### Table 1. Comparison of results between grids with and without diagonals. New results

1994

"... In PAGE 2: ... For two-dimensional n n meshes without diagonals 1-1 problems have been studied for more than twenty years. The so far fastest solutions for 1-1 problems and for h-h problems with small h 9 are summarized in Table1 . In that table we also present our new results on grids with diagonals and compare them with those for grids without diagonals.... ..."

Cited by 11

### Table 1: Evaluation of the performance of the algorithm. A set of pairwise registrations is shown. Each row represents one registered pair of scans. The second column displays the number of line pairs. Column Pre shows the % (over all possible pairs) of line pairs that need to be considered after the preprocessing step of the algorithm. Column S2 shows the % (over all possible combinations) and total number of pairs that reach STAGE 2 and column S3 the same number for STAGE 3, the most expensive stage (in S3 the reduction is computed over all possible pairs of matches ((l1, r1) and (l2, r2))). The efficiency of our algorithm is due to the great reduction of the pairs that need to be considered in this stage. Column M presents the number of matched pairs that the algorithm establishes. The running Time t of the algorithm (in secs) is shown for every pair (2GHz Intel machine). Finally, the pairwise registration Error Err is displayed. This Error is the average distance between matched planar region between the two scans. The error ranges from 1.36mm to 14.96mm for the first data set and from 5.34mm to 56.08mm for the second. Note that the application of the well-known Iterative Closest Point algorithm will improve the results even further.

2003

"... In PAGE 5: ...hown in Fig. 5. Note the registration accuracy. Table1 pro- vides an extensive evaluation of the efficiency and accuracy of our algorithm. The efficiency of the algorithm is demon- strated by the percentage of line pairs that survive after pre- processing, and reach STAGE 2, and STAGE 3 of the algo- rithm.... In PAGE 6: ...details on the performance of pairwise registrations see Table1 .... ..."

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### Table 8: Closest Pair Given a set of line segments in the plane, the line intersection problem is the problem of determining all intersections of line segments in this set. For the rst four problems, algorithms running in O(n log(n)) time were implemented for the rst execu- tion. The second execution, using certi cation trails, runs in linear time. The rst execution algorithm used for line intersection runs in (O((k + n) log(n)) time where k is the number of intersections and n the num- ber of points. The second execution runs in O(k + n) time. Note that k may be quadratic in n.

1993

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### Table 2: Resolution times of the graph coloring problem.

2004

"... In PAGE 10: ...18 1.08 Table2 : Results for the rst method. 1 2 3 Q2 4 Q1 Q3 Q4 1 0 5 4 8 9 10 11 7 6 2 3 15 14 13 12 Figure 11: Literal nodes of 4-queens.... In PAGE 24: ... Problem class: BIBDs modelled as binary matrices. GAP-SBDD GAP-LEX Double Lex GAP-Lex no prop Combined V B R K 3 3 3 3 3 7 7 3 3 1 3 470 3 1150 3 20 21 1389 3 1150 6 10 5 3 2 4 869 29 80100 5 30 29 80100 4 50340 7 14 6 3 2 13 502625 - - 30 110 - - - - 9 12 4 3 1 12 451012 - - 30 120 - - - - 11 11 5 5 2 11 68910 - - 20 140 - - - - 8 14 7 4 3 14 219945 - - 143 720 - - - - - gt; 2 hours 3 Number of Backtracks Total runtime in ms Table2 : Table comparing various symmetry breaking methods. Partial GAP-LEX is where GAP-LEX checks do not commence until after the 1st backtrack.... In PAGE 24: ... Partial GAP-LEX is where GAP-LEX checks do not commence until after the 1st backtrack.GAP-SBDS GAP-SBDD Instance 3 2 4 3 2 4 K3 P2 9 290 110 400 22 310 180 490 K4 P2 165 1140 3590 4730 496 3449 8670 12110 K5 P2 4390 35520 166149 201669 17977 174180 501580 675760 GAP-LEX Partial GAP-LEX Instance 3 2 4 3 2 4 K3 P2 10 160 100 260 12 150 130 280 K4 P2 184 1550 4020 5570 202 670 4980 5650 K5 P2 4722 47870 176200 224070 5024 18820 224310 243130 3 Number of Backtracks 2 Gap Time in ms 4 Eclipse time in ms Total runtime in ms The results for this class of problems ( Table2 ) are more encouraging. We see that, in contrast to BIBDs, GAPLex provides fewer backtracks but performs faster than GAP-SBDD.... In PAGE 39: ... 8 sec. Table2 : Comparison over GraphBase directed graphs. All solutions 5 min.... In PAGE 47: ... None Full Sibl. None Restarted no no no yes yes yes Table2 : Overview of the different algorithm variants: Full refers to the variant where we call for ancestor and sibling- based ltering at every search node. Sibling refers to breaking value symmetry only by performing just sibling-based lter- ing.... In PAGE 47: ... In case of the restarted method, the branching variable is chosen according to a min-domain heuristic over a random subset of 20% of the variables. Table2 summarizes the settings and names the different contestants that we let compete against one another. All experiments in this paper were conducted on a 2 GHz AMD Athlon 64 Processor 3000+ CPU with 512 MByte main memory running Linux 2.... In PAGE 62: ... We present in Table 1. and Table2 . results for var- ious graceful graph problems.... In PAGE 63: ...4 0 1986 139.4 Table2 : Results for computing one solution for graceful graphs Graph No sym break SBDS dynamic lex BT sec. BT sec.... ..."

### Table 2. Search Efficiency on Random and -Colour Problems with Weighted Degree Heuristics

"... In PAGE 7: ...) 4 Search Efficiency with Weighted Degree Strategies The ordinary weighted degree procedure was tested in combination with either max for- ward degree or min dom/fwddeg. Table2 gives results, using the same sets of problems as the results shown in Table 1. When reference heuristics are elaborated by incorporat- ing the results of sampling from wipeouts, there is consistent improvement in average search effort.... ..."

### Table 1. Search Efficiency on Random and -Colour Problems with Selected Heuristics

"... In PAGE 6: ...Selected results for various heuristics are shown in Table1 . These heuristics were chosen because of their association with one or the other of the two basic forms of heuristic action: buildup of contention and simplification of the future part of the prob- lem [8].... In PAGE 7: ...) 4 Search Efficiency with Weighted Degree Strategies The ordinary weighted degree procedure was tested in combination with either max for- ward degree or min dom/fwddeg. Table 2 gives results, using the same sets of problems as the results shown in Table1 . When reference heuristics are elaborated by incorporat- ing the results of sampling from wipeouts, there is consistent improvement in average search effort.... In PAGE 13: ... For colouring problems, simplification heuristics perform poorly, and this is undoubtedly related to the limited domain reduction (hence, the limited simplification) that occurs with these problems. For the present analysis, heuristics based on constraint weighting were added to the set of standard heuristics shown in Table1 . The most important results were, (1) dom/wdeg and weighted degree behaved similarly to their foundation heuristics, so they are most highly correlated with the contention and simplification factors, respec-... ..."

### Table 2 The performance of the coloring heuristics. Heuristic Problem Number of colors

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

1990

"... In PAGE 4: ... The rst experiment shows the performance of the coloring heuristics on LAP5 and LAP9 for which an optimal coloring is known. The results in Table2 show that both algorithms produce optimal or slightly suboptimal colorings but the IDO heuristic is slightly superior. In the second set of experiments, the performance of the coloring heuristics is compared with three other ordering algorithms: minimum degree, reverse Cuthill- McKee (RCM), and nested dissection.... ..."

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### Table 13 - Efficient Set of Genetic Algorithm Parameters Parameter Values/Utilize?

"... In PAGE 8: ... 8 (the paths shown are the best point from each generation). The set of parameters listed in Table13 produced these paths, and was used for all other genetic algorithm runs in this project. Problem 1, Comparison of Methods For this problem, both the polytope and the genetic algorithm worked well.... In PAGE 8: ... Each of the polytope runs is described in Table 15. Genetic Algorithm Solution The genetic algorithm was used with the parameters described in Table13 . Each run converged to the same solution, which was better than any solution found by the polytope routine.... ..."

### Table 2: Comparison of precision and efficiency between the randomized inter-procedural, randomized intra- procedural, and deterministic inter-procedural analyses on SPEC benchmarks.

2004

"... In PAGE 18: ... This is in fact the setup that we used for the experiments described below that compare the precision and cost (in terms of time) of the randomized inter-procedural analysis with that of randomized intra-procedural analysis and deterministic inter-procedural analysis. The first set of columns in Table2 show the results of the inter-procedural randomized analysis for a few benchmarks with more than 1000 lines of code each. The column head- ings are explained in the caption.... In PAGE 18: ... The noteworthy point here is the number of relationships found between the input variables of a procedure. In the second set of columns in Table2 we show how many fewer relationships of each kind are found by the intra- procedural randomized analysis, and how much faster that analysis is, when compared to the inter-procedural one. The intra-procedural analysis obviously misses all of the input re- lationships and consequently misses some internal relation- ships as well, but it is much faster.... In PAGE 18: ... tation based algorithm with an inter-procedural determin- istic algorithm. We have implemented and experimented with the SRH algorithm [20], and the results are shown in the third set of columns in Table2 . SRH is less precise than our algorithm, in that it searches only for equalities with constants (x = c).... ..."

### Table 1. Efficiency comparison

2005

"... In PAGE 11: ...tion schemes, implemented according to their original descriptions. Table1 sum- marises the number of relevant basic operations underlying several identity-based signcryption and signature schemes, namely, GT exponentiations, scalar point multiplications, and pairing evaluations, and compares the observed processing times (in milliseconds) for a supersingular curve of embedding degree k = 6 over F397, using implementations written in C++ and run on an Athlon XP 2 GHz. Subtleties in the algorithms determine somewhat different running times even when the operation counts for those algorithms are equal.... ..."

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