## Operation-valency and the cost of coordination (2003)

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Venue: | In Proceedings of the 22nd Annual ACM Symposium on Principles of Distributed Computing (PODC |

Citations: | 6 - 3 self |

### BibTeX

@INPROCEEDINGS{Hendler03operation-valencyand,

author = {Danny Hendler},

title = {Operation-valency and the cost of coordination},

booktitle = {In Proceedings of the 22nd Annual ACM Symposium on Principles of Distributed Computing (PODC},

year = {2003},

pages = {84--91},

publisher = {ACM Press}

}

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### Abstract

This paper introduces operation-valency, a generalization of the valency proof technique originated by Fischer, Lynch, and Paterson. By focusing on critical events that influ-ence the return values of individual operations rather then on critical events that influence a protocol's single return value, the new technique allows us to derive a collection of realistic lower bounds for lock-free implementations of concurrent objects such as linearizable queues, stacks, sets, hash tables, shared counters, approximate agreement, and more. By realistic we mean that they follow the real-world model introduced by Dwork, Herlihy, and Waarts, count-ing both memory-references and memory-stalls due to con-tention, and that they allow the combined use of read, write, and read-modify-write operations available on current ma-chines. By using the operation-valency technique, we derive an f~(X/~) non-cached shared memory accesses lower bound on the worst-case time complexity of lock-free implementations of objects in Influence(n), a wide class of concurrent objects including all of those mentioned above, in which an individ-ual operation can be influenced by all others. We also prove the existence of a fundamental relationship between the space complexity, latency, contention, and "in-fluence level " of any lock-free object implementation. Our results are broad in that they hold for implementations com-bining read/write memory and any collection of read-modify-write operations, and in that they apply even if shared mem-ory words have unbounded size.

### Citations

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- Fischer, Lynch, et al.
- 1985
(Show Context)
Citation Context ... most notably in the context of mutual exclusion [1, 2, 6] and counting networks [3, 4]. This paper presents ope¢ution-valency, a generalization of the valency proof technique of Fischer et. al (FLP) =-=[9]-=-, and uses it to continue the above work in deriving real-world time complexity lower bounds for state of the art concurrent objects. As surveyed by Lynch [15] and by Fich and Rupert [8], there are nu... |

730 | Wait-free synchronization
- Herlihy
- 1991
(Show Context)
Citation Context ...ing our results in detail, let us briefly describe the operation-valency technique. 1.1 The Operation-Yalency Technique Valency arguments, introduced by Fischer et. al [9], have been used extensively =-=[5, 7, 10, 14]-=- to derive impossibility results and lower bounds for consensus and related problems. In problems such as consensus, a protocol is required to eventually output a single protocol value. Valency argume... |

155 |
Memory requirements for agreement among unreliable asynchronous processes
- Loui, Abu-Amara
- 1987
(Show Context)
Citation Context ...ing our results in detail, let us briefly describe the operation-valency technique. 1.1 The Operation-Yalency Technique Valency arguments, introduced by Fischer et. al [9], have been used extensively =-=[5, 7, 10, 14]-=- to derive impossibility results and lower bounds for consensus and related problems. In problems such as consensus, a protocol is required to eventually output a single protocol value. Valency argume... |

103 | Odd-Even Counting Networks
- Busch, Mavronicolas
(Show Context)
Citation Context ...fs between contention and latency 1 in concurrent data structure design. Their work was extended in several directions, most notably in the context of mutual exclusion [1, 2, 6] and counting networks =-=[3, 4]-=-. This paper presents ope¢ution-valency, a generalization of the valency proof technique of Fischer et. al (FLP) [9], and uses it to continue the above work in deriving real-world time complexity lowe... |

69 |
On processor coordination using asynchronous hardware
- Chor, Israeli, et al.
- 1987
(Show Context)
Citation Context ...ing our results in detail, let us briefly describe the operation-valency technique. 1.1 The Operation-Yalency Technique Valency arguments, introduced by Fischer et. al [9], have been used extensively =-=[5, 7, 10, 14]-=- to derive impossibility results and lower bounds for consensus and related problems. In problems such as consensus, a protocol is required to eventually output a single protocol value. Valency argume... |

62 | Contention in shared memory algorithms
- Dwork, Herlihy, et al.
- 1997
(Show Context)
Citation Context .....$5.00. [Extended Abstract] Nir Shavit School of Computer Science Tel-Aviv University Tel Aviv, Israel 69978 shanir@cs.tau.ac.il General Terms Algorithms Theory 1. INTRODUCTION In 1993, Dwork et. al =-=[7]-=- introduced a formal model to capture the real world phenomenon of memory contention on today’s shared memory machines, machines that allow read, write, and read-modify-write (RMW) operations. Using F... |

40 | An improved lower bound for the time complexity of mutual exclusion
- Anderson, Kim
- 2001
(Show Context)
Citation Context ... that there are inherent tradeoffs between contention and latency 1 in concurrent data structure design. Their work was extended in several directions, most notably in the context of mutual exclusion =-=[1, 2, 6]-=- and counting networks [3, 4]. This paper presents ope¢ution-valency, a generalization of the valency proof technique of Fischer et. al (FLP) [9], and uses it to continue the above work in deriving re... |

37 | The communication requirements of mutual exclusion
- Cypher
- 1995
(Show Context)
Citation Context ... that there are inherent tradeoffs between contention and latency 1 in concurrent data structure design. Their work was extended in several directions, most notably in the context of mutual exclusion =-=[1, 2, 6]-=- and counting networks [3, 4]. This paper presents ope¢ution-valency, a generalization of the valency proof technique of Fischer et. al (FLP) [9], and uses it to continue the above work in deriving re... |

35 | A hundred impossibility proofs for distributed computing
- Lynch
- 1989
(Show Context)
Citation Context ...y proof technique of Fischer et. al (FLP) [9], and uses it to continue the above work in deriving real-world time complexity lower bounds for state of the art concurrent objects. As surveyed by Lynch =-=[15]-=- and by Fich and Rupert [8], there are numerous elegant extensions and reformulations of the FLP-style valency technique. The main difference between the operation-valency approach we present here and... |

22 | Time/contention trade-offs for multiprocessor synchronization
- Anderson, Yang
- 1996
(Show Context)
Citation Context ... that there are inherent tradeoffs between contention and latency 1 in concurrent data structure design. Their work was extended in several directions, most notably in the context of mutual exclusion =-=[1, 2, 6]-=- and counting networks [3, 4]. This paper presents ope¢ution-valency, a generalization of the valency proof technique of Fischer et. al (FLP) [9], and uses it to continue the above work in deriving re... |

21 | A time complexity lower bound for randomized implementations of some shared objects
- Jayanti
- 1998
(Show Context)
Citation Context ...t these accesses cannot be resolved by a local cache. Our lower bounds are the first real-world time bounds for such objects. Though they seem stronger than Jayanti's interesting O(log n) time bounds =-=[13]-=- on similar objects, they are in a sense orthogonal. This is because Jayanti's time metric does not count contention when accessing shared locations. For example, according to Jayant's metric, a share... |

14 |
Orli Waarts, Contention in shared memory algorithms
- Dwork, Herlihy
- 1997
(Show Context)
Citation Context ...5.00. [Extended Abstract] 84 Nir Shavit School of Computer Science TeI-Aviv University Tel Aviv, Israel 69978 shanir@cs.tau.ac.il General Terms Algorithms Theory 1. INTRODUCTION In 1993, Dwork et. al =-=[7]-=- introduced a formal model to capture the real world phenomenon of memory contention on today's shared memory machines, machines that allow read, write, and read-modify-write (RMW) operations. Using F... |

11 |
Knowledge in shared memory systems
- Merrit, Taubenfeld
- 1991
(Show Context)
Citation Context ....1 Shared Memory System Model Our model of an asynchronous shared memory system is based on the model described by Cypher in [6], which is based, in turn, on the model given by Merritt and Taubenfeld =-=[16]-=-. We will assume that shared objects are specified as in [11]. Our model allows three types of shared memory events: atomic Read, atomic Write, arid Read-Modify-Write events. No bound is assumed on re... |

8 | Lower bounds in distributed computing - Fich, Ruppert - 1914 |