### Table 3. Searched nodes

2001

"... In PAGE 12: ...pplied jointly with a domain ltering procedure (e.g. AC) and an accurate vari- able ordering heuristic, has been considered an expensive approach that almost always slows down the search, even when it saves a few constraint checks 5. Table3 gives the results for the number of searched nodes, for each instance and for the di erent con gurations. It is plain from the results that CB and CBJ in general need to search more nodes to nd a solution than the other algorithms.... ..."

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### Table 3. Searched nodes

"... In PAGE 11: ...hen applied jointly with a domain filtering procedure (e.g. MAC) and an accu- rate variable ordering heuristic, has been considered an expensive approach that almost always slows down the search, even if it saves a few constraint checks 6. Table3 gives the results for the number of searched nodes, for each instance and for the different configurations. It is plain from the results that MAC-CB and MAC-CBJ in general need to search more nodes to find a solution.... ..."

### Table 1. The Number of Searched Nodes the Minimum Tree

### Table 1: Percentages of nodes searched.

1997

"... In PAGE 8: ...Table 1: Percentages of nodes searched. Table1 shows the result of the experiment by displaying the percentage of nodes searched with the program using the new pruning method compared to the same program without the pruning. The total savings are shown both as a percentage of nodes searched in total, as well as the average percent saving over all the positions.... ..."

Cited by 1

### Table 1. Results with Repeated dom/wtdg Total Search Nodes

2006

"... In PAGE 4: ... (Since nodes, constraint checks, and runtime were all highly correlated in these experiments, for brevity, results will be reported in terms of nodes.) Summary results for the tests of dom/wtdg with restart are given in Table1 . The table shows means for total nodes over the 100 (soluble) problems for each condition.... In PAGE 4: ... In addition, the anal- ysis of variance (ANOVA) showed no statistically signifi- cant differences for either the cutoff or restarts factors. This means that differences among the means in Table1 are not evidence of reliable differences between conditions. Table 1.... ..."

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### Table 8: Search nodes required by our backtrack algorithm on ICCS graphs.

1998

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### Table 8: Search nodes required by our backtrack algorithm on ICCS graphs.

1998

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### Table 5. Repeated Random Variable Selection: Final Run (Search Nodes)

2006

"... In PAGE 5: ...For comparisons of means in Table5 , a second ANOVA was done with only the Restarts and Cutoff factors, using the means for the ten tests for each problem and condition. Again, the restarts factor was highly significant statistically (F(2, 891) = 8.... ..."

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### Table 2. Results For Unsatisfiable Embedded Problems Average Total Search Nodes

"... In PAGE 9: ... In the first set, ehi-85-297, each problem contains 297 variables (85 in the original sat problems), in the second set, ehi-90-315, each problem contains 315 variables (90 in the original sat problems). The last problem set reported in Table2 is a set of 100 composed random prob- lems, consisting of a main under-constrained component in the form lt;n,d,m,t gt; where n is the number of variables, d the uniform domain size, m the graph density of the component and t the constraint tightness, and k satellite components also in this form attached to the main component by links lt;m,t gt;. For the problem set reported, each problem had main component lt;100,10,0.... ..."

### Table 3: Reduction of nodes by the search enhancements.

2003

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