### Table 2: The average maximal Max Clique per generation found in all generations.

"... In PAGE 6: ... For the FC family of graphs, hmcs(G) is independent of the max clique size and hnce(G) is independent of the number of cliques. We present the average of 20 runs for both the maximum found of the maximum clique per generation ( Table2 ) and the average of the maximum found clique cover per generation (Table 3). We averaged the maximum value found in order to be fair to RS, which is not likely to keep a good solution once found.... In PAGE 6: ...clq and fc16-8.clq should be equally di cult to solve, yet we see in Table2 that HC comes closer to the max clique for fc8-16.clq (found 7.... ..."

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### Table 4.6. Retention Statistics. g number of genes in cluster; r(G) retention rate of genes; P(1st) fraction of rst order paralogous genes; #pX number of plesiomorphic phylogenetic footprint cliques or PFCs, Tab. 4.5); r(X) retention rate of footprint cliques or PFCs; r(XjG) retention rate conditional on gene retention; r0 predicted conditional retention rate assuming stochastic resolution of genetic redundancy, lower bound on the rate PF loss due to non-structural reasons [95]. See text for details.

### Table 1 lists the linking strategies used. We started by disconnecting all the links between the participating nodes, that yields a minimum of ranking without collu- sion at all. After that, we returned to the normal situation. Then we added a central site that lists all the participat- ing sites, then a ring of all the sites in alphabetical order, and then an inverted ring. Finally, we also added a star and a clique. Figure 10 lists the resulting rankings under different strategies.

"... In PAGE 7: ...roup is 0.75. Note that this only takes into account the Pagerank value, while the quality of a site may come from very different factors. Table1 : Linking strategies. Strategy Average ranking Disconnect group 0.... ..."

### Table 3 gives the distribution of the number of T-frequent itemsets of size s for di erent values of s and T. The last row provides a heuristic estimate of the induced width w of the graphs of the model, using the maximum cardinality ordering d on all attributes. The largest clique in the trian- gulated graph of the retail data set mentions roughly half of all variables, while the same parameter for the Web data is only 10% of the number of all variables, despite the order of magnitude di erence between the corresponding thresholds T. Thus, even for queries on the retail data that mention only 6 to 8 variables, we can expect to get much more dense graphs in the maxent models and correspondingly higher online query times.

### Table 3. Clique Analysis

"... In PAGE 2: ... The degree to which intra- clique connectivity is larger than inter-clique connectivity is measured by the cohesion index (C-Idx). Table3 presents the clique structures of the two communities. Note that there are two cliques in the non- structured community, vs.... ..."

### Table 3 Comparison of orderings.

in Parallel Iterative Solution Of Sparse Linear Systems Using Orderings From Graph Coloring Heuristics

1990

"... In PAGE 6: ...Table3 , where (G) is the maximum degree of a node in G(A) and cl(G) is the largest apparent clique,2 or r-element, used in constructing G(A). For each problem, the numbers in the rst row are the number of iterations required for convergence, and the numbers is the second row give the number of levels in the dependence graph.... ..."

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### Table III shows the best values obtained in this work for degree less than or equal to 14 that improve previous values (see [23]). The method put forward in this paper enables one to improve many values for diameter 6 and degree D greater than 14, by means of the corresponding family of [l, l]-cliques. For instance, using d-graphs for degree D5q 1 1 (with q a prime power), this method gives graphs on order about

1992

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### Table 1: The effect of clique separators

2004

"... In PAGE 13: ...reprocessing rules. Such separators generate lots of small graphs that can be neglected anyway. We carried out three experiments on these instances: the effect of (i) clique separators, (ii) clique and almost clique separators, and (iii) clique and almost clique separators as well as separators of size three. For the first experiment, Table1 shows the results for those graphs that contain clique separators. The graphs not reported on do not contain clique separators.... In PAGE 14: ... Note that by each decomposition the total number of vertices (over all graphs) increases by at least one. Table1 shows that sometimes large components are decomposed from the rest of the graph; by that reducing the size of the largest component significantly. The computation times (in seconds) for this separation are very small.... ..."

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### Table 1: The effect of clique separators

2004

"... In PAGE 13: ...reprocessing rules. Such separators generate lots of small graphs that can be neglected anyway. We carried out three experiments on these instances: the effect of (i) clique separators, (ii) clique and almost clique separators, and (iii) clique and almost clique separators as well as separators of size three. For the first experiment, Table1 shows the results for those graphs that contain clique separators. The graphs not reported on do not contain clique separators.... In PAGE 14: ... Note that by each decomposition the total number of vertices (over all graphs) increases by at least one. Table1 shows that sometimes large components are decomposed from the rest of the graph; by that reducing the size of the largest component significantly. The computation times (in seconds) for this separation are very small.... ..."

Cited by 15

### Table 1: The effect of clique separators

2004

"... In PAGE 13: ...reprocessing rules. Such separators generate lots of small graphs that can be neglected anyway. We carried out three experiments on these instances: the effect of (i) clique separators, (ii) clique and almost clique separators, and (iii) clique and almost clique separators as well as separators of size three. For the first experiment, Table1 shows the results for those graphs that contain clique separators. The graphs not reported on do not contain clique separators.... In PAGE 14: ... Note that by each decomposition the total number of vertices (over all graphs) increases by at least one. Table1 shows that sometimes large components are decomposed from the rest of the graph; by that reducing the size of the largest component significantly. The computation times (in seconds) for this separation are very small.... ..."

Cited by 15