## What Cannot Be Computed Locally! (2004)

### Cached

### Download Links

- [distcomp.ethz.ch]
- [distcomp.ethz.ch]
- [www.dcg.ethz.ch]
- [www.distcomp.ethz.ch]
- [www.dcg.ethz.ch]
- [www.dcg.ethz.ch]
- [www.distcomp.ethz.ch]
- DBLP

### Other Repositories/Bibliography

Venue: | In Proceedings of the 23 rd ACM Symposium on the Principles of Distributed Computing (PODC |

Citations: | 103 - 26 self |

### BibTeX

@INPROCEEDINGS{Kuhn04whatcannot,

author = {Fabian Kuhn and Thomas Moscibroda and Roger Wattenhofer},

title = {What Cannot Be Computed Locally!},

booktitle = {In Proceedings of the 23 rd ACM Symposium on the Principles of Distributed Computing (PODC},

year = {2004},

pages = {300--309}

}

### Years of Citing Articles

### OpenURL

### Abstract

We give time lower bounds for the distributed approximation of minimum vertex cover (MVC) and related problems such as minimum dominating set (MDS). In k communication rounds, MVC and MDS can only be approximated by factors# /k) and # /k) for some constant c, where n and # denote the number of nodes and the largest degree in the graph. The number of rounds required in order to achieve a constant or even only a polylogarithmic approximation ratio is at log n/ log log n) and#1 #/ log log #). By a simple reduction, the latter lower bounds also hold for the construction of maximal matchings and maximal independent sets.

### Citations

1455 | Impossibility of distributed consensus with one faulty process
- Fischer, Lynch, et al.
- 1985
(Show Context)
Citation Context ...ph with a variety of node degrees! Not many graphs with these "non-properties" are known in distributed computing. The proof of our lower bounds is based on the timeless indistinguishability=-= argument [7, 12]-=-. In k rounds of communication, a network node can only gather information about nodes which are at most k hops away and hence, only this information can be used to determine the computation's outcome... |

1273 | The Byzantine Generals Problem - Lamport, Shostak, et al. - 1982 |

650 | A threshold of ln n for approximating set cover - Feige - 1998 |

371 | A simple parallel algorithm for the maximal independent set problem - Luby - 1986 |

305 |
Distributed Computing: A Locality-Sensitive Approach
- Peleg
- 2000
(Show Context)
Citation Context ...e outputs. For randomized algorithms, the outcome of v is also dependent on the randomness computed by the nodes in Tv,k . The model presented is in accordance with the one used in [15] and textbooks =-=[19]-=-. It is the strongest possible model when proving lower bounds for local computations because it focuses entirely on the locality of distributed problems and abstracts away other issues arising in the... |

178 |
Locality in distributed graph algorithms
- Linial
- 1992
(Show Context)
Citation Context ...r and Stockmayer [18] raised this for the distributed computing community vital question over a decade ago, and though the price of locality has puzzled researchers ever since, results have been rare =-=[15]-=-. The importance of locality stems from the desire of achieving a global goal based on local information only. This is not only one of the key challenges when developing fast distributed algorithms, b... |

114 | Constant-time distributed dominating set approximation - Kuhn, Wattenhofer |

114 | What can be computed locally - Naor, Stockmeyer - 1993 |

110 | An Ω(D log(N/D)) Lower Bound for Broadcast in Radio Networks
- Kushilevitz, Mansour
- 1998
(Show Context)
Citation Context ...r bound has been cherished by researchers as a fundamental advancement in the theory of distributed algorithms. For di#erent models of distributed computation, there is a number of other lower bounds =-=[6, 11]-=-, most notably for the problem of constructing a minimum spanning tree (MST) of the network graph [3, 4, 16, 20]. With the exception of [3], the MST lower bounds apply to a model where message size is... |

108 | Deterministic coin tossing with applications to optimal parallel list ranking - Cole, Vishkin - 1986 |

52 | A fast and simple randomized parallel algorithm for maximal matching - Israeli, Itai - 1986 |

42 | A near-tight lower bound on the time complexity of distributed mst construction
- Peleg, Rabinovich
- 1999
(Show Context)
Citation Context ...ithms. For di#erent models of distributed computation, there is a number of other lower bounds [6, 11], most notably for the problem of constructing a minimum spanning tree (MST) of the network graph =-=[3, 4, 16, 20]-=-. With the exception of [3], the MST lower bounds apply to a model where message size is bounded. In [4], the lower bounds of [16, 20] are extended to approximation algorithms. To the best of our know... |

41 | E.: Hundreds of Impossibility Results for Distributed Computing - Fich, Ruppert - 2003 |

41 | Ustimenko V., Explicit construction of graphs with an arbitrary large girth and of large size - Lazebnik - 1995 |

40 | A New Series of Dense Graphs of High Girth - Lazebnik, Ustimenko, et al. - 1995 |

39 |
Unconditional lower bounds on the time-approximation tradeoffs for the distributed minimum spanning tree problem
- Elkin
- 2004
(Show Context)
Citation Context ...ithms. For di#erent models of distributed computation, there is a number of other lower bounds [6, 11], most notably for the problem of constructing a minimum spanning tree (MST) of the network graph =-=[3, 4, 16, 20]-=-. With the exception of [3], the MST lower bounds apply to a model where message size is bounded. In [4], the lower bounds of [16, 20] are extended to approximation algorithms. To the best of our know... |

36 | A faster distributed protocol for constructing a minimum spanning tree
- Elkin
- 2004
(Show Context)
Citation Context ...ithms. For di#erent models of distributed computation, there is a number of other lower bounds [6, 11], most notably for the problem of constructing a minimum spanning tree (MST) of the network graph =-=[3, 4, 16, 20]-=-. With the exception of [3], the MST lower bounds apply to a model where message size is bounded. In [4], the lower bounds of [16, 20] are extended to approximation algorithms. To the best of our know... |

25 | Distributed MST for constant diameter graphs - Lotker, Patt-Shamir, et al. |

23 | The Local Detection Paradigm and its Applications to Self-Stabilization. Theoretical Computer Science
- Afek, Kutten, et al.
- 1997
(Show Context)
Citation Context ...is not only one of the key challenges when developing fast distributed algorithms, but it also improves fault-tolerance and allows detecting illegal global configurations by checking local conditions =-=[1]-=-. Recent advances in networking and ever-growing distributed systems drive the need for a thorough understanding of locality issues. In the present paper, we study the impact of locality in the classi... |

22 | L.: Local computations on static and dynamic graphs - Mayer, Naor, et al. - 1995 |

13 | Distributed Combinatorial Optimization - Kuhn, Wattenhofer - 2003 |

2 | Locality in Distributed Graph Algorithms.SIAM - Linial - 1992 |

1 | 3] U. Feige. A Threshold of ln n for Approximating SetCover - Information, Control - 1986 |

1 | Impossibility of Distributed Consensus With One Faulty Process - Israeli, Itai - 1985 |