### Table 1: Distinct phase meshes

1999

"... In PAGE 12: ...Table 1: Distinct phase meshes The problems are constructed by taking a set of 2D amp; 3D meshes, some regular grids and some with irregular (or unstructured) adjacencies and geometrically bisecting them so that one half is assigned to phase 1 and the other half to phase 2. Table1 gives a summary of the mesh sizes and classification, where CEBD represents the number of type 1 vertices and similarly for CEBE. These are possibly the simplest form of two-phase problems that one could imagine and provide a demonstration of the need for multiphase mesh partitioning.... ..."

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### Table 1: Distinct phase meshes

1999

"... In PAGE 12: ...Table 1: Distinct phase meshes The problems are constructed by taking a set of 2D amp; 3D meshes, some regular grids and some with irregular (or unstructured) adjacencies and geometrically bisecting them so that one half is assigned to phase 1 and the other half to phase 2. Table1 gives a summary of the mesh sizes and classi cation, where a8a18a52 represents the number of type 1 vertices and similarly for a8a18a56 . These are possibly the simplest form of two-phase problems that one could imagine and provide a demonstration of the need for multiphase mesh partitioning.... ..."

Cited by 24

### Table 2: Distinct phase results

1999

"... In PAGE 12: ... The multiphase version of jos- tle, JOSTLE-M and the parallel multiphase version, PJOSTLE-M, incorporate the multiphase partitioning paradigm as described in this paper. The results in Table2 show for each mesh and value of a31 the proportion of cut edges, a16 a12 a72 a16 a83a87a16 a12a153a16 , (which gives an indication of the partition quality in terms of communication overhead) and the imbalance for the two phases, a157 a52 amp; a157 a56 respectively. These three quality metrics are then averaged for each partitioner and value of a31 .... In PAGE 14: ...a8a18a52 a8a20a56 a12 description 4elt 30269 15606 181614 2D triangular mesh t60k 60005 30570 360030 2D triangular mesh cs4 22499 4083 161574 3D tetrahedral mesh mesh100 103081 20596 742162 3D tetrahedral mesh Table 3: Node/element meshes Table 4 shows the partitioning results in the same form as Table2 . Interestingly, the single phase al- gorithm, JOSTLE-S, actually does a very good job for the 2D meshes, balancing both mesh elements and nodes well.... In PAGE 14: ...000 1.011 Table 4: Node/element results The multiphase results again bear out the trends seen in Table2 ; the multiphase partitioners balance both phases well with the parallel version, PJOSTLE-M achieving the best balances. Meanwhile the cut-weight is even closer to that attained by the single-phase algorithm and, respectively, the results of JOSTLE-M amp; PJOSTLE-M are just 8.... ..."

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### Table 2: Distinct phase results

1999

"... In PAGE 12: ... The multiphase version of jos- tle, JOSTLE-M and the parallel multiphase version, PJOSTLE-M, incorporate the multiphase partitioning paradigm as described in this paper. The results in Table2 show for each mesh and value of C8 the proportion of cut edges, CYBXCRCYBPCYBXCY, (which gives an indication of the partition quality in terms of communication overhead) and the imbalance for the two phases, ALBD amp; ALBE respectively. These three quality metrics are then averaged for each partitioner and value of C8.... In PAGE 14: ...CEBD CEBE BX description 4elt 30269 15606 181614 2D triangular mesh t60k 60005 30570 360030 2D triangular mesh cs4 22499 4083 161574 3D tetrahedral mesh mesh100 103081 20596 742162 3D tetrahedral mesh Table 3: Node/element meshes Table 4 shows the partitioning results in the same form as Table2 . Interestingly, the single phase al- gorithm, JOSTLE-S, actually does a very good job for the 2D meshes, balancing both mesh elements and nodes well.... In PAGE 14: ...000 1.011 Table 4: Node/element results The multiphase results again bear out the trends seen in Table2 ; the multiphase partitioners balance both phases well with the parallel version, PJOSTLE-M achieving the best balances. Meanwhile the cut-weight is even closer to that attained by the single-phase algorithm and, respectively, the results of JOSTLE-M amp; PJOSTLE-M are just 8.... ..."

Cited by 24

### Table 1 Distinct phase meshes

"... In PAGE 12: ...ultiphysics computational mechanics applications such as solidification, e.g. [1]. The problems are constructed by taking a set of 2D and 3D meshes, some regular grids and some with irregular (or unstructured) adjacencies and geometrically bisecting them so that one half is assigned to phase 1 and the other half to phase 2. Table1 gives a summary of the mesh sizes and classification, where V1 and V2 represent the number of type 1 and type 2 vertices, respectively, and E is the number of edges. These are possibly the simplest form of two-phase problems and provide a clear demonstration of the need for multiphase mesh partitioning.... ..."

### Table 3: Time for Reading Distinct Sections

1995

"... In PAGE 17: ...Figure 11: The Distinct Sections listed in Table3 (not to scale)... In PAGE 18: ... Finally,in row VIII, the sections haveoverlap in both dimensions and the Extended Two-Phase Method again performs better. Table3 compares the performance of the Extended Two-Phase Method and the Direct Method for reading distinct sections. Figure 11 shows approximately where these sections are located in the array.... In PAGE 19: ... Table 4 compares the performance of the Extended Two-Phase Method and the Direct Method for writing distinct sections. The sections chosen are the same as those for reading in Table3 , and are shown in Figure 11. We use the most general algorithm for writing in the Extended Two-Phase Method, which requires an extra read for each write.... ..."

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### Table 2: The number of distinct possible schedules for each jobmix, and the time to run at most 10 schedules during the sample phase.

2000

"... In PAGE 3: ... The number of cycles required to pro le 10 schedules given a timeslice of 5 million cycles varies according to the size of the jobmix, the multithread- ing level and the job replacement policy. So the number of cycles spent in the sample phase depends on the experiment and is given in Table2 . In the sample phase the jobsched- uler randomly permutes the sets of coscheduled jobs and records dynamic execution information to observehow the coschedules are performing.... In PAGE 7: ... Thus, we use the information gathered in the sample phase to predict the performance of 10 random schedules and then proceed to run each one to validate our guesses. Note that while there are only 10 possible sched- ules for Jsb(6,3,3), there are manymorefor other experi- ments (see Table2 )sothat10schedules is just a statistical sample of the performance space in most cases. Figure 3 con rms our nding that 10 random schedules of anygiven jobmix produced a substantial di erence between a best and a worst schedule and even between a best and an average schedule, and thus was su cient to identify a good schedule.... ..."

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### Table 2: The number of distinct possible schedules for each jobmix, and the time to run at most 10 schedules during the sample phase.

"... In PAGE 4: ... The number of cycles required to pro le 10 schedules given a timeslice of 5 million cycles varies according to the size of the jobmix, the multithreading level and the job replacement policy. So the number of cycles spent in the sample phase depends on the experiment and is given in Table2 . In the sample phase the jobscheduler randomly permutes the sets of coscheduled jobs and records dynamic execution information to observe how the coschedules are performing.... In PAGE 4: ... For Jsb(4,2,2) there are only 3 possible schedules. See Table2 . Schedules are represented... In PAGE 11: ... Thus, we use the information gathered in the sample phase to predict the performance of 10 random schedules and then proceed to run each one to validate our guesses. Note that while there are only 10 possible schedules for Jsb(6,3,3), there are many more for other experiments (see Table2 ) so that 10 schedules is just a statistical sample of the performance space in most cases. Figures 3 and 4 con rm our nding that 10 random schedules of any given jobmix produced a substantial di erence between a best and a worst schedule and even between a best and an average schedule, and thus was su cient to identify... ..."

### Table 4: Time for Writing Distinct Sections

1995

"... In PAGE 19: ...1 Performance We only consider the case where each processor writes a distinct section to the le, because it is unlikely that processors will want to write overlapping or common sections. Table4 compares the performance of the Extended Two-Phase Method and the Direct Method for writing distinct sections. The sections chosen are the same as those for reading in Table 3, and are shown in Figure 11.... ..."

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### Table 6. Counting the ambiguous predictions and the correct choices

2003

"... In PAGE 10: ...The first column of Table6 is the number of distinct text fragments Ti, as defined in section 3.1, for all pages in the testing corpus.... ..."

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