## On the Generalized Dining Philosophers Problem (2001)

Citations: | 8 - 2 self |

### BibTeX

@MISC{Herescu01onthe,

author = {Oltea Mihaela Herescu and Catuscia Palamidessi and Oltea Mihaela and Herescu Catuscia Palamidessi},

title = {On the Generalized Dining Philosophers Problem},

year = {2001}

}

### OpenURL

### Abstract

We consider a generalization of the dining philosophers problem to arbitrary connection topologies. We focus on symmetric, fully distributed systems, and we address the problem of guaranteeing progress and lockout-freedom, even in presence of adversary schedulers, by using randomized algorithms. We show that the well-known algorithms of Lehmann and Rabin do not work in the generalized case, and we propose an alternative algorithm based on the idea of letting the philosophers assign a random priority to their adjacent forks.

### Citations

995 | A calculus of mobile processes
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ...her will starve (lockout-freedom). The algorithms are robust wrt every fair scheduler. Our motivation for this work comes from the project of providing a distributed implementation for the π-calculus =-=[5]-=-. So far, only the so-called asynchronous subset has been implemented [8]. In [7], the second author has shown that the full π-calculus is strictly more expressive than its asynchronous subset, and, m... |

265 | Probabilistic simulations for probabilistic processes - Segala, Lynch - 1995 |

251 | Pict: A Programming Language Based on the Pi-Calculus
- Pierce, Turner
- 2000
(Show Context)
Citation Context ...ir scheduler. Our motivation for this work comes from the project of providing a distributed implementation for the π-calculus [5]. So far, only the so-called asynchronous subset has been implemented =-=[8]-=-. In [7], the second author has shown that the full π-calculus is strictly more expressive than its asynchronous subset, and, more in general, that there is no hope of implementing the π-calculus with... |

230 |
Modeling and verification of randomized distributed real-time systems
- Segala
- 1995
(Show Context)
Citation Context ...st guarantees progress, the second guarantees also lockout-freedom. There are two proofs of correctness of the Lehmann and Rabin algorithms, one in [9] and another one, more structured and formal, in =-=[4, 10]-=-. They both depend in an essential way on the topology. In particular, they depend on the fact that one fork can only be shared by two philosophers (cfr. Lemma 1 in [9], Lemma 7.13 in [4], and Lemma 6... |

196 |
Hierarchical Ordering of Sequential Processes
- Dijkstra
- 1971
(Show Context)
Citation Context ...g Systems—Process Management; C.2.4 [Computer Systems Organization]: ComputerCommunication Networks—Distributed Systems 1. INTRODUCTION The problem of the dining philosophers, proposed by Dijkstra in =-=[1]-=-, is a very popular example of control problem in distributed systems, and has become a typical benchmark for testing the expressiveness of concurrent languages and of resource allocation strategies. ... |

154 | Comparing the expressive power of the synchronous and the asynchronouspi-calculus
- Palamidessi
- 1997
(Show Context)
Citation Context ...uler. Our motivation for this work comes from the project of providing a distributed implementation for the π-calculus [5]. So far, only the so-called asynchronous subset has been implemented [8]. In =-=[7]-=-, the second author has shown that the full π-calculus is strictly more expressive than its asynchronous subset, and, more in general, that there is no hope of implementing the π-calculus with determi... |

78 |
On the advantages of free choice: A symmetric and fully distributed solution to the dining philosophers problem
- Rabin, Lehmann
- 1981
(Show Context)
Citation Context ...entation of concurrent languages, as it allows a compositional compilation. Full distribution is usually convenient as it avoids the overhead of a centralized control. Lehmann and Rabin have shown in =-=[9]-=- the remarkable result that there are no deterministic solutions to the dining philosophers problem, if symmetry and full distributions are imposed, and if no assumption (except fairness) are made on ... |

64 | What is a ‘good’ encoding of guarded choice
- Nestmann
- 2000
(Show Context)
Citation Context ... has shown that the full π-calculus is strictly more expressive than its asynchronous subset, and, more in general, that there is no hope of implementing the π-calculus with deterministic methods. In =-=[6]-=- Nestmann has shown that the gap in expressive power, and the difficulty in the implementation with deterministic methods, is due to the mixed (input and output) guarded choice construct of the π-calc... |

34 | Proving time bounds for randomized distributed algorithms
- Lynch, Saias, et al.
(Show Context)
Citation Context ...st guarantees progress, the second guarantees also lockout-freedom. There are two proofs of correctness of the Lehmann and Rabin algorithms, one in [9] and another one, more structured and formal, in =-=[4, 10]-=-. They both depend in an essential way on the topology. In particular, they depend on the fact that one fork can only be shared by two philosophers (cfr. Lemma 1 in [9], Lemma 7.13 in [4], and Lemma 6... |

18 |
A Distributed Abstract Data Type Implemented by a Probabilistic Communication Scheme
- Francez, Rodeh
- 1980
(Show Context)
Citation Context ... of providing a compositional translation. To our knowledge, there has been only a previous proposal for a symmetric and fully distributed implementation of a concurrent language with guarded choice (=-=[2]-=-), but such proposal works only under the assumption of “good” schedulers, i.e. a scheduler which behaves uniformly through the computation regardless of the actions performed by the processes. 2. THE... |

17 | C.: Probabilistic asynchronous π-calculus
- Herescu, Palamidessi
- 2000
(Show Context)
Citation Context ... it provides a powerful programming primitive for solving distributed conflicts. Thus, we are considering a randomized implementation. We have developed an asynchronous probabilistic π-calculus (πpa, =-=[3]-=-), and we are currently investigating a translation from π to πpa that requires solving a resource allocation problem similar to the one of the generalized dining philosophers (the resources correspon... |

5 | Probabilistic asynchronous -calculus - Herescu, Palamidessi - 2000 |