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Table 2: A summary of linear matroid algorithms for the matroid intersection problem. The quantities n and r respectively denote the number of columns and rows of the given matrix.

in Algebraic Algorithms for Matching and Matroid Problems
by Nicholas J. A. Harvey
"... In PAGE 3: ... The quantities n and r respectively denote the number of elements and rank of the matroid; they are analogous to the quantities n and r mentioned in Table 2. Table2 and Table 3 provide a brief summary of the existing algorithms for matroid intersection. It should be noted that the Gabow-Xu algorithm achieves the running time of O(nr1:62) via use of the O(n2:38) matrix multiplication algorithm of Coppersmith and Winograd [10].... ..."

Table 6: Numbers of matroids, base-orderable matroids, strongly base-orderable matroids and transversal matroids.

in unknown title
by unknown authors 2008
"... In PAGE 18: ... Determining whether a matroid is base-orderable or strongly base-orderable is straightforward, and we implemented the algorithm given by Brualdi amp; Dinolt [3] for testing transversality. Table6 gives these numbers where each cell of the table contains four numbers which, reading from top to bottom are the total number of matroids and the number of base- orderable, strongly base-orderable and transversal matroids respectively. For the omitted ranks (ranks 0, 1, 7, 8 and 9) all the matroids in the catalogue are transversal.... ..."

Table 1: All matroids on up to 9 elements

in unknown title
by unknown authors 2008
"... In PAGE 8: ... Therefore Xk+1 contains exactly one matroid isomorphic to M. 5 Results We implemented the algorithm described in the previous section, and the resulting numbers of matroids constructed are summarized in Table1 (the totals form sequence A055545 in... ..."

Table 1. Intersection timing (points vs. triangles).

in Ray Tracing Point Sampled Geometry
by Gernot Schaufler, Henrik Wann Jensen 2000
"... In PAGE 5: ...024x1024 with 4 samples per pixel in approx. 4 hours. To test the speed of our point intersection code we compared it with triangles in a number of simple test scenes: one containing the bunny and one containing the Buddha appearing in the video. Table1 shows the resulting timings. The points code has not yet been optimized, and it can be observed from the table that our optimized triangle intersection code is approximately 3-4 times faster.... ..."
Cited by 20

Table 2. The numbers of small 3-connected matroids representable over small elds (generated all as unlabeled represented matroids).

in Equivalence-Free Exhaustive Generation of Matroid Representations
by Petr Hlineny 2004
"... In PAGE 17: ... The last two lines exhibit a somehow di erent behavior, probably related to the existence of many inequivalent repre- sentations of matroids over larger elds. Note the di erence between the numbers of generated matroids in Table2 , and here in the last two lines of Table 4 where the GF (q)-representable matroids for q = 4, resp. q = 4; 5; 7, are not excluded.... In PAGE 17: ... The author also thanks Geo Whittle for helpful ideas and comments in early stages of Macek development. The large-scale computations leading to the enumeration data summarized in Table2 have been run (in 2003{2004) on the minos cluster at the West Bohemia University (The ITI center, supported by the Ministry of Education of the Czech Republic as the project LN00A056).... ..."

Table 4: Simple paving matroids on up to 9 elements

in unknown title
by unknown authors 2008
"... In PAGE 11: ...Welsh [14] asked whether most matroids are paving matroids. Examining the catalogue of 9-element matroids and tabulating the results in Table4 we see that 71.71% of the simple matroids on 9 elements are paving matroids, compared to 49.... ..."

Table 4: SIMD intersection performance for real- world scenes. Again, our new algorithm is signif- icantly faster than the Schwarze method, but com- putes the same correct results.

in Fast and Accurate Ray-Voxel Intersection Techniques for Iso-Surface Ray Tracing
by Gerd Marmitt, Andreas Kleer, Ingo Wald, Heiko Friedrich 2004
Cited by 11

Table 1. The numbers of labeled = unlabeled represented matroids over small elds.

in Equivalence-Free Exhaustive Generation of Matroid Representations
by Petr Hlineny 2004
"... In PAGE 4: ... (For example, these two notions are identical over binary matroids.) Table1 presents, for an illustration, the num- bers of labeled and unlabeled represented matroids isomorphic to selected small matroids over several elds. (The numbers have been computed with Macek [4], using its representability-testing feature.... ..."

Table 3: Sparse graph concepts and analogs in matroids and rigidity.

in unknown title
by unknown authors 1992
"... In PAGE 7: ... While the de nitions in this section are made for families of sparse graphs, they can be interpreted in terms of matroids and rigidity theory. Table3 relates the concepts in this section to matroids and generic rigidity, and can be skipped by readers who are not familiar with these elds. Fundamental hypergraphs.... ..."
Cited by 2

Table 3: Simple and cosimple matroids on up to 9 elements

in unknown title
by unknown authors 2008
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