## Blooming Trees for Minimal Perfect Hashing

Citations: | 1 - 0 self |

### BibTeX

@MISC{Antichi_bloomingtrees,

author = {Gianni Antichi and Domenico Ficara and Stefano Giordano and Gregorio Procissi and Fabio Vitucci},

title = {Blooming Trees for Minimal Perfect Hashing},

year = {}

}

### OpenURL

### Abstract

Abstract—Hash tables are used in many networking applications, such as lookup and packet classification. But the issue of collisions resolution makes their use slow and not suitable for fast operations. Therefore, perfect hash functions have been introduced to make the hashing mechanism more efficient. In particular, a minimal perfect hash function is a function that maps a set of n keys into a set of n integer numbers without collisions. In literature, there are many schemes to construct a minimal perfect hash function, either based on mathematical properties of polynomials or on graph theory. This paper proposes a new scheme which shows remarkable results in terms of space consumption and processing speed. It is based on an alternative to Bloom Filters and requires about 4 bits per key and 12.8 seconds to construct a MPHF with 3.8 × 10 9 elements. I.

### Citations

153 |
Data Structures and Algorithms 1: Sorting and Searching
- Mehlhorn
- 1984
(Show Context)
Citation Context ...o construct MPHFs, which uses a space of the order of n + o(n). The construction time of this model, based on hashing properties, is O(n), and the same result is also obtained in [10], [11]. Mehlhorn =-=[12]-=- shows that at least 1.44 bits per key are needed to represent a MPHF. Fox et. al. [13] illustrate an algorithm whose encoding size is very close to such a theoretical bound (i.e., around 2.5 bits per... |

45 | An optimal algorithm for generating minimal perfect hash functions
- Czech, Havas, et al.
- 1992
(Show Context)
Citation Context ...efficient structure to construct MPHFs, which uses a space of the order of n + o(n). The construction time of this model, based on hashing properties, is O(n), and the same result is also obtained in =-=[10]-=-, [11]. Mehlhorn [12] shows that at least 1.44 bits per key are needed to represent a MPHF. Fox et. al. [13] illustrate an algorithm whose encoding size is very close to such a theoretical bound (i.e.... |

41 |
Practical minimal perfect hash functions for large databases
- Fox, Heath, et al.
- 1992
(Show Context)
Citation Context ...f this model, based on hashing properties, is O(n), and the same result is also obtained in [10], [11]. Mehlhorn [12] shows that at least 1.44 bits per key are needed to represent a MPHF. Fox et. al. =-=[13]-=- illustrate an algorithm whose encoding size is very close to such a theoretical bound (i.e., around 2.5 bits per key) and which uses the well-known mapping-ordering-searching scheme. However, [8] pro... |

16 |
Storing a sparse table with 0(1) worst case access time
- Fredman, Komlós, et al.
- 1984
(Show Context)
Citation Context ...II. RELATED WORKS In this section, we present the major results about the construction of MPHF. For further details, [8] gives a comprehensive survey on perfect hashing. Fredman, Komlós and Szemerédi =-=[9]-=- present a space efficient structure to construct MPHFs, which uses a space of the order of n + o(n). The construction time of this model, based on hashing properties, is O(n), and the same result is ... |

15 | Simple and space-efficient minimal perfect hash functions
- Botelho, Pagh, et al.
(Show Context)
Citation Context ...of up to 9 bits for each key, which is optimal for huge sets.2 To the best of our knowledge, the solution which offers the best tradeoff between construction time and storage space is illustrated in =-=[15]-=-. It uses r-uniform random hypergraphs given by function values of r hash functions on the keys to be processed. Such an algorithm will be the reference for the performance evaluation of our solution.... |

11 |
Fundamental study - perfect hashing
- Czech, Havas, et al.
- 1997
(Show Context)
Citation Context ...the comparison with the other most efficient solutions proposed in the literature. II. RELATED WORKS In this section, we present the major results about the construction of MPHF. For further details, =-=[8]-=- gives a comprehensive survey on perfect hashing. Fredman, Komlós and Szemerédi [9] present a space efficient structure to construct MPHFs, which uses a space of the order of n + o(n). The constructio... |

11 | Perfect hashing for network applications
- Prabhakar, Bonomi
- 1999
(Show Context)
Citation Context ...r-uniform random hypergraphs given by function values of r hash functions on the keys to be processed. Such an algorithm will be the reference for the performance evaluation of our solution. Finally, =-=[16]-=- introduces a novel scheme for MPHF which requires about 8.6 bits per key. The construction is several orders of magnitude faster than existing perfect hashing schemes based on mapping-partitioning-se... |

9 | Hash and displace: Efficient evaluation of minimal perfect hash functions
- Pagh
- 1999
(Show Context)
Citation Context ...ent structure to construct MPHFs, which uses a space of the order of n + o(n). The construction time of this model, based on hashing properties, is O(n), and the same result is also obtained in [10], =-=[11]-=-. Mehlhorn [12] shows that at least 1.44 bits per key are needed to represent a MPHF. Fox et. al. [13] illustrate an algorithm whose encoding size is very close to such a theoretical bound (i.e., arou... |

5 | Multilayer compressed counting bloom filters
- Ficara, Giordano, et al.
- 2008
(Show Context)
Citation Context ...of keys. It inspires this work in the use of BF-like structures for MPHFs. Instead of standard BFs, a composed data structure is used: a first level is given by a Huffman Spectral Bloom Filter (HSBF) =-=[17]-=- while the remaining part is based on a novel filter, the so–called Blooming Tree (BT) [2]. This way, a novel method is proposed, which allows for an easy MPHF construction and fast retrieval, with lo... |

4 |
New directions in privacypreserving anomaly detection for network traffic
- Bianchi, Teofili, et al.
- 2008
(Show Context)
Citation Context ...es: the capability of efficiently revealing the presence of certain strings allows for a fast detection of attacks or for determining which data have to be anonymized in privacy-preserving approaches =-=[1]-=-. Given the high operating speeds of current links, item retrieval must be very fast. Moreover, item sets can be very large (e.g., search engines are nowadays indexing tens of billions of pages), thus... |

2 |
An approach for minimal perfect hash functions for very large databases,” Universidade Federal de Minas Gerais
- Botelho, Kohayakawa, et al.
- 2006
(Show Context)
Citation Context ...pace required to store the function is O(n log n), which is optimal for order preserving MPHFs [8]. This algorithm takes 32.9s to construct a MPHF for 524288 keys on a Sequent machine. Botelho et al. =-=[14]-=- propose a solution based on the classic divide and conquer technique, which is capable of generating MPHFs for sets of billion of keys. The construction time is O(n log n), the evaluation of h(x) req... |

1 |
Blooming trees: Space efficient structures for data representation
- Ficara, Giordano, et al.
- 2008
(Show Context)
Citation Context ...nstruct a minimal perfect hash function by using specific data structures based This work has been partially supported by the European Project FP7-ICT PRISM, contract number 215350. on Blooming Trees =-=[2]-=-. The main objectives are 1) simple construction process, 2) fast retrievals, and 3) memory savings. The target platforms are network processors (NPs) or general purposes processors (GPPs) that provid... |