### Table 1: Join Example

1984

"... In PAGE 11: ... The same example will be used throughout this section in order to illustrate the approach and performance of the various join algorithms. Consider Table1 . There are 12 distinct values in the underlying domain of the join columns of the two relations R1 and... In PAGE 12: ... These values are labeled A through L. Table1 shows the tuple count for each value and each relation. Notice, for example, that value G occurs 10 times in R1 and 2 times in R2.... In PAGE 12: ...) For simplicity, we shall assume that there are no predicates involved in this join. Table1 also shows the tuple count for each value in the joined relation R1 1 R2. Notice that the values G and B occur 20 and 0 times, respectively.... In PAGE 12: ... (The rst two summands provide a simple measure of work done on input, while the last summand provides a measure of work done on output.) Thus TIMEG = 10 + 2 + 10 2 = 32, while TIMEB = 0 + 1 + 0 1 = 1, as is indicated in Table1 . (Ordering the values by this measure of work, we will call G the largest skew value in this example, and B the smallest.... In PAGE 13: ... A similar statement holds for R2. Our example gives an indication of just how serious the data skew problem is for joins: Notice from Table1 that the join phase work associated with value G is more than a quarter of the total amount of join phase work. Given P = 4 processors, e ective load balancing will not be easy.... In PAGE 32: ...(1). For illustrative purposes, suppose the total number of processors available to execute the pipeline in Table1 is 20. It can be seen that the allocation hnii= (4, 4, 4, 4, 4) leads to max8i WBi ni = 1.... ..."

Cited by 49

### Table 2.1: Complexity of Join Ordering Problems JNLC In P for ASI cost functions. (A consequence of the result for problem JNLA.) JNLS In P for ASI cost functions. (A consequence of the result for problem JNLA.) JNLA In P for ASI cost functions [IK84, KBZ86]. JNLG NP-complete for a (complex) cost function for a special nested-loop join [IK84]. Later, the problem has been proven NP-hard even for the simple cost function Cout [CM95]. JNBC Unknown complexity.

### Table 5. Temporal join of the PROBLEMLIST and DRUGS tables restricted to problems lasting longer than two weeks and whose onset occurs before each drug regimen.

### Table 1. Related streams / tables Table 2. The join stream

"... In PAGE 2: ... The join stream Essentially, this query performs a join on all related data and the joined result is the training set used to build the classifier. Table1 shows a snapshot of such data. The join relationship is indicated by the arrows connecting the join attributes.... In PAGE 2: ... The problem we are addressing in this paper is to build the classifier based on such a join stream, referred to as the join stream classification problem hereinafter. Note static tables are also allowed (as in Table1 ) in the same classification problem by considering them as streams that never change. For join stream classification, the classifier must be updated each time any stream window is updated.... In PAGE 2: ...oin operations, i.e. the join operations are expensive. Yet the classifier must evolve quickly each time the window slides forward, thus there may be no time to perform the join [20][6][23]. Furthermore, the join relationship can be many-to-many as shown in the sample data in Table1 , therefore, there are far more tuples in the join stream than in the input streams. Any method that explicitly generates the join stream will suffer from the blow- up of data arrival rates and is unlikely to be able to keep pace with the incoming data.... ..."

### Table 9. Solving of various problems using the DynVar3 strategy with various depths. (join size: 20% except for uuf75-073: 30%, mos: 10%).

### Table 1: Possible Nesting Orders for Join Evaluation

1993

"... In PAGE 3: ... As the combinatorial explosion makes exhaustive enumeration of all possible solutions infeasible (cf. Table1 ) and the NP-hard characteristic of the problem implies that there (presumably) cannot exist a faster algorithm, we have to rely on heuristics that compute approximative results. 2.... ..."

Cited by 24

### Table A.5 show the number of positions explored and number of joined positions per round for problem sizes 5, 6, and 7, respectively. Table A.6 and Table A.7 show request rates and standard deviations of work queue operations for problem sizes 5 and 6, respec- tively; the data from these tables was used to derive the data in Table 4.5.

1995

### Table A.5 show the number of positions explored and number of joined positions per round for problem sizes 5, 6, and 7, respectively. Table A.6 and Table A.7 show request rates and standard deviations of work queue operations for problem sizes 5 and 6, respec- tively; the data from these tables was used to derive the data in Table 4.5.

1995