The Assignment Problem
Article No.: 14, Pages 1 - 9
Abstract
In the allocation problem, asynchronous processors must partition a set of items so that each processor leave knowing all items exclusively allocated to it. We introduce a new variant of the allocation problem called the assignment problem, in which processors might leave having only partial knowledge of their assigned items. The missing items in a processor's assignment must eventually be announced by other processors.
While allocation has consensus power 2, we show that the assignment problem is solvable read-write wait-free when k processors compete for at least 2k --1 items. Moreover, we propose a long-lived read-write wait-free assignment algorithm which is fair, allocating no more than 2 items per processor, and in which a slow processor may delay the assignment of at most n items, where n is the number of processors.
The assignment problem and its read-write solution may be of practical interest for implementing resource allocators and work queues, which are pervasive concurrent programming patterns, as well as stream-processing systems.
References
[1]
Yehuda Afek, Hagit Attiya, Danny Dolev, Eli Gafni, Michael Merritt, and Nir Shavit. 1993. Atomic Snapshots of Shared Memory. J. ACM 40, 4 (Sept. 1993), 873--890.
[2]
Y. Afek, Y. Babichenko, U. Feige, E. Gafni, N. Linial, and B. Sudakov. 2014. Musical Chairs. SIAM Journal on Discrete Mathematics 28, 3 (Jan. 2014), 1578--1600.
[3]
Yehuda Afek and Eytan Weisberger. 1999. The instancy of snapshots and commuting objects. Journal of Algorithms 30, 1 (1999), 68--105.
[4]
H. Attiya, A. Bar-Noy, D. Dolev, D. Koller, D. Peleg, and R. Reischuk. 1987. Achievable cases in an asynchronous environment. In 28th Annual Symposium on Foundations of Computer Science, 1987. 337--346.
[5]
Hagit Attiya, Amotz Bar-Noy, Danny Dolev, David Peleg, and Rüdiger Reischuk. 1990. Renaming in an asynchronous environment. Journal of the ACM (JACM) 37, 3 (1990), 524--548.
[6]
Elizabeth Borowsky and Eli Gafni. 1993. Immediate Atomic Snapshots and Fast Renaming. In Proceedings of the Twelfth Annual ACM Symposium on Principles of Distributed Computing (PODC '93). ACM, 41--51.
[7]
J. E. Burns and G. L. Peterson. 1989. The Ambiguity of Choosing. In Proceedings of the Eighth Annual ACM Symposium on Principles of Distributed Computing (PODC '89). ACM, New York, NY, USA, 145--157.
[8]
Armando Castañeda, Pierre Fraigniaud, Eli Gafni, Sergio Rajsbaum, and Matthieu Roy. 2016. Asynchronous Coordination Under Preferences and Constraints. In Structural Information and Communication Complexity (Lecture Notes in Computer Science), Vol. 9988. Springer, Cham, 111--126.
[9]
E. W. Dijkstra. 1977. Two starvation free solutions of a general exclusion problem, 1978. EWD.
[10]
Cynthia Dwork, Joseph Y. Halpern, and Orli Waarts. 1998. Performing work efficiently in the presence of faults. SIAM J. Comput. 27, 5 (1998), 1457--1491.
[11]
Michael J. Fischer, Nancy A. Lynch, James E. Burns, and Allan Borodin. 1989. Distributed FIFO Allocation of Identical Resources Using Small Shared Space. ACM Trans. Program. Lang. Syst. 11, 1 (Jan. 1989), 90--114.
[12]
Eli Gafni, Michel Raynal, and Corentin Travers. 2007. Test & set, adaptive renaming and set agreement: a guided visit to asynchronous computability. In 26th IEEE International Symposium on Reliable Distributed Systems, 2007. IEEE, 93--102.
[13]
Paris C. Kanellakis and Alex A. Schwarzmann. 1992. Efficient parallel algorithms can be made robust. Distributed Computing 5, 4 (1992), 201--217.
[14]
Sotirios Kentros, Chadi Kari, and Aggelos Kiayias. 2012. The strong at-most-once problem. In International Symposium on Distributed Computing. Springer, 386--400.
[15]
Sotirios Kentros and Aggelos Kiayias. 2012. Solving the at-most-once problem with nearly optimal effectiveness. In International Conference on Distributed Computing and Networking. Springer, 122--137.
[16]
Sotirios Kentros, Aggelos Kiayias, Nicolas Nicolaou, and Alexander A. Schwarzmann. 2009. At-most-once semantics in asynchronous shared memory. In International Symposium on Distributed Computing. Springer, 258--273.
[17]
Leslie Lamport. 1974. A new solution of Dijkstra's concurrent programming problem. Commun. ACM 17, 8 (1974), 453--455.
[18]
Leslie Lamport. 1986. On interprocess communication: Part II. Distributed Computing 1, 2 (June 1986), 86--101.
[19]
Leslie Lamport. 2009. The PlusCal Algorithm Language. In ICTAC, Vol. 5684. Springer, 36--60.
[20]
Michael C. Loui and Hosame H. Abu-Amara. 1987. Memory requirements for agreement among unreliable asynchronous processes. Advances in Computing research 4, 163--183 (1987), 31.
[21]
Mark Moir and James H. Anderson. 1995. Wait-free algorithms for fast, long-lived renaming. Science of Computer Programming 25, 1 (Oct. 1995), 1--39.
[22]
Mark Moir and Juan A. Garay. 1996. Fast, long-lived renaming improved and simplified. In Distributed Algorithms (Lecture Notes in Computer Science). Springer, Berlin, Heidelberg, 287--303.
[23]
Gary L. Peterson. 1981. Myths about the mutual exclusion problem. Inform. Process. Lett. 12, 3 (1981), 115--116.
[24]
Yuan Yu, Panagiotis Manolios, and Leslie Lamport. 1999. Model checking TLA+ specifications. In CHARME, Vol. 99. Springer, 54--66.
Index Terms
- The Assignment Problem
Recommendations
The assignment problem
Highlights- Shared memory.
- Fault tolerance.
AbstractIn the allocation problem, asynchronous processors must partition a set of items so that each processor leaves knowing all items exclusively allocated to it. We introduce a new variant of the allocation problem called the assignment ...
The notion of a timed register and its application to indulgent synchronization
SPAA '07: Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architecturesA new type of shared object, called timed register, is proposed and used to design indulgent timing-based algorithms. A timed register generalizes the notion of an atomic register as follows: if a process invokes two consecutive operations on the same ...
Evaluation of scheduling techniques on a SPARC-based VLIW testbed
MICRO 30: Proceedings of the 30th annual ACM/IEEE international symposium on MicroarchitectureThe performance of Very Long Instruction Word (VLIW) microprocessors depends on the close cooperation between the compiler and the architecture. This paper evaluates a set of important compilation techniques and related architectural features for VLIW ...
Comments
Information & Contributors
Information
Published In
January 2018
494 pages
ISBN:9781450363723
DOI:10.1145/3154273
Copyright © 2018 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
In-Cooperation
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 04 January 2018
Check for updates
Author Tags
Qualifiers
- Research-article
- Research
- Refereed limited
Funding Sources
Conference
ICDCN '18
ICDCN '18: 19th International Conference on Distributed Computing and Networking
January 4 - 7, 2018
Varanasi, India
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 221Total Downloads
- Downloads (Last 12 months)61
- Downloads (Last 6 weeks)8
Reflects downloads up to 04 Oct 2024
Other Metrics
Citations
View Options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in