### Table 6: NMI scores of the algorithms on bi-partite graphs

"... In PAGE 9: ... 6.2 Results and Discussion Table6 shows the NMI scores of the nine algorithms on the bi-partite graphs. For the BP-b1 graph, all the algo- rithms provide perfect NMI score, since the graphs are gen- erated with very clear structures, which can be seen from the parameter matrix in Table 2.... ..."

### Table 4. NMI of Bipartite Graph Clustering

in Abstract

"... In PAGE 6: ...Table 4. NMI of Bipartite Graph Clustering Table4 summarizes the results for the bipartite graph clustering. Again, the results indicate that refinement leads to better clustering.... ..."

### Table 1 instead of the bipartite graphs to be readable.

"... In PAGE 6: ... Eight and sixteen I/O transfers are applied for the first and second cases respectively. In each case, there are three patterns of I/O transfers as shown in Table1 . The edge tk=ei,j in Table 1 means a data (tk) is going to be transferred between the processor number i and disk number j.... In PAGE 6: ... t10 = e 23, t11= e 34, t12=e 54, t13=e 65, t14=e 67, t15=e 76, t16=e 87 16 8 6 t1=e 11, t2=e 22, t3=e 33, t4=e 44, t5=e 55, t6=e 66, t7=e 12, t8=e 21, t9=e 23, t10= e 34,t11= e 43, t12= e 54, t13= e 65, t14 = e75, t15= e73, t16= e 84 16 8 4 t1= e11, t2= e22, t3= e33, t4= e44, t5= e21, t6= e12, t7= e53, t8= e84, t9= e31, t10= e52, t11= e63, t12= e74, t13= e41, t14= e62, t15= e73, t16= e84 16 8 2 t1= e11, t2= e12, t3= e21, t4= e42, t5= e31, t6= e33, t7= e41, t8= e42, t9= e51, t10= e52, t11= e61, t12= e62, t13= e71, t14= e72, t15= e81, t16= e82 Table1 : No.... ..."

### Table 4: Graph Theoretic Methods Method Approach References Graph Partitioning Algorithms [13, 98, 279, 278]

"... In PAGE 12: ... The measures c and g are discussed in Section 10. 6 Graph Theoretic Approaches Graph theoretic approaches, listed in Table4 , structure the cell formation problem in the form of networks, bipartite graphs, etc. Rajagopalan and Batra were among the rst to apply a purely graph theoretic approach to the cell formation problem in which the nodes represent the machines and the arcs indicate the similarity among the machines.... ..."

### Table 1: Results for bipartite graphs with |Vi| vertices per bipartition and |E| edges.

2003

"... In PAGE 10: ...158 Graphbase [11] that were used in the experiments of Mutzel [13, 14]2. The results of our experiments are shown alongside the results of Mutzel [14] in Table1 . Each row in the table corresponds to the average values from applying the algorithm to 100 different graphs3.... In PAGE 10: ... It is, however, meaningful to compare the shapes of the |E| versus running time graphs. In the first 17 rows of Table1 , we see that the FPT implementation is quite efficient up to |E| = 55, finding exact solutions to all input graphs. After |E| = 55, the FPT implementation is able to obtain exact solutions to only a few input graphs for the maximum time of 600 seconds (10 minutes) per graph.... In PAGE 10: ... 2We note that Theorem1 does not require the input graph G to be bipartite; consequently, our implementation is not limited to bipartite graphs. 3The graphs for the experiments corresponding to the first 17 rows of Table1 can be repro- duced using the Stanford Graphbase [11]. We first generate 1700 random integers beginning with seed 5841.... ..."

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### Table 4: Parameters and distributions for synthetic tri-partite graphs

"... In PAGE 8: ... The synthetic tri-partite graphs are generated similarly to the bi-partite graphs. The distributions and parameters are documented in Table4 . Let V1 denote the central type nodes.... In PAGE 8: ... Let V1 denote the central type nodes. In Table4 , S(12) denotes the true means of distri- butions for generating the links between V1 and V2, and similarly for S(13). The numbers of clusters for each type of nodes are given by dimensions of S(12) and S(13) and each cluster has 100 nodes.... In PAGE 8: ... The numbers of clusters for each type of nodes are given by dimensions of S(12) and S(13) and each cluster has 100 nodes. In Table4 , TP-large is a large graph with 20 clusters of V1, 20 clusters of V2, and 18 clusters of V3 (due to the space limit, the details of parameters are omit-... ..."

### Table 2: Comparing partitioning results of uni-directional bipartitioning

1998

"... In PAGE 8: ...used to solve the scheduling problem and has the advantage of yielding much smaller net cuts. Table2 compares the number of uni-directional cut nets of bipartitioning by FBP-m #28when k = 2#29 with that of list scheduling. The number of levels in each of the two stages is set to be d depth 2 e and #0B is set to be w#28V #29 2 with #065#25 variation.... In PAGE 8: ... It is observed that our algorithm consistently achieved larger improvement on the larger circuits. Table2 also shows the CPU time for FBP- m. Since incremental #0Dow computation is employed, FBP-m is very e#0Ecient.... ..."

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### Table 5.1: Size of bi-partitioned SBDDs.

Cited by 1

### Table 3: Comparison of OPAS1 Heuristics for Bipartite Join Graphs

1995

"... In PAGE 14: ... given join graph size (i.e. jV j), the performance gain of the COH heuristic over the FPH heuristic decreases as the edge ratio increases. Table 2: Comparison of OPAS1 Heuristics for General Join Graphs jV j Edge Ratio B(FPH) B(COH) B(FPH) - B(COH) (pages) (%) (pages) (pages) (pages) 5 396:7 341:6 55:1 10 443:8 403:5 40:3 15 461:1 430:2 30:9 500 20 471:5 446:2 25:2 25 477:6 455:9 21:6 30 481:9 463:5 18:4 5 883:0 801:2 81:8 10 938:9 883:8 55:1 15 958:4 918:8 39:6 1000 20 968:4 937:0 31:4 25 975:4 948:8 26:6 30 980:2 958:2 22:0 5 1872:8 1760:7 112:2 10 1933:2 1866:6 66:7 15 1955:7 1906:9 48:8 2000 20 1966:4 1929:2 37:2 25 1974:0 1943:2 30:8 30 1978:9 1953:1 25:8 The results for bipartite join graphs are shown in Table3 for cases when (a) jV1j = jV2j and (b) jV1j lt; jV2j. For both cases, the COH heuristic outperforms the FPH heuristic with the performance margin increasing with the edge ratio.... ..."

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