### Table 8: Simulated average flit traversal energy (10a1 10J) of tori, hierarchical tori and express cubes, with the minimal energy at each technology highlighted.

2005

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### Table 2. Embeddings into the x #02 y grid.

1995

"... In PAGE 3: ... The virtual topol- ogy library enables one to port these algorithms for PARIX directly and makes two kinds of functional services available to the user: The computation of an e#0Ecientembedding of a concrete instance of a virtual topology into an arbi- trary but #0Cxed 2-dimensional grid and the realization of a concrete instance of a virtual topology. The following virtual topologies are available: The 2- and 3- dimensional grid or torus, the binary hypercube and deBruijn network, the complete k-ary tree, the clique, star, pipe and ring network #28for a short description of these networks see Table2 #29. We establish a concrete instance of a virtual topology via distributed computation.... In PAGE 4: ... These algorithms could be part of the library but this requires additional algorithms to handle the remaining instances of the topology. Table2 presents a summary of the used embeddings and upper bounds of the achieved dilations. For more detailed descriptions of the used embeddings see #5BRSS#5D.... ..."

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### Table 3: Grid Statistics for Shock on Cube

"... In PAGE 15: ... of C = 1:0, and run to a time of t = 1:70. The statistics for the three runs (unstructured, cartesian core, hybrid cartesian- gridless) have been compiled in Table3 . The two cartesian core runs correspond to Courant-nrs.... ..."

### Table 2. Comparing the Up*/down* routing algorithm based on the DFS methodology (UD DFS), the Flexible routing (FX), and the e-cube algorithm for 2D and 3D tori.

"... In PAGE 6: ... The analysis is performed by comparing some behavioral routing metrics: (1) The average distance metric, which is the average num- ber of crossed links in the shortest path between any pair of nodes3; (2) the crossing path metric, which shows the maxi- mum number of routing paths crossing through any network channel; and (3) the deviation crossing metric, which refers to the standard deviation of the crossing path metric. Table2 shows the values of these behavioral routing met- rics computed for each routing algorithm for 2D torus net- works with sizes of 4 4, 6 6, and 8 8 switches, and 3D tori with sizes of 3 3 3 and 4 4 4 switches. These net- work configurations provide up to 64 switches in the net- work, which seems adequate in small and medium scale clusters or NOWs.... ..."

### Table 1 The sequence of CFs between the cube and its environment. For each CF the di- mension of the twist and wrench space is given. CF Principal Contacts dim(W) dim(T )

"... In PAGE 26: ...ig. 10. The experiment executes a sequence of contact formations including differ- ent contact relaxations and the creation of new contacts under force control. The sequence starts at a locally most constrained pose CF1, and continues clockwise through the CFs listed in Table1 . The figure only shows the CF sequence, not all CF-compliant poses.... ..."

### Table 1. Embeddings of the a #02 b grid into the x #02 y grid.

1995

"... In PAGE 11: ... Table 1 gives an overview of the used embeddings and upper bounds for the achieved dilations. Additionally,wehave implemented the folding technique introduced in #5B1#5D that provides dilation 2 under certain conditions #28see Table1 #29. Table 1.... ..."

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