### 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.... ..."

Cited by 4

### Table 1: A summary of algorithms for the non-bipartite matching problem. The quan- tities n and m respectively denote the number of vertices and edges in the graph.

"... In PAGE 1: ...1 Matching algorithms The literature for non-bipartite matching algorithms is quite lengthy. Table1 provides a brief summary; further discussion can be found in [48, x24.4].... ..."

### Table 1: Summary of results for 1000 points 6 Analysis of Results on Matchings One of the most striking results in our experimental work is the fact that the maximum cardinality matching gave perfect, or near perfect, matchings in all the cases. While this is not surprising for serpentine triangulations (whose duals admit a hamiltonian path, as pointed our earlier), it is unexpected for the Delaunay and HVP-triangulations. However, we are able to explain this phenomenon. We show that the number of leftover triangles in a maximum cardinality matching of the dual graph of any triangulation of a point set depends only on the number of convex hull vertices. For randomly generated point sets in a disc or square, this number is relatively small [13]. In fact, the number of unmatched nodes in a maximum cardinality matching of the dual graph of a triangulation of a point set cannot exceed a third of the number of convex hull vertices. We prove this bound below.

"... In PAGE 14: ... The experiments conducted support this intuition. As the data in Table1 clearly shows, Delaunay triangulations consistently give the best results in terms of element quality. In particular, the maximum weighted matching algorithm run on the Delaunay triangulation dual has the best overall output with 99% of the triangles matched, 98% of the resulting quadrangles convex, mean maximum angle of 2.... ..."

### Table 4: Maximum Cardinality Search-Minimal for instances

2004

"... In PAGE 17: ... Here, the annex +MC denotes that a chordal minimization algorithm [6] is run afterwards. In Table4 we compare the values and computation times of the MCS-M heuristic for the original graphs, the graphs preprocessed by the graph reduction rules, and the graphs decomposed by safe separators. Moreover, we report on the lower bound provided by the graph reduction rules [10] and the one that results from the safe separator decomposition, as already listed in the previous tables.... ..."

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### Table 4: Maximum Cardinality Search-Minimal for instances

2004

"... In PAGE 17: ... Here, the annex +MC denotes that a chordal minimization algorithm [6] is run afterwards. In Table4 we compare the values and computation times of the MCS-M heuristic for the original graphs, the graphs preprocessed by the graph reduction rules, and the graphs decomposed by safe separators. Moreover, we report on the lower bound provided by the graph reduction rules [10] and the one that results from the safe separator decomposition, as already listed in the previous tables.... ..."

Cited by 15

### Table 4: Maximum Cardinality Search-Minimal for instances

2004

"... In PAGE 17: ... Here, the annex +MC denotes that a chordal minimization algorithm [6] is run afterwards. In Table4 we compare the values and computation times of the MCS-M heuristic for the original graphs, the graphs preprocessed by the graph reduction rules, and the graphs decomposed by safe separators. Moreover, we report on the lower bound provided by the graph reduction rules [10] and the one that results from the safe separator decomposition, as already listed in the previous tables.... ..."

Cited by 15

### Table 4: Maximum Cardinality Search-Minimal for instances

2004

Cited by 15

### Table 2: Graph sequence information and running time [sec.]. The last two columns show average incremental lay- out time for one graph. Total running times for the CPU only and GPU accelerated variant of the algorithm are shown.

"... In PAGE 6: ... Our algorithm was implemented using C++, Cg and OpenGL. Table2 gives information about the graph se- quences and running times. As can be seen in the table, our GPU implementation provides a signi cant speedup of up to 8 compared to the CPU.... ..."

### 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 3 Parallel algorithms for maximum matchings in particular graphs Families of graphs Authors Time Processors Year

"... In PAGE 115: ...Table3 : Performance Evaluation of four partitioning algorithms with respect to the satis ability of criteria (i){(iv) and minimization of local communication time. (iv) (i) (ii) (iii) Splitting of Algorithm Load Balance Interfaces Connectivity subdomains P Q Perfect Very good Small Most of the time 1 Q Perfect Poor Small Always CM-Clust Perfect Poor Large Always Hybrid Good Very good Small Sometimes machines.... ..."