### Table 2. Observed average-case algorithmic counts, as the value of the sampling pa- rameter c is varied. The average error percentage is the deviation of the estimated score from the exact score, and the k n percentage indicates the number of samples/SSSP com- putations.

"... In PAGE 11: ... We can also vary the parameter c, which afiects both the percentage of BFS/SSSP computations and the approximation quality. Table2 summarizes the average performance on each graph instance, for difierent values of c. Taking only high-centrality vertices into consideration, we report the mean approxima- tion error and the number of samples for each graph instance.... ..."

### Table 2. Observed average-case algorithmic counts, as the value of the sampling pa- rameter c is varied. The average error percentage is the deviation of the estimated score from the exact score, and the k n percentage indicates the number of samples/SSSP com- putations.

"... In PAGE 11: ... We can also vary the parameter c, which afiects both the percentage of BFS/SSSP computations and the approximation quality. Table2 summarizes the average performance on each graph instance, for difierent values of c. Taking only high-centrality vertices into consideration, we report the mean approxima- tion error and the number of samples for each graph instance.... ..."

### Table 5: Estimates of Fixed Parameters in the Immigrant Model (Estimated via PML and PQML) and in the Nationality Model (Estimated via PML)

"... In PAGE 17: ... Therefore the immigrant and nationality indicators are to be inter- preted relative to the native average. Table5 presents the estimation results of the immigrant model in the rst column. As always in the framework of Poisson regressions, the estimated co- e cients can be interpreted as semi-elasticities.... In PAGE 18: ...15 We are most interested in the set of variable immigrant coe cients which is depicted in Figure 2. The un-dotted bands represent the coe cient estimates corresponding to the PML column of the immigrant model in Table5 . Figure 2 contains three interpretable pieces of information: First, over the entire range of fertile years that are possibly spent in Germany the immigrant e ect is positive.... In PAGE 19: ... As described in the methodology section above we developed an estimator that provides correct estimates if the equidispersion assumption is violated. The results based on this penalized quasi-maximum-likelihood estimation (PQML) are presented in the second coe cient column in Table5 . A comparison of the coe cient estimates yields that they are basically not a ected.... In PAGE 19: ...The con dence bands of the PQML estimation are within those derived by the PML estimation. Finally, Table5 provides some information on starting values as well as the nal estimates of the hyperparameters and shows some characteristics of the algo- rithm. The variability parameter Q is estimated slightly higher using the PQML estimation which corresponds to a slightly steeper decline in the immigrant e ect in Figure 2.... In PAGE 19: ... In step two of our empirical analysis we generalize the immigrant model to allow for nation-speci c fertility adjustments. Given the limited e ect of the underdispersion control for the immigrant model, the estimation results presented in the last column of Table5 are derived using the PML estimation. The estimates 16The equidispersion hypotheses is rejected even at a level of 0.... In PAGE 20: ...spent in Germany, hardly di er from those presented in the rst two columns of Table5 . The magnitudes of the coe cient for age increases and those for female schooling degrees fall slightly.... ..."

### TABLE III AVERAGE RUNNING TIME OF DIFFERENT APPROXIMATION ALGORITHMS FOR RANDOM DIRECTED GRAPHS.

### Table 3. Approximating SP

2001

"... In PAGE 4: ... It may be expected that if the ratio between the relative weights is sufficiently large, WFQ, WRR and PP could offer the same performance in terms of average waiting time as SP. To investigate such ex- pectation, assume D6 BD BM D6 BE BM D6 BF BM D6 BG BP BIBG BM BDBI BM BG BM BD for Table3 . Also for Table 3, AQ CX BPBCBMBEBEBH for CX BPBDBN BMBMBMBN BG.... In PAGE 4: ...Table 3. Approximating SP Table3 shows that WFQ does approximate very well the performance of SP in terms of average waiting time. PP also roughly offers a similar performance when the as- signed probability parameters are set as CJ BIBG BKBH BN BDBI BEBD BN BG BH BN BDCL.... In PAGE 4: ...How- ever, WRR cannot be considered as an approximation of SP for this case. Table3 shows that under WRR, the average waiting times of classes 1 and 2 are much larger than those provided by SP. This is due to the unfair nature of WRR: the service counters are reset after every round of service in WRR, a queue with high relative weight will not receive additional service at a later time if it has missed any ser- vice in a previous round.... In PAGE 4: ... This explains why PP outperforms WRR in this case. Table3 also shows that PP can offer the same perfor- mance as SP or reverse SP by setting D4 CX BPBDfor CX BPBDBN BMBMBMBN BG or D4 CX BPBCfor CX BPBDBN BEBN BF and D4 BG BPBD. 4 Group Segregation In the previous section, we investigated and compared the performance of PP with WFQ and WRR through simu- lation.... ..."

Cited by 10

### Table 2: Lookup performance for di erent graphs. The average number of lookup probes is approximately equal to the number of replicas. Measured quantities are averaged over 10,000 trials for each of 60 generated graphs, excluding the Gnutella graph.

2005

"... In PAGE 10: ... 5.1 Lookup performance The results of the rst set of experiments are shown in Table2 . The Gnutella graph represents a crawl of the actual deployed system [27, 28], while the others are generated.... ..."

Cited by 12

### Table 2: Information about topology graphs. We provide approximate values for some parameters of ISP areas due to proprietary nature of the data.

### Table 6. Accuracy of Greedy on random graphs with a fixed average degree

"... In PAGE 10: ... Distribution of dynamic de- grees for graphs with average degree 6 Using the data collected above we are able to evaluate the accuracy of Greedy using the bound in Lemma 2. Table6 shows the approximation ratio for Greedy on average degree graphs with up to 50,000 vertices. The ratio shown is the average upper bound on the size of independent set derived from the dynamic degrees over the average size found by the... In PAGE 10: ...Table 6. Accuracy of Greedy on random graphs with a fixed average degree Our interpretation of the data presented in Table6 is that Greedy is very near optimal for graphs with average degree 1 and 2, and probably 3 as well (asymptotically). 3.... ..."

### Table 6. Accuracy of Greedy on random graphs with a fixed average degree

"... In PAGE 10: ... Distribution of dynamic de- grees for graphs with average degree 6 Using the data collected above we are able to evaluate the accuracy of Greedy using the bound in Lemma 2. Table6 shows the approximation ratio for Greedy on average degree graphs with up to 50,000 vertices. The ratio shown is the average upper bound on the size of independent set derived from the dynamic degrees over the average size found by the... In PAGE 10: ...Table 6. Accuracy of Greedy on random graphs with a fixed average degree Our interpretation of the data presented in Table6 is that Greedy is very near optimal for graphs with average degree 1 and 2, and probably 3 as well (asymptotically). 3.... ..."