## Hash Tables With Finite Buckets Are Less Resistant To Deletions

### Cached

### Download Links

Citations: | 3 - 1 self |

### BibTeX

@MISC{Kanizo_hashtables,

author = {Yossi Kanizo and David Hay and Isaac Keslassy},

title = {Hash Tables With Finite Buckets Are Less Resistant To Deletions},

year = {}

}

### OpenURL

### Abstract

Abstract — We show that when memory is bounded, i.e. buckets are finite, dynamic hash tables that allow insertions and deletions behave significantly worse than their static counterparts that only allow insertions. This behavior differs from previous results in which, when memory is unbounded, the two models behave similarly. We show the decrease in performance in dynamic hash tables using several hash-table schemes. We also provide tight upper and lower bounds on the achievable overflow fractions in these schemes. Finally, we propose an architecture with contentaddressable memory (CAM), which mitigates this decrease in performance. A. Background I.

### Citations

600 | Queuing Systems
- Kleinrock
- 1975
(Show Context)
Citation Context ... of the distribution of p and of the overflow fraction. ( ) n 1 ℓ ( m−1 )ℓ. In the discrete Theorem 1: Let C = ∑h ℓ=0 model, (i) the distribution of p(t) converges to the Engset distribution πn [15], =-=[16]-=-; namely, π n k = 1 C · ( n k ) · ( ) k 1 . (1) m − 1 (ii) the overflow fraction converges to 1 C · ( ) ( ) h n 1 · · h m − 1 ( 1 − h n ) . (2) Proof: [Proof Outline] As mentioned, the full proof appe... |

208 | The power of two choices in randomized load balancing
- Mitzenmacher
(Show Context)
Citation Context ...he limit of the discrete and continuous finite models behaves indeed like in the fluid model. In simulations, we will also show that the scaled systems converge fast to their fluid model. We refer to =-=[14]-=- for a more complete discussion of the sufficient conditions for the convergence to the fluid-limit fixed-point solution. III. A SINGLE-CHOICE HASHING SCHEME We start by analyzing a simplistic hashing... |

136 | Cuckoo Hashing
- Pagh, Rodler
- 2004
(Show Context)
Citation Context ...es. new elements are moved when they cannot be inserted in the hash table. Fig. 1(a) and 1(b) show the overflow fraction of the d-random algorithm with a stash [4] and the cuckoo hashing with a stash =-=[7]-=-–[9]. The overflow fractions are obtained in simulations using 2048 buckets, 10 6 rounds with one random element deletion and one element insertion in each round, and a standard pseudorandom number ge... |

126 |
Introduction to Queueing Theory
- Cooper
- 1981
(Show Context)
Citation Context ...limits of the distribution of p and of the overflow fraction. ( ) n 1 ℓ ( m−1 )ℓ. In the discrete Theorem 1: Let C = ∑h ℓ=0 model, (i) the distribution of p(t) converges to the Engset distribution πn =-=[15]-=-, [16]; namely, π n k = 1 C · ( n k ) · ( ) k 1 . (1) m − 1 (ii) the overflow fraction converges to 1 C · ( ) ( ) h n 1 · · h m − 1 ( 1 − h n ) . (2) Proof: [Proof Outline] As mentioned, the full proo... |

102 | The power of two random choices: a survey of techniques and results
- Mitzenmacher, Richa, et al.
(Show Context)
Citation Context ...t three cases: (a) In the static case in which n elements are uniformly hashed into n infinite buckets, the maximum bucket size is known to be approximately log n/log log n with high probability [2], =-=[3]-=-. The dynamic case yields the same result, assuming alternate departures and arrivals of random elements while keeping n elements in the hash table after each arrival. (b) Likewise, when inserting eac... |

84 | How Asymmetry Helps Load Balancing
- Vöcking
- 1999
(Show Context)
Citation Context ...ain, the dynamic case yields the same result [3], [4]. (c) Similarly, using the asymmetric d-left algorithm, the static case and the dynamic case yield again the same bound on the maximum bucket size =-=[5]-=-. Therefore, as illustrated in these three cases, given a large number of elements, it appears that the network designer could use the simpler static model for the dynamic case. In this paper, we focu... |

83 | Expected length of the longest probe sequence in hash code searching - Gonnet - 1981 |

80 | Traffic Models in Broadband Networks
- Adas
- 1997
(Show Context)
Citation Context ...iment yields 25.67%. C. Experiments Using an On-off Arrival Model We also consider a queueing model where at each step i, bi elements arrive according to k independent on-off bursty flows of elements =-=[21]-=-; then, after the arrival phase, one element is randomly deleted. Therefore, the number of elements in the system keeps changing, contrarily to the previous models with a constant load. Fig. 6 shows t... |

20 | More Robust Hashing: Cuckoo Hashing with a Stash. To appear
- Kirsch, Mitzenmacher, et al.
- 2008
(Show Context)
Citation Context ...ing the degradation of performance in dynamic hash tables. the hash table. Fig. 1(a) and 1(b) show the overflow fraction of the d-random algorithm with a stash [4] and the cuckoo hashing with a stash =-=[7]-=-, [8]. The overflow fractions are obtained in simulations using 2048 buckets, 10 6 rounds with one random element deletion and one element insertion in each round, and a standard pseudorandom number g... |

17 | The power of one move: Hashing schemes for hardware
- Kirsch
- 2008
(Show Context)
Citation Context ...in this paper, and presented in full in the online technicalreport [11]. II. PROBLEM STATEMENT A. Terminology and Notations This paper considers single- and multiple-choice hash schemes with a stash =-=[12]-=-, [13]. Such schemes consist of two data structures: (i) A hash table of total memory size m · h, partitioned into m buckets of size h; (ii) An overflow list, usually stored in an expensive CAM. Note ... |

11 | The Convexity of the Mean Queue Size of the M/M/C Queue with Respect to the Traffic Intensity - Grassmann - 1987 |

9 | Hash-based techniques for high-speed packet processing
- Kirsch, Mitzenmacher, et al.
- 2009
(Show Context)
Citation Context ...nitially estimated. Using the static model seems natural. In fact, dynamic hash tables are known for being typically harder to model than static ones, sometimes even lacking any mathematical analysis =-=[1]-=-. Therefore, the static model appears to be a simpler and more accessible option to the network designer. More significantly, past studies have also found the same asymptotic behavior in dynamic and i... |

9 |
Qualitative properties of the Erlang blocking model with heterogeneous user requirements. Queueing Syst
- Nain
- 1990
(Show Context)
Citation Context ... function, as defined in Section II. The more general case with several hash functions using different subtable-based distributions appears in Section V. The proof relies on the following result from =-=[17]-=-. Consider an Erlang blocking model with N servers, and suppose that the arrival rate depends on the system. Let λk be the arrival rate when there are k transmissions in progress, k = 0,1,...,N − 1. T... |

7 | Peacock hashing: Deterministic and updatable hashing for high performance networking
- Kumar, Turner, et al.
- 2008
(Show Context)
Citation Context ...lutions exist to reduce the drop rate (or collision probability) in a dynamic system. One such solution uses limited hash functions in order to be able to rebalance the hash table in case of deletion =-=[18]-=-. However, this approach gives up randomness, and the efficiency of a similar approach appears limited [6]. Another solution, based on the second-chance scheme [12], moves elements from one bucket to ... |

6 | Optimal fast hashing
- Kanizo, Hay, et al.
- 2009
(Show Context)
Citation Context ...s paper, and presented in full in the online technicalreport [11]. II. PROBLEM STATEMENT A. Terminology and Notations This paper considers single- and multiple-choice hash schemes with a stash [12], =-=[13]-=-. Such schemes consist of two data structures: (i) A hash table of total memory size m · h, partitioned into m buckets of size h; (ii) An overflow list, usually stored in an expensive CAM. Note that t... |

6 |
Integer Hash Function. http://www.concentric.net/ Ttwang/tech/inthash.htm
- Wang
(Show Context)
Citation Context ...erage overflow fraction retrieved using our models for SINGLE and MULTIPLE with the corresponding overflow fraction when using a real hash function on a real-life trace. We used a 64-bit mix function =-=[20]-=- to implement two 16-bit hash functions. Weγ 0.8 0.6 0.4 0.2 SINGLE (sim) SINGLE (model) MULTIPLE (sim) MULTIPLE (model) 0 0 100 200 300 400 500 600 700 total num of elements Fig. 6. Marginal overflo... |

5 | The convexity of loss rate in an Erlang loss system and sojourn in an Erlang delay system with respect to arrival and service rates - Krishnan - 1990 |

3 | On the performance of multiple choice hash tables with moves on deletes and inserts
- Kirsch, Mitzenmacher
(Show Context)
Citation Context ... shows the overflow fraction for both a static system, where there are only insertions, and a dynamic system, where we alternate between deletions and insertions while a fixed load is maintained [4], =-=[6]-=-. To measure the overflow fraction, it relies on an overflow list, called stash, to which. . . . (i) (ii) H ( x1 ) x0 x1 x0 1 x (i) (ii) H ( x1 ) x0 x1 x0 x1 Therefore, in the dynamic case with finit... |

3 | CAIDA Anonymized 2008 Internet Trace equinix-chicago 2008-03-19 - Shannon, Aben, et al. |

1 |
A further analysis of cuckoo hashing with a stash and random graphs of excess r,” Submitted for publication
- Kutzelnigg
- 2009
(Show Context)
Citation Context ...new elements are moved when they cannot be inserted in the hash table. Fig. 1(a) and 1(b) show the overflow fraction of the d-random algorithm with a stash [4] and the cuckoo hashing with a stash [7]–=-=[9]-=-. The overflow fractions are obtained in simulations using 2048 buckets, 10 6 rounds with one random element deletion and one element insertion in each round, and a standard pseudorandom number genera... |

1 | A precise analysis of cuckoo hashing
- Drmota, Kutzelnigg
- 2009
(Show Context)
Citation Context ... an overflow fraction of 0.52% and 2.97% in the static and dynamic models, respectively. Moreover, while for cuckoo hashing scheme with load of 0.5 the overflow fraction in the static model goes to 0 =-=[10]-=-, it does so more slowly in the dynamic case. For instance, for m = 1024 we got an overflow fraction in the static and dynamic models of 0.05% and 0.44%, where for m = 16384 we got 0.0012% and 0.0606%... |