### Table 1. Orders of the largest known broadcast networks with degree and broadcast time T .

"... In PAGE 4: ... Details of our methodology are delayed until Sec- tion 5. Table1 presents the best known lower bounds on B( ; T ) for small values of and T , T 3. In Table 1, bold entries are known to be optimal.... In PAGE 4: ... Table 1 presents the best known lower bounds on B( ; T ) for small values of and T , T 3. In Table1 , bold entries are known to be optimal. All of these in fact attain the upper bound on B( ; T ) given in Table 2.... In PAGE 4: ... Italicized entries are new results. All entries in Table1... In PAGE 6: ... In addition, each best broadcast graph is bipartite (many of the others are not). We now discuss our new entries in Table1 in more detail (see [4] for previous details). (3; 5): There are exactly four cubic transitive graphs with 24 vertices and broadcast time 5, all of which are Cayley graphs.... ..."

### Table 2.2: Broadcast times for common networks While improving the bounds for these networks is still of great interest, the search for new interconnection structures with better broadcasting capabilities is also going on. E.g. in [BHLP92], new families of graphs are presented achieving broadcasting in time 1:8750 log2 n and 1:4167 log2 n for degree 3 and 4, respectively, further closing the gap towards the lower bounds of 1:4404 log2 n and 1:1374 log2 n from Theorem 2.3.1. For general xed degree, other constructions of networks with e cient broadcasting schemes are given in [CGV89]. Broadcast- ing (and also gossiping) in the lately proposed star graph and pancake graph (as special csaes of Cayley graphs, see [AK89, ABR90]) has been investigated in [MS90b, BFP92, Go92] where e cient broadcast schemes are presented. The star graph and pancake graph have become very popular because they have a very regular interconnection pattern, sublogarithmic degree and diameter.

### Table 1: Summary of wormhole attack modes

2005

"... In PAGE 8: ...Table 1: Summary of wormhole attack modes Summarizing, the different modes of the wormhole attack along with the associated requirements are given in Table1 . Many applications in ad-hoc and sensor networks become vulnerable once a successful wormhole attack has been launched.... ..."

Cited by 15

### Table 3. Vital statistics of the largest-known cubic broadcast networks.

"... In PAGE 5: ... For the origin of these bounds, see Section 3. Table3 shows the properties of the largest cubic broadcast graphs for T 12. All of these graphs are transitive.... ..."

### Table 3. Vital statistics of the largest-known cubic broadcast networks.

"... In PAGE 6: ... For the origin of these bounds, see Section 3. Table3 shows the properties of the largest cubic broadcast graphs for T n14 12. All of these graphs are transitive.... ..."

### Table 1: Comparison of routing algorithms for wormhole networks. comm. routing no. of applicable network topologies

### Table 2a: Slowdown of idempotent messaging protocol compared to buffered wormhole routing on a perfect network

2002

"... In PAGE 8: ... The idempotent messag- ing protocol was simulated using 16-entry send tables and 32- entry receive tables. The results of the comparison are shown in Table2 a. We see that the actual slowdown, which ranges from as little as 1.... In PAGE 8: ... Table2 b: Slowdown when 40 bit flits and a 60% faster clock are used for the idempotent messaging protocol 2D Grid 3D Grid Fat Tree topology: buffered (cycles) idempotent (cycles) slow- down buffered (cycles) idempotent (cycles) slow- down buffered (cycles) idempotent (cycles) slow- down add 814 848 1.04 645 709 1.... ..."

Cited by 3

### Table 2a: Slowdown of idempotent messaging protocol compared to buffered wormhole routing on a perfect network

2002

"... In PAGE 8: ... The idempotent messag- ing protocol was simulated using 16-entry send tables and 32- entry receive tables. The results of the comparison are shown in Table2 a. We see that the actual slowdown, which ranges from as little as 1.... In PAGE 8: ... Table2 b: Slowdown when 40 bit flits and a 60% faster clock are used for the idempotent messaging protocol 2D Grid 3D Grid Fat Tree topology: buffered (cycles) idempotent (cycles) slow- down buffered (cycles) idempotent (cycles) slow- down buffered (cycles) idempotent (cycles) slow- down add 814 848 1.04 645 709 1.... ..."

Cited by 3

### Table 7: Comparison of interconnection network graphs One of the trade-o s of xed-degree graphs is an increased diameter. However, the n-SCC can be built with very high speed buses in the local links. Therefore, the n-SCC can present communication delays comparable to the n-star, if we consider that the lateral links often use serial links for making their lay-out simpler. In addition, many practical algorithms present locality of operation and require just a limited region of the interconnection network to run. This reduces even more the requirements for long communication paths in the graph and contributes to high performance in parallel computers. Another disadvantage of xed-degree graphs is a reduced fault tolerance in comparison to variable- degree graphs. The fault tolerance of the n-SCC graph is 2, while the fault tolerance of the n-star and the n-cube is respectively equal to (n ? 2) and (n ? 1). However, since the underlying topology 33

"... In PAGE 35: ... Such algorithm is actually an extension of the routing algorithm presented in this report and can be based on dynamic fault-tolerant routing and broadcasting algorithms already developed for the n-star [3], [16], [17] and the cube-connected cycles [18]. Table7 also shows another type of I/O-bounded interconnection network, namely the cube- connected cycles or CCC. An n-CCC graph can be built by replacing each node of an n-cube with a ring of n or more nodes.... In PAGE 35: ... An n-CCC graph can be built by replacing each node of an n-cube with a ring of n or more nodes. Table7 shows typical values for n-CCC graphs containing n nodes in each ring. The number of nodes and diameter of an n-CCC graph formed under such structure are given respectively by N = n2n and dCCC = 2n + bn=2c ? 2 [19].... In PAGE 35: ...-SCC. However, it has been shown that the n-star outperforms the n-cube on these aspects [1], [3]. If we recall that the n-SCC not only uses the n-star as its quotient Cayley graph but also has fewer nodes in each ring, then it seems that we should expect favorable results when compared with the CCC. Table7 also compares the n-SCC with other graphs from the viewpoint of one-port broadcasting algorithms. Theorem 11 shows that the selection of a proper value for the ratio of the transmission rates in the local and lateral links of an n-SCC graph can reduce the running time of a broadcasting algorithm to about twice the time spent in the lateral link steps.... In PAGE 35: ... This results in an O(n) running time, while a one-port broadcasting in an n-star has a O(n log n) running time. The values shown for one-port broadcasting in the n-star in Table7 are optimal and have been extracted from [15]. By inspecting Table 7, we notice that the one-port broadcasting in an n-SCC graph can be accomplished with running time better than or equal to that of an n-star containing (n ? 1) times fewer nodes.... In PAGE 35: ... The values shown for one-port broadcasting in the n-star in Table 7 are optimal and have been extracted from [15]. By inspecting Table7 , we notice that the one-port broadcasting in an n-SCC graph can be accomplished with running time better than or equal to that of an n-star containing (n ? 1) times fewer nodes. For n = 4 and n = 6, the total number of steps required by the one-port broadcasting algorithm is about 50% greater than the diameter of the corresponding SCC graph.... In PAGE 36: ... Since the diameter of an n-star is less than that of a hypercube of similar size, we simply extend this result to conclude that broadcasting in the n-SCC graph can be achieved in shorter running time than in a CCC of similar size. As a matter of fact, an inspection of Table7 allows us to con rm that.... ..."

### Table 1. Orders of the largest known broadcast networks with degree n14 n01

"... In PAGE 5: ... Details of our methodology are delayed until Sec- tion 5. Table1 presents the best known lower bounds on Bn28n01;Tn29 for small values of n01 and T , T n15 n01 n15 3. In Table 1, bold entries are known to be optimal.... In PAGE 5: ... Table 1 presents the best known lower bounds on Bn28n01;Tn29 for small values of n01 and T , T n15 n01 n15 3. In Table1 , bold entries are known to be optimal. All of these in fact attain the upper bound on Bn28n01;Tn29 given in Table 2.... In PAGE 5: ... Italicized entries are new results. All entries in Table1... In PAGE 7: ... In addition, each best broadcast graph is bipartite n28many of the others are notn29. Wenow discuss our new entries in Table1 in more detail n28see n5b4n5d for previous detailsn29. n283; 5n29: There are exactly four cubic transitive graphs with 24 vertices and broadcast time 5, all of which are Cayley graphs.... ..."