### Table 1: Memory for k-way partitioning

2002

"... In PAGE 4: ... Instead of giving a detailed analysis, we give an impression of the memory explosion reporting some numbers derived by the k-way partitioning approach of METIS [12, 13], a state-of-the-art partitioning algorithm. In Table1 the memory needed for k-way par- titioning and for recursive bi-partitioning using benchmark ibm06 from ISPD98 [1] is given for growing k. As can easily be seen, if k gets larger these approaches cannot be used any longer.... ..."

Cited by 2

### Table 1: Various graphs used in evaluating the parallel multilevel k-way graph partitioning al- gorithm.

1998

"... In PAGE 11: ... However, due to the k-way refinement performed in the uncoarsening phase, the final partitions are only slightly worse than those produced by the serial k-way algorithm (that uses the multilevel recursive bisection al- gorithm for computing initial partitions). Partition Quality Table 2 shows the quality of the partitions produced by the parallel k-way al- gorithm as well as the amount of time it took to produce these partitions on a Cray T3D for the problems of Table1 . Partitions for in 16, 32, 64, and 128 parts are shown, each produced on 16, 32, 64, and 128 processors, respectively.... ..."

Cited by 333

### Table 1: Various graphs used in evaluating the parallel multilevel k-way graph partitioning algorithm.

1997

Cited by 25

### Table 1: Various graphs used in evaluating the parallel multilevel k-way graph partitioning algorithm.

1997

Cited by 25

### Table 1: Various graphs used in evaluating the parallel multilevel k-way graph partitioning algorithm.

1997

Cited by 25

### Table 1. Memory for k-way partitioning a9 a9

2002

"... In PAGE 2: ... Instead of giving a detailed analysis, we give an impression of the memory explosion reporting some numbers derived by the a9 -way partitioning approach of METIS [13, 14], a state-of-the-art partitioning algorithm. In Table1 the mem- ory needed for a9 -way partitioning and for recursive bi- partitioning using benchmark ibm06 from ISPD98 [1] is given for growing a9 . As can easily be seen, if a9 gets larger these approaches cannot be used any longer.... ..."

Cited by 2

### Table 2: Finding all graceful labelings of the graph in Figure 2, with k-way branching or binary branching with different value orderings.

2005

"... In PAGE 3: ... This suggests that the reduction in search is mainly due to the symmetry con- straints: any propagation due to the other constraints would not be restricted to the largest and smallest value in the do- main. Table2 shows the results of solving this problem with dif- ferent variable and value orders. As well as lexicographic and reverse lexicographic variable order, we use the orders that we found to be respectively best and worst, when assigning the values in increasing order [Sturdy, 2003].... In PAGE 3: ... (Hence, when the variables are assigned in reverse lexicographic order, decreasing order for all variables is best.) Table2 shows that the heuristic is at least as good as the bet- ter of increasing or decreasing order in all cases, and this was true for the other variable orders that we tried. The heuristic was derived empirically by trying increasing or decreasing order for each variable, with a range of variable orders.... ..."

Cited by 3

### Table 2: The performance of the parallel multilevel k-way partitioning algorithm on Cray T3D. For each graph, the performance is shown for 16-, 32-, 64-, and 128-way partitions on 16, 32, 64, and 128 processors, respectively. The times are in seconds.

1998

"... In PAGE 11: ... However, due to the k-way refinement performed in the uncoarsening phase, the final partitions are only slightly worse than those produced by the serial k-way algorithm (that uses the multilevel recursive bisection al- gorithm for computing initial partitions). Partition Quality Table2 shows the quality of the partitions produced by the parallel k-way al- gorithm as well as the amount of time it took to produce these partitions on a Cray T3D for the problems of Table 1. Partitions for in 16, 32, 64, and 128 parts are shown, each produced on 16, 32, 64, and 128 processors, respectively.... In PAGE 13: ...Parallel Runtime From Table2 we can see that the run time of the parallel algorithm is very small. For 9 out of the 12 graphs, the parallel algorithm requires less than one second to produce an 128-way partition on 128 processors.... In PAGE 15: ... For each graph, the speedup on 16, 32, 64, and 128 processors is shown. Effects of Initial Graph Distribution The experiments shown in Table2 were performed by ini- tially distributing the graphs to the processors in a block distribution. That is as the graphs were read from the file, consecutive n/p vertices were assigned to each processor.... ..."

Cited by 333

### Table 5 Branch-and-Price Results on k-way Equipartition for Microaggregation Prob- lems for S = 4

"... In PAGE 16: ... An example of the solution on this kind of data is shown in Figure 2. Table5 shows the results for graphs with S = 4, graph size n ranging from 40 to 100. The table is divided into three parts to represent the performance of the heuristic algorithm, the root node of the branch-and-price-and-cut algorithm, and the branch-and-price tree.... ..."