### Table I Dilation 2 embedding Of 2 12 mesh in An 4-rotator graph

### Table 2 Recognition results from graph matching for the first experiment not using the rotational fitness function

in Inexact

2007

"... In PAGE 9: ...1. Table2 shows the results of recognizing the graphs when the rotational fitness function was not used. By applying the rotational fitness function, an accuracy of 99.... ..."

### Table 1 Recognition results from graph matching for the first experiment using the rotational fitness function

in Inexact

2007

"... In PAGE 9: ... The test graph in each suit was tried twice and the best match between the trials was selected. The best results from the experiments are shown in Table1 . The best results were achieved with a crossover rate of 0.... ..."

### Table 3: Times and number of rotations required to determine if the Kneser graph K(n; k) and bipartite Kneser graph H(n; k) are Hamiltonian

"... In PAGE 7: ... To accomplish this we wrote a flle containing the partial path along with some key graph information every half hour. We have summarized the running times and number of rotation oper- ations needed in Table3 . Note that the times shown here include (i) the time to test hamiltonicity of K(n; k), (ii) the time to take a checkpoint... ..."

Cited by 1

### Table 4 is robust with respect to . The convergence gets even better for increasing con- vection. The coarse graphs show a rotating structure re ecting the rotating convection.

### Table 1: Transition Matrix for One Year Rotational Rules (probabilities in %).

1996

"... In PAGE 7: ...g. see Table1 ). A probabilistic state transition graph can be used to depict the same data in graphical format, with the thickness of the arcs corresponding to the state transition probability.... In PAGE 7: ....3.1 One Year Rotational Rules The transition matrix for one-year rotation rules (ie. given the crop in year Y ? 1, predict the crop in year Y ) which was extracted is shown in Table1 . The same data is presented in the probabilistic state transition graph shown in Figure 1, which nicely illustrates the likely transitions.... ..."

Cited by 2

### Table 4: Performance of Algo 1 for the 29 nodes-35 arcs graph

"... In PAGE 13: ... Even the gap between the initial lower bound and the optimum (computed as Opt?LB Opt ) does not give a good prediction of problem di culty: the largest gap in rotation 28 is closed after 111 nodes, while smaller gaps (for example in rotation 3, 7 or 9) are closed only after a larger number of nodes. Similar results can be obtained for the 29 nodes - 35 arcs obtained from the previous graph by removing, for example, arcs 8 and 18 (In Table4 the computational results for the rst 15 rotations are reported ). The order strength of the resulting graph is now approximately 0.... ..."

### Table 2: Computation times obtained with different methods for rotation of a discrete tool for different resolutions (averaged times for various rotation angles). 8x8x8 16x16x16 32x32x32 64x64x64

"... In PAGE 7: ...In order to reduce aliasing, we compute the value of a rotated voxel from a trilinear interpolation of its 8 neighbours in the original image. Much better results are obtained (figure 5b) to the price of slightly higher computation times (On average, +25% for the brute force rotation, +5% for the optimised rotation as reported on Table2 ). As for graph1, we can see on graph 2 that the computation times depend on angle of rotation.... ..."

### Table 1: Summary of the results of Hogsted, Carter, and Ferrante execution time tP with P processors, and we state that P tP = Ia + Tseq; where Tseq is the sequential time, that is, the sum of all tile weights (see Figure 3). We describe the tiled iteration space as a task graph G = (V; E), where vertices represent the tiles and edges represent dependencies between tiles. A handy view of the graph is obtained by \rotating quot; the iteration space so that rtile = 0. Dependencies between tiles are now summarized

1997

"... In PAGE 6: ... More- over, no communication cost is paid between a tile and its top neighbor, because both are assigned to the same processor2. We summarize in Table1 the results obtained in [12]. In this table, Ia denotes the cumulated idle time spent by the P processors while executing the tiled iteration space.... In PAGE 6: ... As pointed out in [12], idle time can occur for two di erent reasons: (i) a processor may have to wait for data from another processor; or (ii) a processor may have nished all of the tiles assigned to it, and it is waiting for the last processor to terminates execution. In Table1 , condition (C) is a technical condition (M (1 + c + r)P) that states than no processor is kept idle when ending the processing of one column of tiles assigned to it; in other words, it can move on to its next column without waiting for any data to be communicated. 3 New Results In this section we propose new proofs and extend the work of [12].... In PAGE 8: ... In Table 2 we assume that M is su ciently large (see Sections 3.3 to 3.6 for a more precise statement). This hypothesis was implicit in the results in Table1 quoted from [12] (see Remark 2). We use a slightly di erent model for border tiles (the rst and the last one in each column).... In PAGE 11: ... We summarize both cases with the single formula tP = [M + (P ? 1)(1 + r + c)+]Tcomp: The formula for Ia is derived from the equation PtP = Ia + Tseq, with Tseq = MPTcomp. Remark 1 We see that the results in [12], as reported in Table1 , are inaccurate. A small rise does not prevent from a quadratic idle time; the precise condition is 1 + c + r 0, which makes good sense because the communication-to-computation ratio of the target architecture has to play a role.... ..."

### Table 5: Arc weights for the 29 nodes-37 arcs graph

"... In PAGE 13: ...e. rotation i is obtained by assigning weight of arc j in Table5 to arc (i + j) mod n. Notice that the order strenght for this graph is approximately 0.... ..."