GenBank及EMBL等基因序列資料庫，都是常被分子生物學家用來做同源相似關係的搜尋。因為存放於資料庫中的基因序列，每筆資料長度由數千到數百萬字元長不等，而且每年成長數量驚人，因此提供一個良好的資料結構支援索引，並且配合有效率的搜尋方法，已成為當務之急。基因序列是由四核

Genomic sequence databases, like GenBank, EMBL, are widely used by molecular biologists for homology searching. Because of the long length of each genomic sequence and the increase of the size of genomic sequence databases, the importance of efficient searching methods for fast queries grows. The DNA sequences are composed of four kinds of nucleotides, and these genomic sequences can be regarded as the text strings. However, there is no concept of words in a genomic sequence, which makes the search of the genomic sequence in the genomic database much difficult. Approximate String Matching (ASM) with k errors is considered for genomic sequences, where k errors would be caused by insertion, deletion, and replacement operations. Filtration of the DNA sequence is a widely adopted technique to reduce the number of the text areas (i.e., candidates) for further verification. In most of the filter methods, they first split the database sequence into q-grams. A sequence of grams (subpatterns) which match some part of the text will be passed as a candidate. The match problem of grams with the part of the text could be speed up by using the index structure for the exact match. Candidates will then be examined by dynamic programming to get the final result. However, in the previous methods for ASM, most of them considered the local order within each gram. Only the (k + s) h-samples filter considers the global order of the sequence of matched grams. Although the (k + s) h-samples filter keeps the global order of the sequence of the grams, it still has some disadvantages. First, to be a candidate in the (k + s) h-samples filter, the number of the ordered matched grams, s, is always fixed to 2 which results in low precision. Second, the (k + s) h-samples filter uses the query time to build the index for query patterns. In this thesis, we propose a new approximate string matching method, the hash trie filter, for efficiently searching in genomic databases. We build a hash trie in the pre-computing time for the genomic sequence stored in database. Although the size q of each split grams is also decided by the same formula used in the (k + s) h-samples filter, we have proposed a different way to find the ordered subpatterns in text T. Moreover, we reduce the number of candidates by pruning some unreasonable matched positions. Furthermore, unlike the (k + s) h-samples filter which always uses s = 2 to decide whether s matched subpatterns could be a candidate or not, our method will dynamically decide s, resulting in the increase of precision. The simulation results show that our hash trie filter outperforms the (k +s) h-samples filter in terms of the response time, the number of verified candidates, and the precision under different length of the query patterns and different error levels.

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Genomics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Query Types of Genomic Databases . . . . . . . . . . . . . . . . . . . 5
1.3 String Matching Methods . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.1 Indexing Methods for Exact Match . . . . . . . . . . . . . . . 8
1.3.2 Approximate String Match (ASM) . . . . . . . . . . . . . . . 9
1.4 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 20
2. A Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1 Linear Scan Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Index Structures for ASM . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Inverted Indices . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 The Suffix Tree . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.3 ASM Methods on Index Structures . . . . . . . . . . . . . . . 26
2.3 Filter Methods for ASM . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 The q-gram Filter . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.2 LET & SET Filters . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.3 The l-tuple Filter . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.4 The h-samples Filter . . . . . . . . . . . . . . . . . . . . . . . 31
2.3.5 The (k+s) h-samples Filter . . . . . . . . . . . . . . . . . . . 32
2.3.6 The Counting Filter . . . . . . . . . . . . . . . . . . . . . . . 33
ii
Page
3. A Hash Trie Filter Approach for ASM . . . . . . . . . . . . . . . . . 36
3.1 The Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 The Construction of a Hash Trie . . . . . . . . . . . . . . . . . . . . . 37
3.3 Query and Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3.1 Step 1: Deciding the Length q0 of a Subpattern . . . . . . . . 39
3.3.2 Step 2: Construct the Table PT for the Subpatterns . . . . . 45
3.3.3 Traversing the Hash Trie . . . . . . . . . . . . . . . . . . . . . 46
3.3.4 Step 3: The Pruning Step . . . . . . . . . . . . . . . . . . . . 48
3.3.5 Step 4: Finding the Ordered Subpatterns . . . . . . . . . . . . 51
3.3.6 Step 5: Verification with Dynamic Programming . . . . . . . . 59
4. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1 The Real DNA Sequences . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.1 Time for Constructing a Hash Trie . . . . . . . . . . . . . . . 63
4.2.2 Performance under Short Query Patterns . . . . . . . . . . . . 65
4.2.3 Performance under Long Query Patterns . . . . . . . . . . . . 66
4.2.4 Performance under Low Error Levels . . . . . . . . . . . . . . 71
4.2.5 Performance under High Error Levels . . . . . . . . . . . . . . 74
4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

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