### Table 2: Selection functions used in algorithms links are considered. For example, an adaptive random algo- rithm randomly selects from the list of candidate directions until it nds a direction which it can successfully route the packet on. This paper examines how message destination distribu- tions a ect routing algorithm performance. In particular, we focus on how routing adaptivity and selection functions combine with a set of destination distributions to deter- mine network performance. While other studies have looked at comparing various routing algorithms over di erent pat- terns, most studies limit the selection functions used, the range of algorithms evaluated, or the destination distribu- tions considered [5,7,8, 11,12].

1997

"... In PAGE 3: ... Under these patterns, we evaluate a range of routing al- gorithms in order to characterize their performance. Specif- ically, we consider oblivious minpath algorithms using three di erent selection functions as shown in Table2 . The obliv- ious dimension-ordered algorithm chooses the lowest dimen- sion link out of all of the minimal-path links.... ..."

Cited by 10

### Table 1: Average values for jL1j and jL2j for a 32 32 mesh using dimension order ecube grouping. The rows represent di erent grouping levels whereas the columns show the number of destinations.

"... In PAGE 15: ...log2 (jL2j + 1)e+2. It should be noted that for a k k mesh, 1 jL2j k. Using the notation developed earlier, L1 = Fe(L0); L2 = Fe(L1) = Fe(Fe(L0)). Table1 shows the average values for L1 and L2 obtained using the dimension order scheme discussed in this section for di erent number of destinations. The average is taken over randomly generated destination sets for each destination set size in a 32 32 mesh.... ..."

### Table 1: Average values for jL1j and jL2j for a 32 32 mesh using dimension order ecube grouping. The rows represent di erent grouping levels whereas the columns show the number of destinations.

"... In PAGE 16: ...log2 (jL2j + 1)e+2. It should be noted that for a k k mesh, 1 jL2j k. Using the notation developed earlier, L1 = Fe(L0); L2 = Fe(L1) = Fe(Fe(L0)). Table1 shows the average values for L1 and L2 obtained using the dimension order scheme discussed in this section for di erent number of destinations. The average is taken over randomly generated destination sets for each destination set size in a 32 32 mesh.... ..."

### Table 1. Comparison of area

"... In PAGE 3: ... In order to have a fair comparison, we do not place any constraints on timing and area for synthesis. Table1 shows the synthesized results for switch area in gates when CF CUD0CXD8 BP BFBE and DA BP BG. The routing al- gorithm implemented is dimension-ordered X-Y routing, which is deterministic.... ..."

### Table 2: A Tighter Upper Bound on Number of Consumption Channels Required from Topology and Routing Constraints. Virtual Channel Characteristics and Usage of Two Routing Algorithms are Shown. Number of virtual Number of messages that Number of messages that can

"... In PAGE 18: ...Table2 summarizes the virtual channel usage characteristics of two routing algorithms: a) dimension-order [12] as discussed above and b) Duato apos;s fully adaptive routing [15] on three di erent topologies. The last column in this table shows the maximum number of messages that can simultaneously enter a node from all dimensions for di erent topologies.... In PAGE 28: ... Hence, with increase in dimensionality of hypercubes more consumption channels are not useful. c) It is also reassuring to observe that the values for ca2o t;r derived here are much smaller than the corresponding values of ct;r obtained in Table2 in Sec.... ..."

### Table 2: Source and destination of the BPC permutation [?0; 1; 2; ?3] in a 16 processor OTIS- Hypercube

1998

"... In PAGE 5: ... The BPC permutation [?0; 1; 2; ?3] requires data from each processor m3m2m1m0 to be routed to processor (1 ? m0)m1m2(1 ? m3). Table2 lists the source and destination processors of the permutation. The permutation vector A for each of the permutations of Table 1 is given in Table 3.... ..."

Cited by 9

### Table 2. The number of communication links in networks

2007

"... In PAGE 4: ... Routers implement a simple dimension-order routing scheme where the trans- fers are first directed to the correct row and then to the requested column. The number of communication links L of networks are listed in Table2 . A single bus has only one communication link, whereas in a hierarchical bus there are as many links as there are bus segments.... ..."

Cited by 1

### Table 1: Parameters used for all validation experiments with Orion

"... In PAGE 6: ....7.1 Experimental setup We validate our results by comparing against simulation results from Orion, a cycle-accurate network power-performance simula- tor. All parameters for Orion remain constant across validation runs, and are summarized in Table1 . Dimension-ordered X-Y rout- ing is assumed.... ..."

### Table 1: Parameters used for all validation experiments with Orion

"... In PAGE 6: ....7.1 Experimental setup We validate our results by comparing against simulation results from Orion, a cycle-accurate network power-performance simula- tor. All parameters for Orion remain constant across validation runs, and are summarized in Table1 . Dimension-ordered X-Y rout- ing is assumed.... ..."

### Table 1: Optimal moves for N2 = 22d processor hypercube and respective OTIS-Hypercube simu- lations

1998

"... In PAGE 4: ... These algorithms may be simulated by an OTIS-Hypercube using the method of [9] to obtain algorithms to realize these data rearrangement patterns on an OTIS-Hypercube. Table1 gives the number of moves used by the optimal hypercube algorithms; a break down of the number of moves in the group and local dimensions; and the number of electronic and OTIS moves required by the simulation. We shall obtain OTIS-Hypercube algorithms, for the permutations of Table 1, that require far fewer moves than the simulations of the optimal hypercube algorithms.... In PAGE 4: ... Table 1 gives the number of moves used by the optimal hypercube algorithms; a break down of the number of moves in the group and local dimensions; and the number of electronic and OTIS moves required by the simulation. We shall obtain OTIS-Hypercube algorithms, for the permutations of Table1 , that require far fewer moves than the simulations of the optimal hypercube algorithms. As mentioned before, each processor is indexed as (G; P ) where G is the group index and P the local index.... In PAGE 4: ... An index pair (G; P ) may be transformed into a singleton index I = GP by concatenating the binary representations of G and P . The permutations of Table1 are members of the BPC ( bit-permute-complement ) class of permutations de ned in [6]. In a BPC permutation, the destination processor of each data is given by a rearrangement of the bits in the source processor index.... In PAGE 5: ... Table 2 lists the source and destination processors of the permutation. The permutation vector A for each of the permutations of Table1 is given in Table 3. 3.... ..."

Cited by 9