### TABLE I STEINER TREE HEURISTIC STATISTICS

1992

Cited by 96

### Table 1: Characteristics of published Steiner heuristics.

1995

"... In PAGE 4: ... Path-distance heuristics are further divided between variants of the shortest-path heuristic and other path-distance heuristics. Table1 summarizes known results on the asymptotic time-complexities of these algorithms, together with the known upper bounds on the ratio of the quality of solution produced to that of an optimal solution.... In PAGE 5: ...1 Unconstrained Steiner Tree Heuristics Many Steiner heuristics have been proposed in the literature [12, 19, 26, 27] and form a suitable basis for DCSP-speci c heuristics. In this section, we rst examine the heuristics for the unconstrained Steiner problem listed in Table1 . These heuristics are then modi ed to handle degree constraints and compared by way of simulation.... ..."

Cited by 38

### Table 2.1: Steiner Tree Heuristics [8]

### Table 8: Two-Pole simulation results comparing CS-Steiner trees with 1-Steiner heuristic trees. Eachentry

in References

"... In PAGE 28: ... Our inputs correspond to the four distinct technologies described in Table 1. Table8 gives delay and tree cost #28WL#29 results and comparisons. The delays at all sink nodes correspond to 50#25 rise times estimated using the Two-Pole simulator #5B37#5D#5B38#5D.... In PAGE 28: ... The delays at all sink nodes correspond to 50#25 rise times estimated using the Two-Pole simulator #5B37#5D#5B38#5D. Eachentry in Table8 represents an average taken over every sink node in 50 random pointsets. We emphasize that the 1-Steiner algorithm #28or the BRBC, AHHK, etc.... ..."

### Table 1: Complexity of rectilinear trees.

"... In PAGE 1: ... However, it is still a major open problem in VLSI whether the RSA problem can be solved in polynomial time. For completeness, previous results on the complex- ity of rectilinear trees are listed in Table1 . More infor- mation can be found in the book by Hwang, Richards and Winter [9].... ..."

### Table 13. Computational results for Steiner #5CD quot; tree problems

1997

"... In PAGE 8: ... EDPL apos;s advantage diminishes with increasing numbers of unsatis#0Ced clauses #28for example the series of problems in Tables 5#7B7#29; however, even here, EDPL performs better. We also examine the Steiner #5CD quot; weighted tree problems #5B22#5D #28see Table13 #29. Our current implementation of the primal heuristic is too primitive to handle these large variable problems well.... ..."

Cited by 12

### Table 1: Performance of non-Manhattan routing metrics; reported are the percentage reduction in wire length, relative to rectilinear (AL BPBE) minimum spanning tree lengths.

2000

"... In PAGE 4: ... We first show the wire length reductions ob- tained by constructing Steiner and spanning trees for all signal nets (we ignore large clock nets and reset nets). In Table1 , the average reduction in tree length (compared to rectilinear minimum span- ning trees) is reported. While lengths under AL BP BF may exceed those of a rectilinear equivalent, we find that the average improve- ment across all nets is substantial.... ..."

Cited by 16

### Table 1: Performance of non-Manhattan routing metrics; reported are the percentage reduction in wire length, relative to rectilinear (AL BP BE) minimum spanning tree lengths.

"... In PAGE 4: ... We first show the wire length reductions ob- tained by constructing Steiner and spanning trees for all signal nets (we ignore large clock nets and reset nets). In Table1 , the average reduction in tree length (compared to rectilinear minimum span- ning trees) is reported. While lengths under AL BP BF may exceed those of a rectilinear equivalent, we find that the average improve- ment across all nets is substantial.... ..."

### Table 8: Two-Pole simulation results comparing CS-Steiner trees with 1-Steiner heuristic trees. Each entry corresponds to an average over delay computations for random critical sinks in each of 100 di erent random signal nets. 1-Steiner results are reported in the physical units (nanoseconds or centimeters) while other results are reported by their percent di erence from the 1-Steiner results. Note that 1-Steiner and 1-Steiner plus GSR always produced nearly identical average costs.

1986

"... In PAGE 28: ... Our inputs correspond to the four distinct technologies described in Table 1. Table8 gives delay and tree cost (WL) results and comparisons. The delays at all sink nodes correspond to 50% rise times estimated using the Two-Pole simulator [37] [38].... In PAGE 28: ... The delays at all sink nodes correspond to 50% rise times estimated using the Two-Pole simulator [37] [38]. Each entry in Table8 represents an average taken over every sink node in 50 random point sets. We emphasize that the 1-Steiner algorithm (or the BRBC, AHHK, etc.... ..."

### Table 3. Percentage increase of supporting receiver loads on an international networks using dedicated line, minimum distance shared trees, truncated minimum spanning trees, and a Steiner tree heuristic, rather than the modified heuristic. Five percent of the receivers require 20 time the rate of the others.

1997

"... In PAGE 27: ... . . . . . . . . . . . . . . . . . . . . . . . . 21 Table3 . Percentage increase of supporting receiver loads on an international networks using dedicated line, minimum distance shared trees, truncated minimum spanning trees, and a Steiner tree heuristic, rather than the modified heuristic.... ..."

Cited by 22