### Table 4 Performance of Directed Minimum Spanning Tree

Cited by 1

### Table 1: Expected Random Minimum Spanning Tree Weight: 500 Trials

"... In PAGE 2: ... Then: lim n!1 Efs(n)g = (3) = 1 X k=1 k ;3 =1:202 ::: And, for every gt;0, lim n!1 Pfjs(n) ; (3)j g =0: Although the theorem describes limiting behavior, students will nd that the minimum weight spanning tree is concentrated near (3) even for relatively small values of n. In Table1 we present the results from a sample simulation;; vehundred trials were performed for eachnumberofvertices. Even at n = 100, the expectation derived from the simulation is very close to the limiting value.... ..."

### Table 1: Average Minimum Spanning Tree Weight: 500 Trials

### Table 1: Overview of previous and new results related to the computation of minimum-distance spanning trees and minimum distance-approximating spanning trees.

"... In PAGE 4: ...n Section 5). Finally, we extend results by Gerey et al. [GLJ78] and Hassin amp; Tamir [HT95] concerning the minimization of the distance matrix DT under various matrix norms, integrating the previous findings into a unifying framework in Theorem 1. (See Table1 for an overview of previous and new results.) This work is structured as follows: Section 2 gives an overview of previous results related to this work and new results obtained, followed by some definitions and easy observations in Section 3.... ..."

### TABLE IV BRBC TREE AND SHORTEST PATH TREE RADIUS AND COST STATISTICS FOR RANDOM NETS, EXPRESSED AS A FRACTION OF TIIE CORRESPONDING MINIMUM SPANNING TREE VALUES

1992

Cited by 76

### 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

### Table 9: Two-Pole simulation results for Elmore routing tree variants. Spanning ERT constructions are

in References

"... In PAGE 27: ...2 Elmore Routing Trees We constructed Elmore routing trees for the same sets of random inputs used in the CS-Steiner exper- iments. Delaysimulation results, again obtained using the Two-Pole simulator, are presented in the upper parts of Table9 . For comparison, the table includes data for the minimum spanning tree and AHHK tree #5B1#5D constructions.... ..."

### 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.... ..."