### Table 1: Results on random geometric problems

2001

"... In PAGE 25: ... Ten problems of each size were generated. Table1 shows that the cutting plane algorithm was typically able to solve these problems to within about 2% of optimality. The rows in the table give the number of problems solved exactly with the cutting plane algorithm, the average nal gap for the cutting plane code, the average runtime in seconds for the cutting plane code, the average number of cuts added, the average number of outer iterations, and the average number of interior point iterations.... ..."

### Table 1 Combinatorial optimization problems and their geometric equivalents

"... In PAGE 10: ... Similarly, if we color the graph with a minimum number of colors, then this is equivalent with dividing the collection of lines into a minimum number of subcollections such that each subcollection contains no parallel pairs of lines. Table1 gives an overview of problems in graph theory and their geometric equivalent. Since in this paper we focus on parallel line grouping, we propose two combi- natorial algorithms that can be used to partition a graph of parallel pairs into subgraphs which are or which resemble cliques.... ..."

### Table 3: Geometric means of the comparative results of LANCELOT

"... In PAGE 15: ... Problems CHENHARK (number 3), JNLBRNG1 (number 5) and JNLBRNGB (number 8) are more favorable to the nonmonotone strategy, whereas the opposite happens to problems NCVXBQP2 (number 10), OBSTCLAL (number 14) and OBSTCLBU (number 17), for which the monotone algorithm performs better. In Figures 2 and 3 we can visualize the comparative results between the nonmonotone algorithm and the combination that performed best for LANCELOT according to Table3 , namely, using preconditioned conjugate gra- dient and computing the exact Cauchy point (PCGEX). We plot the loga- rithms, to the base 10, of the ratios between the results of the nonmonotone algorithm and LANCELOT, analyzing, in Figure 2, the number of iterations performed, and, in Figure 3, the CPU time spent.... ..."

### 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.... ..."

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### Table 1: Performance Guarantees for Geometric Intersection Graph Problems. (The parameter k can be any fixed integer 1.)

"... In PAGE 18: ... For the sake of simplicity, we assume that the BOW-specification is 1-near-consistent. Given a maximization problem in Table1 11, our approxi- mation algorithm takes time O(N T (Nl+1)) to achieve a performance guarantee of ( l l+1) F BEST . Here, l is a constant that depends only on the performance guarantee parameter , T (Nl+1) denotes the running time of a heuristic which can process flat specifications of size O(Nl+1) and which has a performance guarantee F BEST .... ..."

### Table 6. Results for Weighted Sums with Geometric Problems

2006

"... In PAGE 6: ... 10, and tightness = 0.18. These were fairly easy for most, but not all, heuristics, with greater relative differences than those found with the homogeneous random problems. Nonethess, synergies could be readily obtained ( Table6 ). Thus, the effects generalise to at least some structured problems.... ..."

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### Table 1. Mapping to geometric solutions.

2006

"... In PAGE 5: ... This provides a framework in which to handle these problems in a clean and uniform way by considering their geometric meaning. Table1 shows a number of distributed systems problems and their mapping to geometric techniques. Note that there are geometric solutions that do not correspond immediately to networking problems.... ..."

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### Table 1: Geometric Calibration Algorithm Breakdown

1996

"... In PAGE 65: ... The dataset volumes for the period after launch may be different and they are NOT DEFINED at this time. Table1 0: Volume estimates of the datasets used for in-flight creation of PP and ROI (reported size/unit) Dataset Estimates kbytes CGM (single camera 73 (parameters) x 4 (byte/parameters) = 292 add 1% 0.3 DID (single file 10 x 10 degree, 3 sec.... In PAGE 66: ... Figure 8 shows IGC related data to be exchanged between these two facilities. Table1 1: Development period: Volume estimates of the datasets to be used for in-flight creation of PP and ROI: A) total required to store, B) required to be on-line Input data Total On-line Number of units Mbytes (add 100%) Min Max Number of units Mbytes Number of units Mbytes CGM 9 0.0054 9 0.... In PAGE 68: ... The assumption is that PP and ROI are required only for the land portion of Earth surface (30%) and surrounding water (20%). Table1 2: Estimate of IGC data I exchange rate. GCP MISR imagery Nav.... In PAGE 69: ...4 IGC PROCESSING LOAD ESTIMATES This will be estimated at the beginning of 1997 once version 1 of the IGC software is completed. Table1 3: Estimate of IGC data II exchange rate. Orbit paths MISR imagery Nav.... In PAGE 69: ...5 Gbyte / 150 days = 6.1 Gbyte/day Table1 4: Estimate of GCD (PP, ROI, CGM) exchange rate. PP ROI CGM Rate 233 orbit paths x 72727 line/orbit x 1504 pixel/line x 4 byte/pixel = 102 Gbyte x 9 cameras = 1835.... ..."

### Table 4. Distribution of Geometric Constraints.

2004

"... In PAGE 16: ... We assume that all intersections are generic, as is usual in degrees of freedom analysis. In Table4 we list the di erent options for distribution of constraints. Note that we do not consider all possible distributions of the dimensions, but only those which have a simple geometric meaning.... In PAGE 16: ...eft can also be distributed to the distance parameter, i.e. the xed positions set the value of the distance. Constraints requiring positions to lie on a surface or curve are omitted from Table4 . Surfaces and curves are usually described by a combination of po-... In PAGE 17: ... Algorithm 2 is the overall constraint distribution algorithm. A constraint can be distributed directly if one of the distribution options in Table4 can be applied using the previous reasoning without doing any redistribution (step I). Otherwise, starting at the constraint which should be distributed, we do a breadth- rst search of the constraint graph until a constraint is found which can be redistributed (steps II and III are initialization; step IV does the search).... ..."

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### Table 11: Random Geometric Problems (IBM 590, seconds)

1999

"... In PAGE 13: ...10 2927.3 To give an indication of the growth in running time for Blossom IV as the problem size increases, we present in Table11 results for our code over a range of random geometric instances. In these instances, the Delaunay graph was computed using the \triangle quot; code of Shewchuk [60].... ..."

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