### Table 1. Local computing rules

"... In PAGE 1: ... N={0,1,2} is the set of the inputs; d=100 is the transport delay for each cell. :N S is the local computing function defined by Table1 with V(cij,1,t)=U(cij,n,t)+E(cij,n,t)-P(cij,t), for n=1 or 2 (U, ... ..."

### Table 1: Locally Computed Tightest Bounds

1999

"... In PAGE 11: ...MN O Q R S T U P 3 2 10strata 4 Figure 3: Directed Tree #28B; !#29 of computing tightest bounds at a node #28the common nodes for Chaining and Fusion are #0Clled black#29. Table1 shows the greatest lower and the least upper bounds that are computed... In PAGE 11: ...Table1... ..."

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### Table 1: Locally Computed Tightest Bounds

1999

"... In PAGE 11: ...M N O Q R S T U P 3 2 1 0 strata 4 Figure 3: Directed Tree (B; !) of computing tightest bounds at a node (the common nodes for Chaining and Fusion are lled black). Table1 shows the greatest lower and the least upper bounds that are computed at each node B of each stratum. More precisely, these bounds are 1 = inf Pr(BD)=Pr(B), 2 = sup Pr(BD)=Pr(B), 2 = sup Pr(BD)=Pr(B), and 2 = sup Pr(D)=Pr(B) subject to Pr j= KB and Pr(B) gt; 0.... In PAGE 11: ... More precisely, these bounds are 1 = inf Pr(BD)=Pr(B), 2 = sup Pr(BD)=Pr(B), 2 = sup Pr(BD)=Pr(B), and 2 = sup Pr(D)=Pr(B) subject to Pr j= KB and Pr(B) gt; 0. Table1 also shows the requested tight answer fx1=0:02; x2=0:17g, which is given by the tightest bounds 1 and 2 that are computed at the premise M.... ..."

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### Table 1: Locally Computed Tightest Bounds st B C

1999

"... In PAGE 6: ...traint tree in Fig. 2, left side. Fig. 4 illustrates the three di erent ways of computing tightest bounds at a node (the common nodes for Chaining and Fusion are lled black). Table1 shows the greatest lower and the least upper bounds that are computed at each node B of each stratum st. More precisely, 1 = inf Pr(BC )=Pr(B), 2 = sup Pr(BC )=Pr(B), 2 = sup Pr(BC )=Pr(B), and 2 = sup Pr(C)=Pr(B) sub- ject to Pr j= KB and Pr(B) gt; 0 (in Table 1, we abbre- viate Leaf, Chaining, and Fusion by Le, Ch, and Fu, respectively).... In PAGE 6: ... Table 1 shows the greatest lower and the least upper bounds that are computed at each node B of each stratum st. More precisely, 1 = inf Pr(BC )=Pr(B), 2 = sup Pr(BC )=Pr(B), 2 = sup Pr(BC )=Pr(B), and 2 = sup Pr(C)=Pr(B) sub- ject to Pr j= KB and Pr(B) gt; 0 (in Table1 , we abbre- viate Leaf, Chaining, and Fusion by Le, Ch, and Fu, respectively). Table 1 also shows the requested tight answer fx1=0:02; x2=0:17g, which is given by the tightest bounds computed at the premise A.... In PAGE 6: ... More precisely, 1 = inf Pr(BC )=Pr(B), 2 = sup Pr(BC )=Pr(B), 2 = sup Pr(BC )=Pr(B), and 2 = sup Pr(C)=Pr(B) sub- ject to Pr j= KB and Pr(B) gt; 0 (in Table 1, we abbre- viate Leaf, Chaining, and Fusion by Le, Ch, and Fu, respectively). Table1 also shows the requested tight answer fx1=0:02; x2=0:17g, which is given by the tightest bounds computed at the premise A. A E F G H G H I A E F F A G I E I H Initialization of a leaf: Fusion of subtrees: Chaining of an arrow and a subtree:... ..."

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### TABLE II POTENTIAL COMMUNICATION SAVINGS FROM USING LOCAL COMPUTATION

2006

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### Table 2: Cost of local computation for some libraries cell

1999

Cited by 1

### TABLE 1. Computation of the accumulative local traffic in

in doi:10.1093/comjnl/bxl026 An Efficient Distributed Algorithm to Identify and Traceback DDoS Traffic

### Table 1: Run-time (in seconds) spent in the problem decomposition and local computation stages for m = n = 30; 000, as the number of processors is varied.

"... In PAGE 11: ... This is a major reason for the superlinear speedup observed. Table1 shows the total run-time and the time spent in the problem decomposition and local computation stages as the number of processors is varied. The local computation stage can scale anywhere between linearly and quadratically (run-time reduces by a factor of 4 for a twofold increase in the number of processors).... ..."