R. Rivest. Partial-match retrieval algorithms. SIAM J. Comput., 5:19--50, 1976.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Given a database of n points in f0; 1g , the partial match problem is: In response to a query x in f0; 1; g database point y such that for every i whenever x i 6= we have x i = y i . In this paper we show randomized lower bounds in the cell probe model for this well studied problem [18, 11, 19, 16, 4, 6]. Our lower bounds follow from a two party asymmetric randomized communication complexity near optimal lower bound for this problem, where we show that either Alice has to send bits. When applied to the cell probe model, it means that if the number of cells is restricted to be poly(n; d) ....

....lower bound for the Hamming nearest neighbor problem; this strengthens the bound on Bob s communication obtained in [2] 1.2 Related work As mentioned earlier, the problem of partial match has been investigated for quite a while. The first non trivial result for this problem was obtained in [18, 19], who showed that for d 2 log n, the exhaustive storage solution can somewhat be improved. Recently, 6] presented two algorithms with the following query time space tradeoffs: n Delta exp(O(d log c= log n) space and O(n=2 ) query time for any c and nd space and O(dn=c) query time ....

R. Rivest. Partial match retrieval algorithms. SIAM J. on Computing, 5:19--50, 1976.

....(m=j) Theta (m=j) Now, in each match with k differences or less necessarily one of those pieces is preserved without differences, since otherwise there should be at least one difference in each piece, for a total of j = b kc 1) k differences overall. This fact was first utilized in [12, 13]. So we search for all the j pieces exactly and check each occurrence for a complete match. Observe that this time the pieces cannot be searched using the center to center assumption, because this holds only for the whole pattern. However, what is really necessary is not that the piece center ....

R. L. Rivest. Partial-match retrieval algorithms. SIAM J. Comput., 5(1):19--50, 1976.

....[16] and the term trie was coined by Fredkin as an derivative from information retrieval [22] Tries are widely used to represent a set of strings [1, 5, 29] that is, for dictionary management. The range of applications encompasses natural language processing [7, 36] pattern matching [20, 42], searching for reserved words for a compiler [2] for IP routing tables [34] and text compression [9] Balanced tries (represented in a single array) are used as a data structure for dynamic hashing [18] This broad range of applications justifies the view of tries as a general purpose data ....

R. L. Rivest. Partial match retrieval algorithms. SIAM Jour. of Computing, 5(1):19--50, 1976.

....where we must store a subset y#[0, 1] so that for any x # [0, 1] the query z # y i: x i #z i can be answered. No solution is known with the worst case query time even polynomial in n when the structure size is polynomial, and it has been conjectured that no such structure exists [Riv76]. Yet not only does communication complexity fail to provide bounds better than n#log s, but for this problem, we only know how to show a log n lower bound when s is polynomial in m, using the techniques of Section 4. Getting bounds for this problem closer to n#log s using communication ....

R. Rivest, Partial-match retrieval algorithms, SIAM J. Comput. 5 (1976), 19#50.

....of size (m=j) m=j) Now, in each match with k di erences or less necessarily one of those pieces is preserved without di erences, since otherwise there should be at least one di erence in each piece, for a total of j = b kc 1) k di erences overall. This fact was rst utilized in [15, 16]. So we search for all the pieces exactly and check each occurrence for a complete match. Observe that this time the pieces cannot be searched for using the center to center assumption, because this holds only for the whole pattern. However, what is really necessary is not that the piece center ....

R. L. Rivest. Partial-match retrieval algorithms. SIAM J. Comput., 5(1):19-50, 1976.

....error level by partitioning P . The pattern is cut in j pieces along each dimension, thus obtaining j pieces of size (m=j) m=j) pixels, in the 2D case. In each match with errors or less, one of those pieces must occur with at most b =j c errors. This type of method was rst used in [25, 29]. The ltering algorithm may now search for each of the j pieces with at most b =j c errors, and for each matching piece, verify if there is a complete match with at most errors. Since we search for j pieces with b =j c errors, the total search cost for the pieces is O(jIjj ....

R. L. Rivest. Partial-match retrieval algorithms. SIAM J. Comput., 5(1):19-50, 1976.

....by the successive symbols of w. By similar means, the trie implements insertions and deletions, so that it is a fully dynamic dictionary data type. In addition, tries eciently support set theoretic operations like union and intersection [27] as well as partial match queries or interval search [7, 23], and suitable adaptions make them a method of choice for complex text processing tasks [9, Ch. 7] These various applications justify to consider the trie structure as one of the central general purpose data structures of computer 1 science [9, 15, 17, 24] The cost of the main operations is ....

Rivest, R. L., Partial match retrieval algorithms, SIAM Journal on Computing 5 (1976) 19-50.

....possible queries into a single bucket. Each bucket remains associated with a subset of the attributes, but may now contain information about many maximal partial match queries. The essential feature of the bucket subsets is that each query subset be contained in at least one bucket subset. Rivest [122] remarks on a practical limitation, the large redundancy introduced by storing accession numbers many times. While this may be quite acceptable for small files, a very large difference in the sizes of records and their Combinatorial Designs in Communications 37 accession numbers would be required, ....

....is so large that we are unwilling to retrieve any record which may prove irrelevant to the query at hand. In the absence of such a prohibitive cost, however, we need only ensure that most of the records retrieved prove relevant; Rivest s scheme, which we explore next, has this property. Rivest [122] considers partial match queries of any size on a file with n binary attributes; a query specifies records which do possess certain properties, do not possess certain others, and may or may not possess the remainder. In this case, records are placed in buckets; however, here the buckets partition ....

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R.L. Rivest, Partial-match retrieval algorithms, SIAM Journal on Computing, 5 (1976), 19--50.

....of size N ) find the n tuples of objects o 1 ; o 2 ; Delta Delta Delta ; o n such that each object o i 2 c i is within r units from each of the other objects of the same n tuple. The type of queries that satisfy Definition 1 and the data structures to support them have been studied in [3, 5, 6, 13, 14]. The queries in Definition 2 are treated in [11] where the search is restricted to finding instances of two keywords separated by less than some fixed distance in a string of text. In this paper, we are interested in the last variant (i.e. Definition 3) Examples of some useful queries that have ....

Ronald L. Rivest. Partial-match retrieval algorithms. SIAM J. Comput, 5(1):19--50, March 1976.

....In addition to the applications described above, several other applications also benefit from a linear mapping that preserves locality: 1. In traditional databases, a multi attribute data space must be mapped into a one dimensional disk space to allow efficient handling of partial match queries [22]; in numerical analysis, large multidimensional arrays [6] have to be stored on disk, which is a linear structure. 2. In image compression, a family of methods use a linear mapping to transform an image into a bit string; subsequently, any standard compression method can be applied [18] A good ....

R. L. Rivest. Partial match retrieval algorithms. SIAM J. Comput, 5(1):19--50, March 1976. 35

....because there is no guarantee that the answer set to such a query is well distributed across disks. Several heuristic methods have been developed to decluster a Cartesian product file [32] which has been known as a multi attribute file structure effective for partial match and best match queries [40]. There are a few well known multidimensional declustering methods for Cartesian product files: Disk Modulo (DM) 14] Fieldwise Xor (FX) 30] Error Correcting Codes (ECC) 17] Hilbert Curve Allocation Method (HCAM) 16] and Vector based declustering method [7] Although ample analytic studies ....

R. L. Rivest. Partial match retrieval algorithms. SIAM Journal of Computing, 5(1):19--50, March 1976.

....by the successive symbols of w. By similar means, the trie implements insertions and deletions, so that it is a fully dynamic dictionary data type. In addition, tries eciently support set theoretic operations like union and intersection [16] as well as partial match queries or interval search [3, 12], and suitable adaptions make them a method of choice for complex text processing tasks [5, Ch. 7] These various applications justify to consider the trie structure as one of the central general purpose data structures of computer science [5, 6, 7, 13] The cost of the main operations is measured ....

Rivest, R. L., Partial match retrieval algorithms, SIAM Journal on Computing 5 (1976) 19-50

....case sensitivity, abbreviations or using the regular expression syntax . and to define a search key pattern. BB. d means return in sequence all keys starting with B in the first two positions, any symbol in the third or fourth position, d in the fifth and any number of any symbols to follow. Rivest [1976] and Bentley and Sedgewick [1997] for a detailed description and analysis. In the first example, keys containing both upper and lower case characters may have been stored in the Tree in the normal way. At query time all the keys matching a query key need to be found irrespective of case. A ....

Rivest, R. 1976. Partial-match retrieval algorithms. SIAM Journal on Computing 5, 1, 19--50.

....not allow modular operations (thereby precluding certain hashing functions) and the analysis used for the Grigoriev lower bound is not applicable for the case of finite domains such as the Hamming cube. A model which does capture hashing and more combinatorial settings is introduced in Rivest [43] and further developed in Dolev, Harari and Parnas [19] and Dolev, Harari, Linial, Nisan and Parnas [20] Rivest studies the all partial match problem and Dolev et al. study the all neighbor problem where for each problem all database points satisfying the query must be found. In this model, ....

....the general cell probe model imply time space tradeoffs for branching programs, one of the notoriously difficult problems in computational complexity. For the best lower bound on branching programs to date, and additional references, see Beame, Saks, and Thathachar [6] As mentioned above Rivest [43] analyses hashing based algorithms for partial match. See Bentley and Sedgewick [8] for a more recent historical account. Rivest conjectures that any O(nd) sized data structure would require Omega Gamma n 1 Gammas=d ) time to search, where s is the number of exposed coordinates. 6 Also as ....

R. Rivest. Partial-match retrieval algorithms. SIAM J. Comput., 5:19--50, 1976.

....a range query. In addition to the applications described above, several other applications also benefit from the mapping which preserves locality: 1. In traditional databases, a multi attribute space must be mapped into a one dimensional space to allow efficient handling of partial match queries [19]; in numerical analysis, large multidimensional arrays [5] have to be stored on disk, which is a linear structure. 2. In image compression, a family of methods use the mapping to transform the image into a bit string; subsequently, any standard compression method can be applied [15] A good ....

R.L. Rivest. Partial match retrieval algorithms. SIAM J. Comput, 5(1):19--50, March 1976.

....LM05118 from the National Library of Medicine. 1. INTRODUCTION Multidimensional searching is an important algorithmic concept in modern computer science. In particular, retrieval of multidimensional data found applications in the design of data base systems and graphics. Bentley [6] and Rivest [22] are founding fathers of multidimensional searching, namely digital M d trees and M d search trees. An early description of these structures can be found in volume three of Knuth s book [19] and a more detailed discussion is in the book of Mahmoud [20] Several applications of multidimensional ....

R. L. Rivest, Partial-Match Retrieval Algorithm, SIAM J. Computing, 5, 19-50, 1976.

....by Knuth (Knuth, 1973) Usually with Two Level SIC though, the number of disk accesses (and hence speed of matching) is related more to the actual number of records that match than to the total number of records. The above property is extremely desirable, and is not found with other techniques. Rivest (Rivest, 1976) looked at several approaches: hash coding methods and tree search algorithms. Performance was considered in terms of retrieving n k bit words that match a query specifying s bits, and it was found that the best these approaches could offer was a performance = O(n log(2 s k) CMM is capable of ....

Rivest R.L. (1976). Partial Match Retrieval Algorithms. SIAM J. Computing 5, 19-50.

....are widely used for storing and matching strings over a given alphabet. Applications include dictionary lookup for text processing [6, 7, 8, 14, 22] itemset lookup for mining association rules in retail transactions [1, 2] IP address lookup in network routers [26, 27] and partial match queries [13, 24]. There has been much work on reducing the storage requirement and the instruction count for tries for example [3, 5, 4, 6, 19, 20, 22] These algorithms, however, do not take the memory hierarchy into account. Given the depth of memory hierarchies on modern machines, good cache performance is ....

R. Rivest. Partial match retrieval algorithms. SIAM Journal on Computing, 5:19--50, 1976.

....hashing looks for an exact match of a key in the hash table, whereas the inclusion condition in Equation (1) must be satisfied in a signature file. Alternately, if we view a signature of m bits as a tuple of m 1 bit attributes, the retrieval of signatures is similar to partial match retrieval [8,14]. However, due to the large value of m, methods for allocating tuples to buckets in partial match retrieval are impractical for allocating signatures into partitions. To simplify our discussion and analysis, we assume that S i s and SQ are random bit vectors uniformly distributed in the range of ....

R.L. Rivest, "Partial-match retrieval algorithms," SIAM J. Computing , Vol. 5, No. 1, 1976, 19--50.

....and the Hilbert curve. The first two have been used before as distance preserving mappings for partial match retrieval. The hypothesis is that the proposed Hilbert curve yields a better distance preserving mapping, because it avoids long jumps between points. Among the different types of queries [16], we focus on range queries and nearest neighbor queries; based on them, we derive measures to quantify the goodness of a distance preserving mapping. The structure of the paper is as follows: Section 2 shows how these three space filling curves are recursively derived. Section 3 briefly ....

Rivest, R.L., "Partial Match Retrieval Algorithms," SIAM J. Comput, vol. 5, no. 1, pp. 19-50, March 1976.

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R. Rivest. Partial-match retrieval algorithms. SIAM J. Comput., 5:19--50, 1976.

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R. L. Rivest. Partial-match retrieval algorithms. SIAM J. Comput., 5(1):19-50, 1976.

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Ronald L. Rivest. Partial-match retrieval algorithms. SIAM J. Comput., 5(1):19--50, 1976.

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Rivest, R. L. Partial match retrieval algorithms. SIAM Journal on Computing 5 (

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R. L. Rivest. Partial-match retrieval algorithms. SIAM Journal on Computing, 5(1):19--50, March 1976.

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