## On the Distributed Complexity of Computing Maximal Matchings (1997)

### Cached

### Download Links

- [www.brics.dk]
- [www.brics.dk]
- [www.brics.dk]
- [www.brics.dk]
- DBLP

### Other Repositories/Bibliography

Citations: | 31 - 5 self |

### BibTeX

@MISC{Hanckowiak97onthe,

author = {Michal Hanckowiak and Michal Karonski and Alessandro Panconesi},

title = {On the Distributed Complexity of Computing Maximal Matchings},

year = {1997}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

1870 | Randomized Algorithms
- Motwani, Raghavan
- 1995
(Show Context)
Citation Context ...admit simple randomized solutions. Randomization is also demonstrably more powerful in synchronous systems, as shown by the important example of oblivious routing in the hypercube (see, for instance, =-=[13, 18]-=-). In this paper we are interested in this question in the context of distributed graph algorithms, where a synchronous, message-passing network without shared memory is to compute a function of its o... |

1533 |
Distributed Algorithms
- Lynch
- 1996
(Show Context)
Citation Context ...admit simple randomized solutions. Randomization is also demonstrably more powerful in synchronous systems, as shown by the important example of oblivious routing in the hypercube (see, for instance, =-=[13, 18]-=-). In this paper we are interested in this question in the context of distributed graph algorithms, where a synchronous, message-passing network without shared memory is to compute a function of its o... |

1137 | Extremal graph theory - Bollobás - 1995 |

367 | A Simple Parallel Algorithm for the Maximal Independent Set Problem
- Luby
- 1986
(Show Context)
Citation Context ...sually extremely simple and their actual complexity is very low. For instance, (∆ + 1)–vertex coloring and MIS can be computed in O(log n) rounds with high probability by exceedingly simple protocols =-=[16, 17, 21]-=-. Another important case is that of (O(log n),O(log n))– decompositions, a very interesting type of graph decomposition with many applications, which can be computed in O(log 2 n) rounds [15]. In fact... |

200 | The Probabilistic Method. Wiley-Interscience Series in Discrete Mathematics and Optimization - Alon, Spencer - 2008 |

169 |
Locality in distributed graph algorithms
- Linial
- 1992
(Show Context)
Citation Context ...ily solvable suddenly become hard or unsolvable efficiently, especially if one is seeking deterministic solutions. The study of distributed graph algorithms goes back to (at least) the work of Linial =-=[14]-=- where an Ω(log ∗ n) lower bound for computing maximal independent sets (MIS’s) in the ring is given. Together with the O(log ∗ n) upper bound given by a beautiful algorithm of Cole and Vishkin, this ... |

110 | What can be computed locally
- Naor, Stockmeyer
- 1995
(Show Context)
Citation Context ...eally of low complexity, i.e. with small exponents and no hidden large constants. Further generalizing from bounded degree graphs to general topologies has proven elusive, in spite of several efforts =-=[1, 2, 15, 20, 23, 24]-=-. The situation here is, more or less, as follows. For a reasonably large class of graph structures, the asymptotically best deterministic algorithm known to date uses O(n ɛ(n) ) rounds, where ɛ(n) is... |

79 | Network decomposition and locality in distributed computation
- Awerbuch, Goldberg, et al.
- 1989
(Show Context)
Citation Context ...s that several classical graph structures of both theoretical and practical interest, including MIS’s, maximal matchings, (∆ + 1)- and even ∆-vertex colorings, can be computed in polylogarithmic time =-=[1, 2, 7, 23]-=-. In fact, many of these algorithms are very satisfactory because they are both quite simple and really of low complexity, i.e. with small exponents and no hidden large constants. Further generalizing... |

68 | Parallel symmetrybreaking in sparse graphs
- Goldberg, Plotkin, et al.
- 1987
(Show Context)
Citation Context ...s that several classical graph structures of both theoretical and practical interest, including MIS’s, maximal matchings, (∆ + 1)- and even ∆-vertex colorings, can be computed in polylogarithmic time =-=[1, 2, 7, 23]-=-. In fact, many of these algorithms are very satisfactory because they are both quite simple and really of low complexity, i.e. with small exponents and no hidden large constants. Further generalizing... |

53 |
Low diameter graph decompositions
- Linial, Saks
- 1993
(Show Context)
Citation Context ...eally of low complexity, i.e. with small exponents and no hidden large constants. Further generalizing from bounded degree graphs to general topologies has proven elusive, in spite of several efforts =-=[1, 2, 15, 20, 23, 24]-=-. The situation here is, more or less, as follows. For a reasonably large class of graph structures, the asymptotically best deterministic algorithm known to date uses O(n ɛ(n) ) rounds, where ɛ(n) is... |

48 | Probabilistic recurrence relations - Karp - 1994 |

43 |
On the Complexity of Distributed Network Decomposition
- Panconesi, Srinivasan
- 1996
(Show Context)
Citation Context ...eally of low complexity, i.e. with small exponents and no hidden large constants. Further generalizing from bounded degree graphs to general topologies has proven elusive, in spite of several efforts =-=[1, 2, 15, 20, 23, 24]-=-. The situation here is, more or less, as follows. For a reasonably large class of graph structures, the asymptotically best deterministic algorithm known to date uses O(n ɛ(n) ) rounds, where ɛ(n) is... |

37 | The Probabilistic Method, Wiley Interscience series in discrete mathematics and optimization - Alon, Spencer - 2000 |

28 |
Fast distributed construction of k-dominating sets and applications
- Kutten, Peleg
- 1998
(Show Context)
Citation Context ...log 6 n) rounds. Unfortunately lack of space (and time!) denies us the possibility of including this solution in this extended abstract and we refer the reader to the full paper. 3sdominating sets of =-=[12]-=- both of which, however, are not “classical” graph structures. We end this section by spelling out our model of computation, the synchronous, message-passing distributed network. Here, a distributed n... |

26 | Nearly optimal distributed edge colouring in o(log log n) rounds
- Grable, Panconesi
- 1997
(Show Context)
Citation Context ...ted, with high probability, by extremely simple, indeed trivial, randomized algorithms in o(log n) (little-oh of n) rounds or even, under suitable degree assumptions, in as few as O(log log n) rounds =-=[8]-=-. The question then is whether, in the context of distributed graph algorithms, randomization is necessary in order to obtain protocols which run in polylogarithmically-many rounds in the size of the ... |

23 |
A lower bound on probabilistic algorithms for distributive ring coloring
- Naor
- 1991
(Show Context)
Citation Context ...ll too rare examples in complexity theory where the complexity of a computational problem can be determined exactly (modulo constants). Interestingly, it can be shown that randomization does not help =-=[19]-=-. Generalizing from rings to bounded degree graphs one sees that several classical graph structures of both theoretical and practical interest, including MIS’s, maximal matchings, (∆ + 1)- and even ∆-... |

20 |
Efficient parallel algorithms for edge coloring problems
- Karloff, Shmoys
- 1987
(Show Context)
Citation Context ... so small that even after O(log n) many iterations the distance from the perfect splitting rate will be (1 ± o(1)). We now describe the protocol. The first step of our solution is to use an idea from =-=[10]-=- to reduce the problem of computing MM’s in general graphs to that of computing MM’s in bipartite graphs. This is an important step because our approximate splitter cannot deal with odd cycles. The re... |

13 | Chromatic number, girth and maximal degree - Bollobás - 1978 |

13 |
Removing randomness in parallel without processor penalty
- Luby
- 1993
(Show Context)
Citation Context ...sually extremely simple and their actual complexity is very low. For instance, (∆ + 1)–vertex coloring and MIS can be computed in O(log n) rounds with high probability by exceedingly simple protocols =-=[16, 17, 21]-=-. Another important case is that of (O(log n),O(log n))– decompositions, a very interesting type of graph decomposition with many applications, which can be computed in O(log 2 n) rounds [15]. In fact... |

11 | Fast network decomposition - Awerbuch, Berger, et al. - 1992 |

8 |
An Improved Algorithm for Maximal Matching
- Israeli, Shiloach
- 1986
(Show Context)
Citation Context ...col presented in this paper is quite high– O(log 7 n) rounds– but it should be remembered that even in the erew-pram model the best asymptotic complexity for computing maximal matchings is O(log 4 n) =-=[9]-=-. 1 Our solution hinges on a distributed procedure which, for almost all vertices in the graph, cuts the degree of a vertex almost perfectly in half. This approximate degree splitter might be useful i... |

7 |
Private communication
- Johansson
(Show Context)
Citation Context ...sually extremely simple and their actual complexity is very low. For instance, (∆ + 1)–vertex coloring and MIS can be computed in O(log n) rounds with high probability by exceedingly simple protocols =-=[16, 17, 21]-=-. Another important case is that of (O(log n),O(log n))– decompositions, a very interesting type of graph decomposition with many applications, which can be computed in O(log 2 n) rounds [15]. In fact... |

2 | The Local Nature of \Delta-coloring and - Panconesi, Srinivasan - 1995 |

1 | Probabilistic recurrence relations revisited, Theoretical computer Science - Chaudhuri, Dubhashi |

1 |
The Local Nature of ∆-coloring and
- Panconesi, Srinivasan
- 1995
(Show Context)
Citation Context ...s that several classical graph structures of both theoretical and practical interest, including MIS’s, maximal matchings, (∆ + 1)- and even ∆-vertex colorings, can be computed in polylogarithmic time =-=[1, 2, 7, 23]-=-. In fact, many of these algorithms are very satisfactory because they are both quite simple and really of low complexity, i.e. with small exponents and no hidden large constants. Further generalizing... |