## Symmetric vs. Asymmetric Multiple-Choice Algorithms

Citations: | 1 - 0 self |

### BibTeX

@MISC{Vöcking_symmetricvs.,

author = {Berthold Vöcking},

title = {Symmetric vs. Asymmetric Multiple-Choice Algorithms},

year = {}

}

### OpenURL

### Abstract

Multiple-choice allocation algorithms have been studied intensively over the last decade. These algorithms have several applications in the areas of load balancing, routing, resource allocation and hashing. The underlying idea is simple and can be explained best in the balls-and-bins model: Instead of assigning balls (jobs, requests, or keys) simply at random to bins (machines, servers, or positions in a hash table), choose first a small set of bins at random, inspect these bins, and place the ball into one of the bins containing the smallest number of balls among them. The simple idea of first selecting a small set of alternatives at random and then making the final choice after careful inspection of these alternatives leads to great improvements against algorithms that place their decisions simply at random. We illustrate the power of this principle in terms of simple balls-and-bins processes. In particular, we study recently presented algorithms that treat bins asymmetrically in order to obtain a better load balancing. We compare the behavior of these asymmetric schemes with symmetric schemes and prove that the asymmetric schemes achieve a better load balancing than their symmetric counterparts. 1

### Citations

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(Show Context)
Citation Context .... We focus on sequential, online balls-and-bins games in which balls are inserted one after the other.s2.1 Symmetric allocation B. Vöcking: Multiple-Choice Algorithms 3 Azar, Broder, Karlin and Upfal =-=[2, 3]-=- investigate multiple-choice allocation for on-line load balancing and hashing. Algorithm sym[d] , for ds2, inserts one ball after the other and chooses d alternative bins independently and uniformly ... |

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(Show Context)
Citation Context ...as been investigated extensively in several variations, e.g., parallel processes [1, 20], infinite sequences of insertions and deletions [3, 7, 8], balls with different weights [5], queuing processes =-=[16, 17, 22]-=- as well as applications to data management and PRAM simulations [9, 7, 10, 14] and routing in interconnection networks [7, 13, 15]. An extensive survey of techniques and results is given in [18]. 2 S... |

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Citation Context ...ion, Fd¢ k£�© Fd¢ k ¦ i£ i� 1 Observe that the sequence F2 corresponds to the standard Fibonacci sequence. © limk� Define φd ∞ k � . Then φ2 corresponds to the so-called golden ratio k£ Fd¢ (see e.g. =-=[12]-=-) and φd is a simple generalization. For example, © 1� φ2 ����� 61 , © φ3 83 ����� , and φ4 © 1� 92 ����� In general, φ2 � φ3 � φ4 ����� � 2 and limd� ∞ φd © 2. 1� d ∑s4 Aracne 2001 Theorem 2 Suppose ... |

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Citation Context ...om and then placing the ball into one of these alternatives, was discovered independently by several groups of researchers for different applications. For example, Karp, Luby, and Meyer auf der Heide =-=[11]-=- introduced this kind of algorithms for PRAM simulations. Azar, Broder, Karlin, and Upfal [3] presented multiple-choice algorithms for on-line load balancing. Following these seminal studies, the mult... |

81 | How Asymmetry Helps Load Balancing
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(Show Context)
Citation Context ...metric and asymmetric allocation schemes All articles mentioned above assume a uniform choice of alternatives from the set of all bins. In particular, bins are treated symmetrically. In a recent work =-=[21]-=-, it is presented an asymmetric variation of multiple-choice processes. This asymmetric scheme partitions bins into groups and treats bins in different groups differently. In fact, the idea is to keep... |

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Citation Context ...as been investigated extensively in several variations, e.g., parallel processes [1, 20], infinite sequences of insertions and deletions [3, 7, 8], balls with different weights [5], queuing processes =-=[16, 17, 22]-=- as well as applications to data management and PRAM simulations [9, 7, 10, 14] and routing in interconnection networks [7, 13, 15]. An extensive survey of techniques and results is given in [18]. 2 S... |

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Citation Context ...is, by moving balls from bins with lower index to bins with higher index wrt the normalized order of bins. In the following we give a formal proof for this theorem. (This proof was first presented in =-=[4]-=-.) Proof of Theorem 4: Let u denote the load vector obtained after inserting some fixed number of balls with left[d] , and let v denote the load vector obtained after inserting the same number of ball... |

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Citation Context ...ed multiple-choice algorithms for on-line load balancing. Following these seminal studies, the multiple-choice method has been investigated extensively in several variations, e.g., parallel processes =-=[1, 20]-=-, infinite sequences of insertions and deletions [3, 7, 8], balls with different weights [5], queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations [9, 7, 10, ... |

43 |
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Citation Context ...as been investigated extensively in several variations, e.g., parallel processes [1, 20], infinite sequences of insertions and deletions [3, 7, 8], balls with different weights [5], queuing processes =-=[16, 17, 22]-=- as well as applications to data management and PRAM simulations [9, 7, 10, 14] and routing in interconnection networks [7, 13, 15]. An extensive survey of techniques and results is given in [18]. 2 S... |

37 |
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Citation Context ...ses [1, 20], infinite sequences of insertions and deletions [3, 7, 8], balls with different weights [5], queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations =-=[9, 7, 10, 14]-=- and routing in interconnection networks [7, 13, 15]. An extensive survey of techniques and results is given in [18]. 2 Symmetric and asymmetric allocation schemes All articles mentioned above assume ... |

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Citation Context ...ses [1, 20], infinite sequences of insertions and deletions [3, 7, 8], balls with different weights [5], queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations =-=[9, 7, 10, 14]-=- and routing in interconnection networks [7, 13, 15]. An extensive survey of techniques and results is given in [18]. 2 Symmetric and asymmetric allocation schemes All articles mentioned above assume ... |

18 | E.: On balls and bins with deletions
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Citation Context .... Following these seminal studies, the multiple-choice method has been investigated extensively in several variations, e.g., parallel processes [1, 20], infinite sequences of insertions and deletions =-=[3, 7, 8]-=-, balls with different weights [5], queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations [9, 7, 10, 14] and routing in interconnection networks [7, 13, 15]. A... |

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Citation Context ...ed multiple-choice algorithms for on-line load balancing. Following these seminal studies, the multiple-choice method has been investigated extensively in several variations, e.g., parallel processes =-=[1, 20]-=-, infinite sequences of insertions and deletions [3, 7, 8], balls with different weights [5], queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations [9, 7, 10, ... |

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(Show Context)
Citation Context .... Following these seminal studies, the multiple-choice method has been investigated extensively in several variations, e.g., parallel processes [1, 20], infinite sequences of insertions and deletions =-=[3, 7, 8]-=-, balls with different weights [5], queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations [9, 7, 10, 14] and routing in interconnection networks [7, 13, 15]. A... |

12 | Allocating Weighted Jobs in Parallel
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(Show Context)
Citation Context ...ultiple-choice method has been investigated extensively in several variations, e.g., parallel processes [1, 20], infinite sequences of insertions and deletions [3, 7, 8], balls with different weights =-=[5]-=-, queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations [9, 7, 10, 14] and routing in interconnection networks [7, 13, 15]. An extensive survey of techniques a... |

12 | Reducing network congestion and blocking probability through balanced allocation
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Citation Context ...ions [3, 7, 8], balls with different weights [5], queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations [9, 7, 10, 14] and routing in interconnection networks =-=[7, 13, 15]-=-. An extensive survey of techniques and results is given in [18]. 2 Symmetric and asymmetric allocation schemes All articles mentioned above assume a uniform choice of alternatives from the set of all... |

9 | Contention Resolution in Hashing Based Shared Memory Simulations
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Citation Context ...ses [1, 20], infinite sequences of insertions and deletions [3, 7, 8], balls with different weights [5], queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations =-=[9, 7, 10, 14]-=- and routing in interconnection networks [7, 13, 15]. An extensive survey of techniques and results is given in [18]. 2 Symmetric and asymmetric allocation schemes All articles mentioned above assume ... |

4 |
Handbook of Randomized Computing, chapter The power of two random choices: A survey of the techniques and results
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Citation Context ..., 17, 22] as well as applications to data management and PRAM simulations [9, 7, 10, 14] and routing in interconnection networks [7, 13, 15]. An extensive survey of techniques and results is given in =-=[18]-=-. 2 Symmetric and asymmetric allocation schemes All articles mentioned above assume a uniform choice of alternatives from the set of all bins. In particular, bins are treated symmetrically. In a recen... |

3 | Routing on networks of optical crossbars
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(Show Context)
Citation Context ...ions [3, 7, 8], balls with different weights [5], queuing processes [16, 17, 22] as well as applications to data management and PRAM simulations [9, 7, 10, 14] and routing in interconnection networks =-=[7, 13, 15]-=-. An extensive survey of techniques and results is given in [18]. 2 Symmetric and asymmetric allocation schemes All articles mentioned above assume a uniform choice of alternatives from the set of all... |