### Table 1. Effect of tiling on fork-join overhead Original parallelism Parallelism after tiling Fork-join overhead [S, P] [S, S, P] increased

"... In PAGE 6: ...Five different scenarios may occur after tiling a doubly nested loop, depend- ing on the parallelism. We list these cases in Table1 . S indicates that the corre- sponding loop is serial; P indicates the loop is parallel.... In PAGE 6: ... (If there are more than two loops, the change in fork-join overhead can be determined by similar anal- ysis.) For example, in the first and second rows of Table1 , the original outer loop is serial and the original inner loop is parallel. Per Section 4, after tiling, the cross-strip loop is serial (in Row 1) or parallel (in Row 2), which results in an increase or decrease of fork-join overhead.... ..."

### Table 1. Scalability of the fork-join parallelization on a 2-way Quad Clovertown system (eight cores total).

2007

"... In PAGE 6: ... Scalability of the fork-join parallelization on a 2-way Quad Clovertown system (eight cores total). Table1 shows the scalability limits of the panel factorization and how this a ects the scalability of the whole operation for the Cholesky, LU and QR fac- torizations respectively on an 2-way quad-core Clovertown system (eight cores total) using the MKL-9.1 parallel BLAS library.... ..."

Cited by 2

### Table 1. Scalability of the fork-join parallelization on a 2-way Quad Clovertown system (eight cores total).

2007

"... In PAGE 5: ... Scalability of the fork-join parallelization on a 2-way Quad Clovertown system (eight cores total). Table1 shows the scalability limits of the panel factorization and how this affects the scalability of the whole operation for the Cholesky, LU and QR fac- torizations respectively on an 2-way quad-core Clovertown system (eight cores total) using the MKL-9.1 parallel BLAS library.... ..."

Cited by 2

### Table 1. Scalability of the fork-join parallelization on a 8-way dual Opteron system (sixteen cores total).

2007

"... In PAGE 5: ...perations (i.e. the panel factorizations) interleaved to parallel ones (i.e., the trailing submatrix updates). Table1 shows the scalability limits of the panel factorization and how this affects the scalability of the whole QR factorization on an 8-way dual-core AMD Opteron system with MKL-9.... ..."

Cited by 4

### Table 2. Operations (read, write, partition) for our parallel hash join algorithm.

"... In PAGE 5: ... Now, the relation S is read from the main memory (or in the worst case, from the main memories distributed in the system), and for each tuple, the hash tables are probed respectively. Table2 summarizes the before process, we have assigned a fundamental operation (read or write) or a partition operation. Assuming that data are in memory, the total time for the algorithm can be expressed as the sum of the time for READ operation (three times), the time for WRITE operation (two times), and the time for partitioning operation (two times).... ..."

### Table 1: The open rcham of the open-join-calculus

"... In PAGE 9: ... We also let S j P abbreviate the open solution D `S A; P , for all processes P and open solutions D `S A obtained from S by -conversion such that fv[P ] \ dv[D] S. The chemical rules for the open rcham are given in Table1 ; they de ne families of transitions between open solutions *, ), ?!, and ?! where ranges over labels of the form Sxhe vi and xhe vi. By convention, each chem- ical rule mentions only the processes and de nitions that are involved in the transition, and the transition applies to every chemical solution S that contains them.... In PAGE 19: ...1 The j-open rcham The j-open rcham is de ned in Table 2 as a replacement for the intrusion rule. In contrast with the rule Int of Table1 , the new rule Int-J permits the intrusion of messages only if these messages are immediately used to trigger a process. This is formalized by allowing labels M0 that are parallel compositions of messages.... ..."

### Table 2: Execution time of PAR JOIN with respect to P, N and Rmax (unit : sec)

"... In PAGE 4: ... The similar results are shown also in [5], where the join step is proportional to the size of the largest bucket. Table2 shows the execution time of the parallel al- gorithm PAR JOIN versus the number of PE apos;s as the number of tuples and Rmax change. Table 3 shows the execution time of the parallel algorithm PAR JOIN P.... ..."

### Table 3: M/M/1 parallel queues with many servers

"... In PAGE 6: ...ork-join queues is very slow. Therefore, figures 3 and 4 only show results up to 25 disks. To show how these results compare as the number of queues gets very large, tables are presented for the cases when there are 40 and 50 parallel queues. Table3 shows mean response times for the M/M/1 fork-join queue described above with arrival rate 1 and service rate 1.1.... ..."