### Table 4.2. The output of an optimal generalized series-parallel scheduling algorithm.

### Table 3. Summary of total resistances required for the series/parallel and parallel/series composites.

"... In PAGE 4: ... 6 designs can be obtained by noting the total resistance of each topology. Table3 shows the total resistance of each topology. Obviously the simple series is the most efficient, but it has poor performance when the resistances are skewed.... ..."

### Table 2 shows numerical results of the methods presented in section 1 and the aggregation al- gorithm on series-parallel graphs. Details on how the tests were performed can be found in the comments of table 1 (section 1). The linear programming and the out-of-kilter methods take ad- vantage of the particular structure of the SP-graphs and behave really better on this class of graphs. However the cost-scaling approach on the dual of the problem does not work that well on this kind of instances, even with an improvement technique like the wave implementation (cf. [2]). The aggregation method reveals quite efficient, and not very sensitive to the graph dimension.

"... In PAGE 12: ... Table2 : Numerical results on series-parallel graphs. 5 Conclusion We show here how to solve the minimum cost tension problem on series-parallel graphs with convex piecewise linear costs in O(m3) operations.... ..."

### Table 1: Comparison of results. N/A=not applicable, seq=sequential, par=parallel, Mall=malleable resource, Non-Mall=non-malleable resource, SPG=series-parallel graph.

1996

"... In PAGE 2: ... Therefore, using known results o -the-shelf from the theory literature for our formulation means we have to com- promise heavily. See Table1 for a succinct comparison with some settings and results close to ours. 1.... ..."

Cited by 28

### Table 3: U-Shaped Distributions 4.2 EXAMPLE 2: A SERIES/PARALLEL POLYNOMIAL We now consider a polynomial representing a slightly more complex con guration. Suppose we have a circuit involving two parts from Population 1 (Part 1A and 1B) and one part from Population 2 (Part 2). In order for this circuit, illustrated in Figure 1, to work, we must have either Part 1A or Part 2 work and Part 1B work. Thus, the probability that a randomly selected circuit will work is Pf(X [ Y ) \ Xg and the parametric function that we are trying to estimate is

1996

"... In PAGE 10: ... This rule is intuitively appealing when one notices that to estimate the product xy of two positive quantities, if x lt; y, then an absolute measurement error of in x a ects the answer more than the same size error in y. Our last two examples in Table3 , one in which we have (p1; p2) [Be(0:1; 0:01); Be(1; 1)] and the other in which (p1; p2) [Be(0:01; 0:1); Be(1; 1)], may appear at rst to be patho- logical since the small values of a1 and b1 indicate that very little information is known in advance. Suppose, however, that the rst of the two batches of parts under consideration comes from a manufacturing process that is either in tolerance (working) or out of tolerance (not working).... ..."

Cited by 5

### Table 3: U-Shaped Distributions 4.2 EXAMPLE 2: A SERIES/PARALLEL POLYNOMIAL We now consider a polynomial representing a slightly more complex con guration. Suppose we have a circuit involving two parts from Population 1 (Part 1A and 1B) and one part from Population 2 (Part 2). In order for this circuit, illustrated in Figure 1, to work, we must have either Part 1A or Part 2 work and Part 1B work. Thus, the probability that a randomly selected circuit will work is Pf(X [ Y ) \ Xg and the parametric function that we are trying to estimate is

1996

"... In PAGE 10: ... This rule is intuitively appealing when one notices that to estimate the product xy of two positive quantities, if x lt; y, then an absolute measurement error of in x a ects the answer more than the same size error in y. Our last two examples in Table3 , one in which we have (p1; p2) [Be(0:1; 0:01); Be(1; 1)] and the other in which (p1; p2) [Be(0:01; 0:1); Be(1; 1)], may appear at rst to be patho- logical since the small values of a1 and b1 indicate that very little information is known in advance. Suppose, however, that the rst of the two batches of parts under consideration comes from a manufacturing process that is either in tolerance (working) or out of tolerance (not working).... ..."

Cited by 5

### Table 4.1: Comparison of results. N/A=not applicable, seq=sequential, par=parallel, SPG=series- parallel graph. A SPG is expressed recursively as follows: every SPG is a single node or a DAG with a source and sink; an SPG is either two SPG apos;s with an edge from the sink of one to the source of the other; or it comprises a new source, with edges to the sources of two SPG apos;s, and edges from their sinks to a new sink.

1996

Cited by 1

### Table 1 : Equivalent relativizations

2006

"... In PAGE 36: ... We have also established a few new cases of validity of the Conjecture. The main results are summarized in Table1 and 2... In PAGE 36: ...Table 1 : Equivalent relativizations Undirected graph classes Directed graph classes Uniformly k-sparse Uniformly k-sparse Line graphs Directed line graphs Quasi-series-parallel partial orders Finite interval graphs Finite partial orders of dimension 2 Interval graphs (for MS-OI) Partial orders of dimension 2 (for MS-OI) Table 2 : Proved relativizations. Table1 shows the equivalent relativizations. One could add the extensions of these classes by vertex and edge labellings.... ..."

Cited by 9

### Table 3. Differences among digraph, block, and digraph-cell models Digraph Block Digcell

"... In PAGE 24: ... Digraphcell structure 6.4 Comparison of digraph, block, and Digraphcell models Table3 shows the differences among digraph, block, and digcell models. Block models use an address based addressing scheme.... ..."

### Table 1: Statistics for Partial Order in Figure 2

1994

"... In PAGE 13: ...3 Comparing Partial Order Services Using arbitrary precision arithmetic routines, programs were developed to compute ei values for an arbitrary series-parallel partial order. Table1 indicates ei values for 0 i lt; N for the Anatomy and Physiology Instructor example in Figure 2. Additionally, the corresponding number of linear extensions for an ordered and unordered service are tabulated.... ..."

Cited by 39