### Table 1. Possible failures and recoveries for an individual island.

in Atomicity, Serialization And Recovery In A Highly Available And Scalable Cluster-Based File System

"... In PAGE 6: ...3 Recovery We have designed a recovery procedure for islands to recover from arbitrary sequences of failures back to consistent states. Table1 shows the possible failures for an individual island and how the island can be recovered ... ..."

### Table 1: Optimal node-disjoint paths in SGn SGn has a vertex connectivity of k(SGn) = (n?1), and therefore can tolerate up to (n ? 2) node failures. Exact values for the fault-diameter of the star graph were derived in [7] and are given below. This result is obtained via a worst-case analysis that considers the impact of up to (n?1) arbitrary faults on the optimal- length node-disjoint paths listed in Table 1. df(SGn) = d(SGn) + 1; if n is odd or n 7 d(SGn) + 2; if n = 4 or n = 6

"... In PAGE 4: ... The rst step in the method consists of selecting a permutation requiring a large number of lateral and local links in the path from u to v. The number of lat- eral links depends on the number of cycles of length at least 2 in (c) and on the number of digits in these cycles (m), as shown in Table1 . The number of lo- cal links also depends on c and m, but can be further increased by a proper selection of the internal compo- sition of the cycles in .... In PAGE 5: ... Initially, we consider some candidates for permutation that are likely to result in the largest possible number of links in the presence of faults. The values of c and m in the selected permutations result in the highest or close to the highest possible number of lateral links along the di erent routes from to the identity node (see Table1 ). Naturally, this selection criterion also increases the number of local links in these routes.... In PAGE 8: ... Due to space constraints, we show in Table 10 only the sequences of lateral links R(`1 7! `s) used to build Table 9d. One possible worst-case fault placement that can be applied to Table 9d is shown in Table1 1a. The costs of the optimal paths for all possible combinations of digits i and j are listed in Table 11b.... In PAGE 8: ... In. Final link link 2 3 4 5 6 2 { 18 19 19 18 3 { { { { { 4 { 20 19 20 19 5 { 19 20 20 19 6 { 20 20 20 19 (a) Worst-case fault placement for = (1 3 5 2)(4 6) i j 2 3 4 5 6 2 19 18 19 19 18 3 20 19 20 20 19 4 20 20 19 20 19 5 20 19 20 20 19 6 20 19 20 20 19 (b) Cost of optimal paths under the fault placement of Table 11a Table1 1: A worst-case fault placement in SCC6 Note that the cost of the longest path in Table 11b is 20. Hence, df(SCC6) = d(SCC6) + 1 = 20.... In PAGE 9: ... Final link link 2 3 4 5 6 2 19 18 19 19 18 3 14 22 16 19 15 4 15 20 19 20 19 5 18 19 20 20 19 6 16 20 20 20 19 (d) = (1 3 5 2)(4 6) Table 9: Cost of paths Q(`1 7! `s) in SCC6 Init. Final link link 2 3 4 5 6 2 (2; 6; 4; 6; 2; 3;5;2) (2; 3; 4; 6; 4; 5; 2; 3) (2; 3; 5; 2; 3;4;6; 4) (2; 6; 4; 6; 5; 2; 3;5) (2; 6; 4; 5; 2;3;5;6) 3 (3; 4; 6; 4; 5;2) (3; 4; 6; 4; 5;3; 2; 3; 2;3) (3; 5; 2; 4; 6;4) (3; 4; 6; 4; 2; 5; 2;5) (3; 5; 2; 6; 4;6) 4 (4; 6; 4; 3; 5;2) (4; 6; 4; 5; 2; 3; 5; 3) (4; 6; 5; 2; 4;3;5; 4) (4; 6; 4; 3; 2; 5; 2;5) (4; 3; 5; 2; 6;4;3;6) 5 (5; 6; 4; 5; 3; 5;6;2) (5; 6; 4; 6; 2; 3; 5; 3) (5; 2; 3; 5; 3;4;6; 4) (5; 6; 4; 6; 2; 5; 3;5) (5; 2; 6; 4; 5;3;5;6) 6 (6; 4; 6; 3; 5;2) (6; 4; 6; 5; 2; 3; 5; 3) (6; 5; 2; 4; 6;3;5; 4) (6; 4; 6; 2; 5; 2; 3;5) (6; 4; 5; 2; 6;3;5;6) Table1 0: Sequences of lateral links R(`1 7! `s) used to build Table 9d to the diameter of a fault-free SCCn?2 graph by the recurrence below. This recurrence holds for n 6 and can be veri ed from Equation 1.... ..."

Cited by 1

### Table 4: Arbitrary logical topology over random network case. Capacity constraint: The values of Table 3 are repeated here to show that improvement concerning the connectivity constraint is not achieved by relaxing the capacity constraint. Connectivity constraint: The percentage of bad elements (which would cause disconnections in the higher level network protected groups) is very low for PIW compared to SPR-P and SPR-CC. There is also a strong reduction achieved by PIW concerning the average number of demands which cannot be restored by the failure of such a bad element.

"... In PAGE 14: ...6 for SPR-P). Table4 shows the measurements for the arbitrary logical topology over random network and for the con- nectivity constraint. The values for the capacity con- straints are the same as those of Table 3 and are re- peated here to show that the improvement concerning the connectivity constraint is not achieved by relax- ing the capacity constraint, but that both are achieved jointly.... ..."

### Table 2 Results of Example 1

in Scheduling of Design Projects with Resource Constraints and Uncertain Number of Design Iterations

### Table 2: Expected execution times (arbitrary units).

1999

"... In PAGE 13: ... Consider the performance of the heuristics for a very simple case of three tasks t0, t1, and t2 arriving in that order. Table2 shows the expected execution times of tasks on the machines in the system. All time values in the discussion below are the expected values.... ..."

Cited by 78

### Table 3: Task set with arbitrary processing times.

1994

"... In PAGE 5: ... This algorithm compacts the schedule S generated in Step 4 of Algorithm H. The example in Table3 and Figure 8 illustrates Algo- rithm H. T3 has the longest processing time on P1, T1 on P2, T4 on P3, and T3 on P4.... ..."

Cited by 61

### Table 3: Task set with arbitrary processing times.

1994

"... In PAGE 5: ... This algorithm compacts the schedule S generated in Step 4 of Algorithm H. The example in Table3 and Figure 8 illustrates Algo- rithm H. T3 has the longest processing time on P1, T1 on P2, T4 on P3, and T3 on P4.... ..."

Cited by 61