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200 9.2 Related String Problems The most contributory substring problem is related to two other well known string problems: the Greatest (or Longest) Common Substring Problem and the All Maximal Repeats Problem (AMRP). However it is distinct from each of these. While the Greatest Common Substring Problem identifies the longest substring common across all strings in a set, the Most Contributory Substring Problem identifies the string that contributes the greatest number of characters to the set of strings. One important distinction between these two problems is that there is no guarantee that the most contributory substring will occur in every string in the set while the greatest common substring problem guarantees that the substring identified is a substring of every string in the set. The greatest common substring problem also ignores multiple occurrences of the same substring within each string in the set while the Most Contributory Substring Problem counts all occurrences of the substring. A variation on the Greatest Common Substring Problem has also been presented that identifies the longest common substring to k strings in a set [56]. This problem is also distinct from the Most Contributory Substring Problem because it fails to consider the value of multiple occurrences of a substring within one string in the input set. The All Maximal Repeats Problem is concerned with finding a substring that occurs twice within a single larger string such that the characters to the immediate left and right of the first occurrence of the string are distinct from the character to the immediate left and right of the second occurrence. This is distinct from the Most Contributory Substring Problem which is intended to be applied to a set of strings. The AMRP is also concerned only with finding a substring that occurs twice while the most contributory substring may occur many times. 9.3 Suffix Trees A substring w of a string s is defined to be a sequence of characters w 0 ...w n such that s i = w 0 , s i+1 = w 1 , ...s i+n = w n for some integer i. Equivalently, a substring w of a string s can be defined as a string for which there exist strings (possibly empty) p and q such that s = pwq. A suffix, w of a string s is defined to be a non empty string meeting the constraint s = pw for some (possibly empty) string p. Let L represent the set of m strings under consideration. A specific string within the set will be denoted as L i such that 0 ≤ i < m. Let Σ 0 ...Σ m−1 represent the
201 alphabet employed by each of the m strings in L. The alphabet used across all strings is constructed as Σ 0 ∪ ... ∪ Σ m−1 and will be denoted by Σ. A generalized suffix tree is a tree data structure that can be constructed from a collection of strings. An equivalent tree can be constructed for a single string that is the concatenation of all of the original strings in the set, provided that a special sentinel character is placed after each original string. Each sentinel character must be unique and must not occur anywhere else in any string. The set of sentinel characters will be denoted as S. The examples used in the remainder of this document will use the punctuation marks # and $ to denote the sentinel characters. The symbol s will be used to represent the string generated by concatenating the strings in L with a distinct sentinel character between each string. Several suffix tree construction algorithms have been developed which are linear in both time and space [119, 78, 112, 113]. Assuming that the string ends in a sentinel character, the following properties hold for a suffix tree: 1. The tree contains n leaves where each leaf corresponds to one of the n suffixes of a string of length n. The number of interior nodes in the tree is bounded by n guaranteeing that the total number of nodes in the tree is O(n). 2. Each branch in the tree is labeled with one or more characters from the string. The label is represented by two integers which specify the starting and ending position as indices in the concatenated string. Collecting the characters as one traverses from the root of the tree to a leaf will give one of the suffixes of the string. 3. The first character on each branch leaving a node is distinct. As a result, no node has more than |Σ| + |S| children. 4. Each non-leaf node has a minimum of two children. 5. The string depth of a node is defined to be the total length of all the labels on the branches that form a path from the root of the tree to the node. Because a branch may be labeled with a string of more than 1 character in length, the string depth of a node will always be greater than or equal to the depth of a node. Figure 9.1 shows a suffix tree constructed for the strings ababab and abab after they have been merged into a single, sentinel character delimited string, ababab$abab#. The suffix generated by traversing the tree is shown in each leaf node.
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OPTIMIZING THE JAVA VIRTUAL MACHINE
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Abstract Since its public introduct
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Acknowledgments While my name is th
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2.4.4 Direct Threading . . . . . .
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7.2 An Overview of Multicodes . . .
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List of Figures 2.1 Core Virtual Ma
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7.11 201 compress Performance by Mu
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B.1 The Steps Followed to Evaluate
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6.1 Most Frequently Occurring Const
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1 Chapter 1 Introduction When Moore
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3 Studies were conducted that consi
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5 Chapter 2 An Overview of Java Thi
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7 Addressing this need led to the d
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9 performs garbage collection, a cl
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11 also has the ability to contain
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13 ... i − 1 iload 0x04 dstore 0x
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15 ... aload 3 iconst 2 faload ...
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17 Condition Equal Unequal Greater
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19 transfered to the start of a new
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21 piled into machine language inst
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23 Figure 2.6: Interpreter Engine C
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25 Figure 2.8: Interpreter Engine C
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27 The following section examines t
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29 execute (JMethod * method, Slot
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31 codelets shown in this example a
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33 3.1 Instruction Set Design The a
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35 is replaced with a new opcode if
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37 method. However, the Java Virtua
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39 3.2.5 Bytecode Optimization Tool
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41 each bytecode executed as was ac
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43 executing the application. The a
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45 Chapter 4 Despecialization The J
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47 ... i − 1 iload 3 iload 0x04 i
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49 purpose bytecodes. The notation,
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51 is present in the constant pool
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53 ... iload 3 iflt ... i − 1 i i
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55 the stack challenging in some ca
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Figure 4.7: Despecialization of Bra
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59 Specialized Bytecode load store
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61 tual machine (RVM). Version 2.3.
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63 Test Total Weighted Condition Pe
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69 4.2.6 Performance Summary Compar
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71 Category Original Desp. Percent
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73 the maximum value encountered af
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75 • Efficient support of new lan
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77 difference in the performance of
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79 JGF RayTracer: A 150 by 150 pixe
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81 # Average % of Specialized Despe
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83 provided by only two vendors. IB
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Figure 5.1: Average Performance Res
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87 Figure 5.4: Performance Results
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89 Figure 5.8: Performance Results
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91 ences in background processes, m
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93 difference in performance due to
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95 when a pure interpreter virtual
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97 It is observed that many of the
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99 Within this category, it was als
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101 machine code for the idioms. As
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103 were performed was less than 0.
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105 these despecializations in a me
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107 Chapter 6 Operand Profiling Cha
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109 the applications. In addition,
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111 The aload 0 bytecode was the mo
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113 function being integrated. Beca
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115 Implementing alignment rules un
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117 these data types in the list of
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Figure 6.3: Distribution of Local V
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121 are never executed by any of th
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123 load and store bytecodes. It is
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125 the time because the index bein
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127 6.2.5 Fields Only four bytecode
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129 Figure 6.8: Data types Accessed
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131 lar, the new set of specialized
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133 multicode block is defined to b
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135 Figure 7.1: Two Bytecodes and t
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137 because of the presence of the
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139 cache performance. As a result,
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141 Block 1: Block 2: aload 0 → g
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143 Sequence Count Score getfield a
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Figure 7.3: Iterative Multicode Ide
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147 number of bytecodes that will b
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Page 173 and 174: 155 Figure 7.7: Number of Unique Ca
Page 175 and 176: Figure 7.9: Cumulative Multicode Bl
Page 177 and 178: 159 However, while considering long
Page 179 and 180: 161 Figure 7.10: 201 compress Perfo
Page 181 and 182: 163 Figure 7.14: Length 209 db Perf
Page 183 and 184: 165 Figure 7.18: 222 mpegaudio Perf
Page 185 and 186: 167 7.6.2 Overall Performance Acros
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Page 189 and 190: 171 // iload_1: stack[sp+1] = local
Page 191 and 192: 173 // iload_1: // iconst_1: // iad
Page 193 and 194: 175 Such bytecodes have a variable
Page 195 and 196: 177 ∆ x1 /x 2 /x 3 /.../x n→ an
Page 197 and 198: 179 Popping any values left on the
Page 199 and 200: 181 7.9 Conclusion This chapter has
Page 201 and 202: 183 ated will differ from that occu
Page 203 and 204: 185 Figure 8.1: A Comparison of the
Page 205 and 206: 187 performed impacts the sequences
Page 207 and 208: 189 Figure 8.2: 201 compress Perfor
Page 209 and 210: 191 Figure 8.5: 213 javac Performan
Page 211 and 212: 193 Compared to the complete despec
Page 213 and 214: 195 Figure 8.10: 209 db Performance
Page 215 and 216: 197 performing multicode substituti
Page 217: 199 Chapter 9 An Efficient Multicod
Page 221 and 222: 9.4 An Algorithm for the Most Contr
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Page 225 and 226: 207 Algorithm NonOverlappingScore(n
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Page 229 and 230: 211 this algorithm did not consider
Page 231 and 232: 213 exceptions if the value being c
Page 233 and 234: 215 Figure 10.1: Multicode Blocks u
Page 235 and 236: 217 approximately 30 percent of the
Page 237 and 238: 219 a strategy other than direct th
Page 239 and 240: 221 10.2.6 Combining Multicodes and
Page 241 and 242: 223 10.2.9 Expanding the Class File
Page 243 and 244: 225 revealed that none of the const
Page 245 and 246: 227 based on these profile results
Page 247 and 248: 229 stitution were performed. It co
Page 249 and 250: 231 [13] B. Alpern, C. R. Attanasio
Page 251 and 252: 233 [33] K. Casey, D. Gregg, M. A.
Page 253 and 254: 235 [55] D. Gregg and J. Waldron. P
Page 255 and 256: 237 [78] E. M. McCreight. A space-e
Page 257 and 258: 239 [100] L. A. Smith, J. M. Bull,
Page 259 and 260: 241 [120] T. A. Welch. A technique
Page 261 and 262: 243 # Len Score Multicode % 1 30 10
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251 # Len Score Multicode % 1 10 10
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253 Table A.5 continued: # Len Scor
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259 the level of entropy within the
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261 there are no pointers to these
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263 information for each method so
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265 to emit four files that were su
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Figure B.1: The Steps Followed to E
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269 B.7 Summary This Chapter has de
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271 Selected Honors and Awards Cont
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273 Departmental and University Pre
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