### Table 17: Run time on random inputs using integer keys (version 1 code) given in Tables 19 and 20. The sum of the run time for parts (b) and (d) of the experiment is graphed in Figure 15 for random data and in Figure 16 for ordered data. The graph of Figure 17 shows only one line MIX for AVL, RB-T, RB-B, WB, and BBST while that of Figure 18 shows MIX for AVL, RB-T, RB-B, and WB as the times for these are very close. With integer keys and random data, unbalanced binary search trees (BSTs) outperformed each of the remaining structures. The next best performance was exhibited by bottom-up red-black trees. They did marginally better than AVL trees. The remaining structures have a noticeably inferior structure. For ordered integer keys, BSTs take more time than we were willing to expend. Of the remaining structures, treaps generally performed best on parts (a), (c), and (e) while BBSTs did best on parts (b) and (d). 50

"... In PAGE 47: ... In fact, BBSTs perform about twice as many rotations as AVL trees. The average run times for the random data tests are given in Table17 and in Table 18 for the ordered data test. Both of these use integer keys.... ..."

Cited by 1

### Table 17: Run time on random inputs using integer keys (version 1 code) given in Tables 19 and 20. The sum of the run time for parts (b) and (d) of the experiment is graphed in Figure 15 for random data and in Figure 16 for ordered data. The graph of Figure 17 shows only one line MIX for AVL, RB-T, RB-B, WB, and BBST while that of Figure 18 shows MIX for AVL, RB-T, RB-B, and WB as the times for these are very close. With integer keys and random data, unbalanced binary search trees (BSTs) outperformed each of the remaining structures. The next best performance was exhibited by bottom-up red-black trees. They did marginally better than AVL trees. The remaining structures have a noticeably inferior structure. For ordered integer keys, BSTs take more time than we were willing to expend. Of the remaining structures, treaps generally performed best on parts (a), (c), and (e) while BBSTs did best on parts (b) and (d). 50

"... In PAGE 47: ... In fact, BBSTs perform about twice as many rotations as AVL trees. The average run times for the random data tests are given in Table17 and in Table 18 for the ordered data test. Both of these use integer keys.... ..."

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### Table 19: Run time on random real inputs (version 1 code) With real keys and random data, BSTs did not outperform the remaining structures. Now, the ve balanced binary tree structure became quite competitive with respect to the search operations (i.e., parts (b) and (d)). RB-B generally outperformed the other structures on parts (a), (c), and (e). Using ordered real keys, the treap was the clear winner on parts (a), (c), and (e) while BBSTs handily outperformed the remaining structures on parts (b) and (d). Some of the experimental results using version 2 of the code are shown in Tables 21{ 24. On the comparison measure, with random data (Table 21), skip lists performed best on part (a). Of the deterministic methods, BBSTs slightly outperformed the others on part (a). On parts (b) { (e), AVL, RB-T, RB-B, WB, and BBSTs were quite competitive and 52

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### Table 19: Run time on random real inputs (version 1 code) With real keys and random data, BSTs did not outperform the remaining structures. Now, the ve balanced binary tree structure became quite competitive with respect to the search operations (i.e., parts (b) and (d)). RB-B generally outperformed the other structures on parts (a), (c), and (e). Using ordered real keys, the treap was the clear winner on parts (a), (c), and (e) while BBSTs handily outperformed the remaining structures on parts (b) and (d). Some of the experimental results using version 2 of the code are shown in Tables 21{ 24. On the comparison measure, with random data (Table 21), skip lists performed best on part (a). Of the deterministic methods, BBSTs slightly outperformed the others on part (a). On parts (b) { (e), AVL, RB-T, RB-B, WB, and BBSTs were quite competitive and 52

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### Table 3: Binary search tree

"... In PAGE 17: ... Table3 shows that if the elements are inserted in ascending order, the constructed tree is in fact a linear list where the element representing the minimum is at the root and the maximum at the end. The method getMax() is called twice in the postcondition, once to get the maximum of the old tree and once to get the maximum of the tree after inserting the new element.... ..."

### Table III. Type inference of Binary Search Trees

### Table 2: Subject programs used in the experiments program size ncnb Jtest JCrasher

2004

"... In PAGE 7: ... The BinarySearchTree and LinkedList classes are data structures from a textbook [34]. The first three columns of Table2 show the class name, the number of public method, and the number of non-comment, non-blank lines of code for each subject respectively. We use two third-party test-generation tools: Jtest [26] and JCrasher [9] to automatically generate test inputs for program sub- jects.... In PAGE 7: ... JCrasher generates tests with the length of calling sequences as one. The last four columns of Table2 show the number of Jtest-generated tests, their exercised method executions, JCrasher-generated tests, and their exercised method executions re- spectively. 5.... ..."

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### Table 3 Time to search and retrieve 1000 keys in Chambers dictionary

"... In PAGE 5: ... This is because the keys in the dictionary are stored in alphabetical order, and consequently there are many runs of 1- bits in the sets. Table3 shows the time it took to search for and retrieve 1000 randomly selected keys for the different methods. The time is measured in CPU seconds on a VAX 6630.... In PAGE 6: ... The cost of searching for a key is (k+1)Ci, and Ci , the cost of intersecting two sets, quickly reduces after each intersection as the number of matching indexes is reduced. The results in Table3 show that a cross- indexed data structure using a 512-way bitmap tree is nearly 4 times slower than a binary search of a sorted list. However, insertion is much faster, requiring just two bit operations.... In PAGE 6: ... This compares with 1.3 Mbytes shown in Table3 required to store the cross-index using partitioned lists of indexes. Cross-indexing also supports anagram searching.... ..."

### Table 1: Methods for orthogonal range search.

"... In PAGE 2: ... This data structure allows them to answer range queries fast. In Table1 the computational complexity of various such approaches is summarized. In detail, for ap- plications of very high dimensionality, data structures like the Multidimensional Binary Tree [22], and Bentley and Maurer [7] seem more suitable.... ..."