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## Near-perfect load balancing by randomized rounding (2009)

Venue: | In 41st Annual ACM Symposium on Theory of Computing (STOC’09 |

Citations: | 15 - 9 self |

### Citations

513 | Randomized gossip algorithms
- Boyd, Ghosh, et al.
- 2006
(Show Context)
Citation Context ...bor than to send one token to each neighbor. This motivates us to study the balancing circuit model [3] where each vertex transfers an arbitrary number of tokens to exactly one neighbor in each round =-=[5, 11, 19]-=-. The load-balancing process of a balancing circuit is governed by a sequence of (not necessarily perfect) matchings together with an orientation of each edge 1 . In each round, two paired vertices ba... |

368 |
Randomized rounding: A technique for provably good algorithms and algorithmic proofs
- Raghavan, Thompson
- 1987
(Show Context)
Citation Context ...x (t) i + x(t) j )/2 shared at time t by two paired vertices i and j at random can be seen as dependent randomized rounding of half-integral numbers. This very general approach of randomized rounding =-=[20]-=- up or down with probability depending on the fractional part is a standard method for approximating the solution of a discrete problem by rounding the solution of an idealized (continuous) problem. O... |

116 | Linearizable counting networks
- Herlihy, Shavit, et al.
- 1996
(Show Context)
Citation Context ...t by Ghosh and Muthukrishnan [11], it is more efficient to send a stream of many tokens to one neighbor than to send one token to each neighbor. This motivates us to study the balancing circuit model =-=[3]-=- where each vertex transfers an arbitrary number of tokens to exactly one neighbor in each round [5, 11, 19]. The load-balancing process of a balancing circuit is governed by a sequence of (not necess... |

60 | Local divergence of Markov chains and the analysis of iterative load-balancing schemes
- Rabani, Sinclair, et al.
- 1999
(Show Context)
Citation Context ...bor than to send one token to each neighbor. This motivates us to study the balancing circuit model [3] where each vertex transfers an arbitrary number of tokens to exactly one neighbor in each round =-=[5, 11, 19]-=-. The load-balancing process of a balancing circuit is governed by a sequence of (not necessarily perfect) matchings together with an orientation of each edge 1 . In each round, two paired vertices ba... |

52 | Tight analyses of two local load balancing algorithms
- Ghosh, Leighton, et al.
- 1995
(Show Context)
Citation Context ...een shown that the deviation can be quite significant [11, 21] and the question of a precise quantitative relationship between the discrete and the idealized process has been posed by several authors =-=[10, 11, 15, 18, 21]-=-. Existing models also differ in the assumptions regarding communication in the underlying network. Some models restrict the number of tokens send across a link at a time [1, 10, 16]. On the other han... |

47 | Approximate load balancing on dynamic and asynchronous networks
- Aiello, Awerbuch, et al.
- 1993
(Show Context)
Citation Context ... authors [10, 11, 15, 18, 21]. Existing models also differ in the assumptions regarding communication in the underlying network. Some models restrict the number of tokens send across a link at a time =-=[1, 10, 16]-=-. On the other hand, the diffusion model allows load to be moved from each processor to all its neighbors in parallel in each time step [8, 18, 21]. As pointed out by Ghosh and Muthukrishnan [11], it ... |

47 | A dynamic distributed load balancing algorithm with provable good performance
- Luling, Monien
- 1993
(Show Context)
Citation Context ... authors [10, 11, 15, 18, 21]. Existing models also differ in the assumptions regarding communication in the underlying network. Some models restrict the number of tokens send across a link at a time =-=[1, 10, 16]-=-. On the other hand, the diffusion model allows load to be moved from each processor to all its neighbors in parallel in each time step [8, 18, 21]. As pointed out by Ghosh and Muthukrishnan [11], it ... |

44 | Simulating a random walk with constant error
- Cooper, Spencer
- 2006
(Show Context)
Citation Context ...ts apply to all graphs. Another very surprising relationship between a discrete process and its idealized (continuous) counterpart appears for so-called deterministic random walks. Cooper and Spencer =-=[7]-=- show a remarkable similarity between the expectation of a random walk (the idealized process) and a deterministic analogue where instead of distributing tokens randomly, each vertex serves its neighb... |

43 | Small-Depth Counting Networks
- Klugerman, Plaxton
- 1992
(Show Context)
Citation Context ...it [3]. They constructed a sequence of Θ(log 2 n) matchings that achieve a discrepancy of one for all inputs for a specific orientation of the edges. This result was improved by Klugerman and Plaxton =-=[13, 14]-=- who constructed for the same problem a sequence of only Θ(log n) matchings. Note that in contrast to the model we have described before, the orientation of all edges must be fixed and there is no res... |

38 |
An analysis of diffusive loadbalancing
- Subramanian, Scherson
- 1994
(Show Context)
Citation Context ...balancing. A common simplifying assumption is that the tokens are divisible. This idealized process is very well understood [18]. However, the divisibility assumption is invalid for many applications =-=[21]-=-. It has been shown that the deviation can be quite significant [11, 21] and the question of a precise quantitative relationship between the discrete and the idealized process has been posed by severa... |

37 |
Dynamic load balancing by random matchings
- Ghosh, Muthukrishnan
- 1996
(Show Context)
Citation Context ...visible. This idealized process is very well understood [18]. However, the divisibility assumption is invalid for many applications [21]. It has been shown that the deviation can be quite significant =-=[11, 21]-=- and the question of a precise quantitative relationship between the discrete and the idealized process has been posed by several authors [10, 11, 15, 18, 21]. Existing models also differ in the assum... |

33 |
E.: Randomized broadcast in networks
- Feige, Peleg, et al.
- 1990
(Show Context)
Citation Context ...g log n to each other, where c1 is a large constant to be determined later. Since for every vertex v ∈ V , |B2c1 log log n(v)| = O(log n), we can find such a subset S of size at least Ω(n/log n) (cf. =-=[9]-=-). Define the load vector x (0) i = max{0, c2 log log n − dist(i, S)}, where c2 � c1 is a small constant that is specified later. Clearly, the initial discrepancy equals c2 log log n. We start by exam... |

27 | Mixing of random walks and other diffusions on a graph
- Lovász, Winkler
- 1993
(Show Context)
Citation Context ...een shown that the deviation can be quite significant [11, 21] and the question of a precise quantitative relationship between the discrete and the idealized process has been posed by several authors =-=[10, 11, 15, 18, 21]-=-. Existing models also differ in the assumptions regarding communication in the underlying network. Some models restrict the number of tokens send across a link at a time [1, 10, 16]. On the other han... |

17 |
secondorder diffusive methods for rapid, coarse, distributed load balancing. Theory Comput
- First-
- 1998
(Show Context)
Citation Context ...009 ACM 978-1-60558-506-2/09/05 ...$5.00. There are various models for load balancing. A common simplifying assumption is that the tokens are divisible. This idealized process is very well understood =-=[18]-=-. However, the divisibility assumption is invalid for many applications [21]. It has been shown that the deviation can be quite significant [11, 21] and the question of a precise quantitative relation... |

11 | Distributing unit size workload packages in heterogeneous networks
- Elsässer, Monien, et al.
(Show Context)
Citation Context ...ct the number of tokens send across a link at a time [1, 10, 16]. On the other hand, the diffusion model allows load to be moved from each processor to all its neighbors in parallel in each time step =-=[8, 18, 21]-=-. As pointed out by Ghosh and Muthukrishnan [11], it is more efficient to send a stream of many tokens to one neighbor than to send one token to each neighbor. This motivates us to study the balancing... |

11 | Small-depth counting networks and related topics
- Klugerman
- 1994
(Show Context)
Citation Context ...it [3]. They constructed a sequence of Θ(log 2 n) matchings that achieve a discrepancy of one for all inputs for a specific orientation of the edges. This result was improved by Klugerman and Plaxton =-=[13, 14]-=- who constructed for the same problem a sequence of only Θ(log n) matchings. Note that in contrast to the model we have described before, the orientation of all edges must be fixed and there is no res... |

8 | A New Analytical Method for Parallel, Diffusion-Type Load Balancing
- Berenbrink, Friedetzky, et al.
- 2009
(Show Context)
Citation Context ...uctured graphs, it is popular to use random matchings 2 Rabani et al. [19] did not consider random matchings, but a straightforward adaptation of their techniques yields this bound. instead, see e.g. =-=[4, 5, 10, 11]-=-. We prove results that hold for a large class of randomly generated matchings including the models of [5, 10, 11]. For arbitrary graphs we prove a ) rounds w.h.p. bound of O (√ log n 1−λ2 log n) afte... |

8 | Randomized Smoothing Networks - Herlihy, Tirthapura - 2006 |

5 | The impact of randomization in smoothing networks
- Mavronicolas, Sauerwald
- 2008
(Show Context)
Citation Context ...be viewed as a balancing circuit on complete graphs). Recently, a special balancing circuit called block network was examined under the assumption that edges are oriented uniformly at random [12]. In =-=[17]-=- the authors showed that the cascade of two block networks gives a discrepancy of17 in 2log n steps. However, the analysis of [17] is rather tailored for this special network, while our results apply... |

4 |
The Convergence of Realistic Distributed Load-Balancing Algorithms
- Cedo, Cortes, et al.
- 2007
(Show Context)
Citation Context ...ng to look at the time-discrepancy trade-off, which can be measured as the product of time and the achieved discrepancy. All previous trade-offs had a time-discrepancy product of Ω(log 2 n + log(Kn)) =-=[1, 8, 10, 18, 19, 6]-=- while we achieve a product O(log(Kn)(log log n) 3 ) which is very close to the natural lower bound of Ω(log(Kn)). Related work Balancing circuits were introduced by Aspnes, Herlihy and Shavit [3]. Th... |

2 | Load balancing: dimension exchange on product graphs
- Arndt
(Show Context)
Citation Context ...e the load quickly. This is different for highly structured graphs. There is for example a canonical choice of matchings for the hypercube that uses in round i all edges across dimension (imod log n) =-=[2]-=-. In general such matching sequences with a fixed period d are called periodic balancing circuits (note that typically d is of order the maximum degree of G). Let x (0) ∈ R n be the initial load vecto... |