### TABLE III A SUMMARY OF How MANY EDGES WERE ADDED BY THE LDRG ALGORITHM, SHOWN AS A PERCENT OF IHE TOIAL NUMBER OF THE 100 CASES TESTED

### Table 1: Edge attrition for activity on 1000 residential accounts over a 6 month period. Month 1 is a \reference month quot; for which we look for those edges in subsequent months. For each subsequent month the table shows how many of the edges are observed again. The column marked Cumulative aggregates the subsequent months to show how many of the edges we have seen overall.

2003

"... In PAGE 5: ... This period was broken up into six 30-day slices, and the edges from the rst month were tracked to see if they appeared in subsequent months. The results in Table1 show that edges seen in one month often do not show up again. Of all the edges observed in the reference month, only 37.... ..."

Cited by 12

### Table 1: Statistics of metamorphosis examples: The number of edge swaps required for connectivity transformation is quite smaller than the edge count of an in-between mesh. The small heights of the dependency graph implies that many edge swaps can be performed simultaneously in connectivity interpolation.

"... In PAGE 5: ... For ex- ample, in [LDSS99], the triangle count of a metamesh is five to ten times larger than the bigger one of input meshes. In contrast, Table1 shows that the vertex count of an in- between mesh is less than the sum of the vertex counts of input meshes. Fig.... In PAGE 5: ...nput meshes. Fig. 6 demonstrates that the proposed tech- nique generates visually pleasing metamorphoses with the smaller numbers of vertices. Table1 summarizes the statistics of the morphing exam- ples. For each example, feature vertices were specified by the user to establish the feature correspondence between input meshes.... In PAGE 5: ... For each example, feature vertices were specified by the user to establish the feature correspondence between input meshes. In Table1 , the size of an in-between mesh does not include the vertices temporarily introduced for geomorphs. In Table 1, we can see that the number of edge swaps re- quired for connectivity transformation is quite smaller than the edge count of an in-between mesh.... In PAGE 5: ... In Table 1, the size of an in-between mesh does not include the vertices temporarily introduced for geomorphs. In Table1 , we can see that the number of edge swaps re- quired for connectivity transformation is quite smaller than the edge count of an in-between mesh. Note that the edge swaps are applied to the converted source and target meshes, Mprime S and Mprime T, which have the same number of edges as an c... In PAGE 6: ... When we compare the results with the re- lated work [LL04], we can see that our approach generates smaller number of edge swaps. In Table1 of this paper, the number of edge swaps is about a half of the edge count of the bigger input mesh. In Table 1 of [LL04], the edge swap count is similar to the bigger edge count.... In PAGE 6: ... In Table 1 of this paper, the number of edge swaps is about a half of the edge count of the bigger input mesh. In Table1 of [LL04], the edge swap count is similar to the bigger edge count. Table 1 also shows the height of a dependency graph con- structed for connectivity interpolation described in Sec.... In PAGE 6: ... In Table 1 of [LL04], the edge swap count is similar to the bigger edge count. Table1 also shows the height of a dependency graph con- structed for connectivity interpolation described in Sec. 4.... ..."

### Table II. Comparison of multi-level graphs computed through min-overlay and according to [Schulz et al. 2002]. opt denotes the number of edges divided by the number of vertices obtained with min-overlay, while blowup indicates the multiplicative factor indicating how many edges in relation are constructed using the non-minimal method. We distinguish the case of unit (left) and genuine (right) edge lengths.

2006

Cited by 6

### Table 1: Some statistics on test models. #nodes describes the number of primitive shapes that were found in the point cloud and by that the number of nodes in the resulting topology graph. #edges states how many edges describing neighborhood relations between the primitive shapes were found. top.graph shows how long it took to build the topol- ogy graph. The last column describes how much time was needed for matching the query graph.

### Table 4. For each benchmark, the rst column shows the number of interference edges right after the rst build phase. The rest of the table shows the ratio of removed edges due to the positive impact for each heuristic, just before the rst selection phase. The table shows that aggressive (optimistic) coalescing removes four times as many interference edges as iterated coalescing does on average. It also shows that optimistic+ coalescing removes an average of 3% more interference edges. Benchmarks Number Conservative Iterated Aggressive Optimistic+

1998

"... In PAGE 21: ... Table4 : The reduction ratio of interference edges due to the positive impact of coalescing. 6.... ..."

Cited by 21

### Table 4 lists the various forms of labels that may appear in a constructed graph. For each form of label, it gives a bound on the number of edges with a label of that form (column 2), and shows the productions in which a label of that form appears on the right-hand side (column 3). Also, for each kind of label, Table 4 shows how many productions the CFL-reachability Algorithm may use with a given edge with that kind of label (column 4), and how many new edges the CFL-reachability 20

"... In PAGE 19: ...2.2, we present Table4 which summarizes all of the di erent types of edge labels that may be used in a constructed CFL-reachability problem, including those introduced by the normalization of the grammar. For every given type of edge label, Table 4 also shows a bound on the number of edges with a label of that type, and a bound on the number of steps the CFL-reachability Algorithm performs on any given edge with a label of that type.... In PAGE 19: ...ion 4.2.2, we present Table 4 which summarizes all of the di erent types of edge labels that may be used in a constructed CFL-reachability problem, including those introduced by the normalization of the grammar. For every given type of edge label, Table4 also shows a bound on the number of edges with a label of that type, and a bound on the number of steps the CFL-reachability Algorithm performs on any given edge with a label of that type. Throughout the rest of the section, we use v to refer to the number of variables in the set constraint problem, t to refer to the number of constraints, n to refer the number of nodes in the graph (n = v + t), and r to refer to the maximum arity of a constructor.... In PAGE 22: ... The accounting is more straightforward in most other cases. Table4 summarizes the results. A bound on the amount of work performed is found by summing column 4 and column 5 and then multiplying by column 2.... In PAGE 23: ...for a given edge Form of label # of edges Productions with label on the right-hand side # ex- amined produc- tions Total # of at- tempts to add an edge Id O(n2) Id ::= Id Id 1 O(n) Id-c?1 i ::= Id c?1 i O(t) O(t) Ground-Id ::= Ground Id 1 1 Rev Id O(n2) Rev Id ::= Rev Id Rev Id 1 O(n) G ::= Rev Id Ground-Id 1 O(n) Rev c?1 i -Rev Id ::= Rev c?1 i Rev Id O(t) O(t) Ground O(v) Ground-EdgeVitoVj ::= Ground EdgeVitoVj O(v) O(v) Ground-Id ::= Ground Id 1 O(n) ci O(t) ci-MarkVa1-VarGrAtV (k) a0 ::= ci MarkVa1-VarGrAtV (k) a0 O(t) O(t) Rev ci O(t) MarkVa1-VarGrAtV (k) a0 -Rev ci ::= MarkVa1-VarGrAtV (k) a0 Rev ci O(t) O(t) c?1 i O(t) Id-c?1 i ::= Id c?1 i 1 O(n) Rev c?1 i O(t) Rev c?1 i -Rev Id ::= Rev c?1 i Rev Id 1 O(n) EdgeVitoVj O(tr) Ground-EdgeVitoVj ::= Ground EdgeVitoVj 1 1 MarkViGrAtVj ::= EdgeVitoVj Ground-EdgeVjtoVi 1 1 EdgeVjtoVj O(v) G-EdgeVjtoVj ::= G EdgeVjtoVj 1 O(n) Ground ::= EdgeVjtoVj G-EdgeVjtoVj 1 1 G O(n2) G-EdgeVjtoVj ::= G EdgeVjtoVj O(v) 1 Ground-Id O(n2) G ::= Rev Id Ground-Id 1 O(n) G-EdgeVjtoVj O(n2) Ground ::= EdgeVjtoVj G-EdgeVjtoVj 1 1 MarkVajGrAtVa0 O(tr) MarkVa1-VajGrAtV (k) a0 ::= MarkVa1-Vaj?1GrAtV (k) a0 MarkVajGrAtVa0 O(tr) O(tr) MarkVa1-Vaj?1GrAtV (k) a0 O(tr) MarkVa1-VajGrAtV (k) a0 ::= MarkVa1-Vaj?1GrAtV (k) a0 MarkVajGrAtVa0 1 1 MarkVa1-VarGrAtV (k) a0 O(t) ci-MarkVa1-VarGrAtV (k) a0 ::= ci MarkVa1-VarGrAtV (k) a0 O(r) O(t) MarkVa1-VarGrAtV (k) a0 -Rev ci ::= MarkVa1-VarGrAtV (k) a0 Rev ci O(r) O(t) Ground ::= MarkVa1-VarGrAtV (k) a0 1 1 Ground-EdgeVjtoVi O(t) MarkViGrAtVj ::= EdgeVitoVj Ground-EdgeVjtoVi 1 1 ci-MarkVa1-VarGrAtV (k) a0 O(t) Id ::= ci-MarkVa1-VarGrAtV (k) a0 Id-c?1 i 1 O(t) MarkVa1-VarGrAtV (k) a0 -Rev ci O(t) Rev Id ::= Rev c?1 i -Rev Id MarkVa1-VarGrAtV (k) a0 -Rev ci 1 O(t) Id-c?1 i O(nt) Id ::= ci-MarkVa1-VarGrAtV (k) a0 Id-c?1 i O(t) O(t) Rev c?1 i -Rev Id O(nt) Rev Id ::= Rev c?1 i -Rev Id MarkVa1-VarGrAtV (k) a0 -Rev ci O(t) O(t) Table4 : Total work performed by the CFL-Reachability Algorithm on a constructed problem. Column 1 shows the forms of the labels used in a constructed problem.... ..."

### Table 3. Number of edges in Canonical Critical Subgraphs of the triangle-free graphs. The canonical critical graph is obtained by deleting as many edges as possible choosing them in vertex order. The size of critical sets and subgraphs are shown in tables 3 and 4. We can do this only up to n = 125 because of the computational expense. As n increases in Table 3, we see that the size of critical subgraphs converges at the rst frozen point and threshold. The size of these graphs grows at least linearly with n, suggesting that critical graphs have size O(n). The size of critical sets in Table 4

1999

Cited by 16

### Table 2: Percentage of nding the best mapping for the adaptive (a.s.) and depth- rst (d.f.s.) sequencings, for several classes of source graphs and target architectures.For nested-dissection graphs, depth- rst sequencing is more e cient on aver- age than adaptive sequencing; it does better for large hypercubes, and its supe- riority is obvious for bidimensional grids, with 72:0 percent against 44:0 percent. Because of the high density and heavy edge weights of nested-dissection graphs, knowing more accurately many edge dilations (and particularly the ones of the heaviest edges) compensates the risk of computing worse partial mappings in the left branches of the bipartitioning tree, all the more when edge dilations 12

1996

Cited by 13

### Table 2: Edge addition for activity on 1000 residential accounts over a 6 month period. For each month we show the percentage of the edges that we observed that we had not seen yet. The column marked Cumulative Percent shows the unique edges we have seen through the entire study up until that point as a percentage of the union of all edges.

2003

"... In PAGE 5: ... The column marked Cumulative aggregates the subsequent months to show how many of the edges we have seen overall. Table2 shows edge addition e ects on the same sample over the same period. This time for each month, we note how many edges are seen for the rst time.... ..."

Cited by 12