − 1*)-renaming can be implemented with reads and writes. This result is optimal with respect to the size of the name space.

## Keywords

Building Block Time Complexity Space Complexity Shared Variable Statement Execution## Preview

Unable to display preview. Download preview PDF.

## References

- 1.J. Anderson and M. Moir, “Fast
*k*-Exclusion Algorithms”, submitted to Distributed Computing. Preliminary version appeared in*Proceedings of the 13th Annual ACM Symposium on Principles of Distributed Computing*, August 1994, pp. 141–150.Google Scholar - 2.H. Attiya, A. Bar-Noy, D. Dolev, D. Koller, D. Peleg, and R. Reischuk, “Achievable Cases in an Asynchronous Environment”,
*Proceedings of the 28th Annual IEEE Symposium on Foundations of Computer Science*, October 1987, pp. 337–346.Google Scholar - 3.A. Bar-Noy and D. Dolev, “Shared Memory versus Message-Passing in an Asynchronous Distributed Environment”,
*Proceedings of the 8th Annual ACM Symposium on Principles of Distributed Computing*, August 1989, pp. 307–318.Google Scholar - 4.E. Borowsky and E. Gafni, “Immediate Atomic Snapshots and Fast Renaming”,
*Proceedings of the 12th Annual ACM Symposium on Principles of Distributed Computing*, August 1993, pp. 41–50.Google Scholar - 5.H. Buhrman, J. Garay, J. Hoepman, and M. Moir, “Long-Lived Renaming Made Fast”,
*Proceedings of the 14th Annual ACM Symposium on Principles of Distributed Computing*, August 1995, pp. 194–203.Google Scholar - 6.J. Burns and G. Peterson, “The Ambiguity of Choosing”,
*Proceedings of the Eighth Annual ACM Symposium on Principles of Distributed Computing*, ACM, New York, August 1989, pp. 145–157.Google Scholar - 7.C. A. R. Hoare, “An Axiomatic Basis for Computer Programming”,
*Communications of the ACM*12, October 1969, pp. 576–580,583.CrossRefGoogle Scholar - 8.M. Herlihy and N. Shavit, “The Asynchronous Computability Theorem for
*t*-Resilient Tasks”,*Proceedings of the 25th ACM Symposium on Theory of Computing*, 1993, pp. 111–120.Google Scholar - 9.L. Lamport, “A Fast Mutual Exclusion Algorithm”,
*ACM Transactions on Computer Systems*, Vol. 5, No. 1, February 1987, pp. 1–11.CrossRefGoogle Scholar - 10.M. Moir and J. Anderson, “Wait-Free Algorithms for Fast, Long-Lived Renaming”,
*Science of Computer Programming*25 (1995), pp. 1–39. Preliminary version appeared in*Proceedings of the 8th International Workshop on Distributed Algorithms*, September, 1994, pp. 141–155.MathSciNetGoogle Scholar - 11.G. Peterson, personal communication, November 1995.Google Scholar