Multiple Key Hashing Research Articles

Optimal bucket allocation design of k-ary MKH files for partial match retrieval

The paper first shows that the bucket allocation problem of an MKH (multiple key hashing) file for partial match retrieval can be reduced to that of a smaller sized subfile, called the remainder of the file. And it is pointed out that the remainder type MKH file is the hardest MKH file for which to design an optimal allocation scheme. The authors then particularly concentrate on the allocation of an important remainder type MKH file; namely, the k-ary MKH file. They present various sufficient conditions on the number of available disks and the number of attributes for a k-ary MKH file to have a perfectly optimal allocation among the disks for partial match queries. Based upon these perfectly optimal allocations, they further present a heuristic method, called the CH (cyclic hashing) method, to produce near optimal allocations for the general k-ary MKH files. Finally, a comparison, by experiment, between the performances of the proposed method and an ideal perfectly optimal method, shows that the CH method is indeed satisfactorily good for the general k-ary MKH files.

Redundant MKH files design among multiple disks for concurrent partial match retrieval

It is known that the average query cost of a file in a multiple disk system can be dramatically reduced by storing redundant records of the file onto different disks. However, additional space is needed for the redundant records. In addition, the achievement of minimum redundance is difficult. Recently, Chen et al. (1994) showed that the problem of allocating all buckets of a multiple key hashing (MKH) file optimally among multiple disks for concurrent partial match retrieval can be reduced to a smaller sized subfile, called the remainder of the file. Based upon their reduction work, this article suggests two redundant storage schemes for MKH files in a multiple disk system. We point out that only modest copies of the remainder are necessary to be redundantly stored, in order to get perfectly optimal average query response time performance for an MKH file. We also emphasize that by using different clusterings for different copies, both the record organization cost and the bucket allocation cost can be simultaneously reduced, and thus, the cost can be dramatically reduced.

A greedy relaxed generalized disc modulo allocation method for multiple key hashing files on multi‐disc systems

Abstract In this paper, we propose an efficient way for the arrangement of multiple key hashing (MKH) files onto a multiple disc system. We present a greedy strategy to find a proper set of parameters of a hashing function that determines the near “optimal” bucket distribution for facilitating the maximal concurrency of disc accesses. Some experimental results are given to show that our greedy method works well in general cases and can achieve the same performance as the previously proposed method, that can only be used in some restricted cases.

Optimal multiple key hashing files for orthogonal range queries

This paper mainly explores the design of the multiple key hashing file (MKHF) for orthogonal range retrieval. First, we show the optimal MKHF design problem for orthogonal range queries (ORQs) is NP-hard. Then the performance formula of the MKHF over all possible ORQs is derived. We also present a theoretical lower bound on the performance of the MKHF over all possible ORQs. Finally, a very interesting phenomenon existing in the optimal orthogonal range information retrieval system and the optimal partial match information retrieval system is presented.

Optimal MMI file systems for orthogonal range retrieval

Range queries are more general and significant than partial match queries (PMQs) in the applications of multi-attribute information retrieval. However, almost all efforts devoted to the design of multi-attribute file systems so far were concentrated on PMQs. In this paper, we are concerned with the problem of designing multi-attribute file systems for facilitating orthogonal range queries (ORQs). A greedy method, called the minimum marginal increase (MMI) method, is presented first. Then we derive the formulas of performance of an important static file and an important dynamic file, namely the multiple key hashing (MKH) file and the extendible hashing (EH) file, for answering ORQs. Based upon these performance formulas, we show that the problem of designing optimal file systems for ORQs is indeed a very difficult problem. Further, we show that the presented MMI method can indeed be used to design optimal MKH files and optimal EH files, in some cases, for ORQs. Finally, some experiments show that the MMI method can still be applied to produce “good” MKH files and “good” EH files for the general case.

Optimality Properties of the Disc Modulo Allocation Method for k-ary Multiple Key Hashing Files

Multiple key hashing files have been shown to exhibit attractive properties for partial match retrieval. The Disc Modulo (DM) allocation method has recently been shown to facilitate partial match retrieval for multiple key hashing files on multiple discs. In this paper, it is shown that the DM allocation method is optimal for k-ary multiple key hashing files under the condition that k ≡ (0 or 1 or m−1) (modm) where m is the number of available discs.

A note on allocating k-ary multiple key hashing files among multiple disks

In this paper, we shall introduce the concept of k-ary multiple key hashing (MKH) files and the disk modulo (DM) allocation method. It is pointed out that k-ary MKH files exhibit the property of facilitating partial match retrieval. We then derive a close-form performance formula of the DM allocation method for k-ary MKH files on multidisk systems. Further more, we show that the DM allocation method is optimal for allocating k-ary MKH files on a k-disk system.

On the design of multiple key hashing files for concurrent orthogonal range retrieval between two disks

This paper concerns the following problem: given a set of multi-attribute records, a fixed number of buckets and a two-disk system, arrange the records into the buckets and then store the buckets between the disks in such a way that, over all possible orthogonal range queries (ORQs), the disk access concurrency is maximized. We shall adopt the multiple key hashing (MKH) method for arranging records into buckets and use the disk modulo (DM) allocation method for storing buckets onto disks. Since the DM allocation method has been shown to be superior to any other allocation methods for allocating an MKH file onto a two-disk system for answering ORQs, the real issue is knowing how to determine an optimal way for organizing the records into buckets based upon the MKH concept. A performance formula that can be used to evaluate the average response time, over all possible ORQs, of an MKH file in a two-disk system using the DM allocation method is first presented. Based upon this formula, it is shown that our design problem is related to a notoriously difficult problem, namely the Prime Number Problem. Then a performance lower bound and an efficient algorithm for designing optimal MKH files in certain cases are presented. It is pointed out that in some cases the optimal MKH file for ORQs in a two-disk system using the DM allocation method is identical to the optimal MKH file for ORQs in a single-disk system and the optimal average response time in a two-disk system is slightly greater than one half of that in a single-disk system.

Performance analyses of multi‐attribute files based upon multiple key hashing functions and haphazard files

Abstract In this paper, a new multi‐attribute file, called haphazard file, is introduced. We derive two formulas for the average number of buckets to be examined over all possible partial match queries for multi‐attribute files based upon multi‐key hashing functions and haphazard files respectively. Theoretical results show that the performance of multi‐attribute files based upon multiple key hashing functions is always superior to that of haphazard files.

Optimal information retrieval when queries are not random

We consider the complexity of the general information retrieval system design problem and multiattribute file systems based upon the multiple key hashing (MKH) design problem. We first show that the problem of designing an optimal multiattribute file system is NP-hard. The performance formula for multiattribute file systems based upon the MKH method is derived. We also show that the design problem for a multiattribute file system based upon the MKH method is related to the prime number problem. We show that the problem of designing optimal multiattribute files based upon the MKH method can be reduced to finding minimal N-tuples, which was discussed by Chang, Lee and Du. We further present a very efficient method for designing good multiple key hashing functions in the case where the number of buckets is a power of a prime number. We also propose a heuristic algorithm to design good multiple key hashing functions in general.

On the complexity of designing optimal partial-match retrieval systems

We consider the problem of designing an information retrieval system on which partial match queries have to be answered. Each record in the system consists of a list of attributes , and a partial match query specifies the values of some of the attributes. The records are stored in buckets in a secondary memory, and in order to answer a partial match query all the buckets that may contain a record satisfying the specifications of that query must be retrieved. The bucket in which a given record is stored is found by a multiple key hashing function, which maps each attribute to a string of a fixed number of bits. The address of that bucket is then represented by the string obtained by concatenating the strings on which the various attributes were mapped. A partial match query may specify only part of the bits in the string representing the address, and the larger the number of bits specified, the smaller the number of buckets that have to be retrieved in order to answer the query. The optimization problem considered in this paper is that of deciding to how many bits each attribute should be mapped by the bashing function above, so that the expected number of buckets retrieved per query is minimized. Efficient solutions for special cases of this problem have been obtained in [1], [12], and [14]. It is shown that in general the problem is NP-hard, and that if P ≠ NP, it is also not fully approximable. Two heuristic algorithms for the problem are also given and compared.

Attribute based file organization in a paged memory environment

The high cost of page accessing implies a need for for more careful data organization in a paged memory than is typical of most inverted file and similar approaches to multi-key retrieval. This article analyses that cost and proposes a method called multiple key hashing which attempts to minimize it. Since this approach is not always preferable to inversion, a combined method is described. The exact specifications of this combination for a file with given data and traffic characteristics is formulated as a mathematical program. The proposed heuristic solution to this program can often improve on a simple inversion technique by a factor of 2 or 3.