### Table 1. The possible conflgurations of three reality edges in a cycle and the category of mutations acting on them. Dotted arcs are not necessarily reality edges but alternating paths of reality end desire edges.

"... In PAGE 6: ...) It is easy to show that cycle-increasing mutations act on one cycle. If three reality edges are in one cycle, they are in one of the eight possible conflgurations on Table1 . The idea of the algorithm is that for each conflguration and reality... In PAGE 7: ... Dotted arcs are not necessarily reality edges but alternating paths of reality end desire edges. Existence of mutations Each conflguration on Table1 can be traversed in... In PAGE 8: ...Table1 can be traversed. Eight conflguration times the six possible traversing gives 48 cases, and this is the 3! possible permutations of the visiting order of the three edges multiplied by the 23 possible signs of the three edges.... ..."

### Table 1: Mesh size and quality for four-element airfoil meshes. Finally, Figures 12 and 13 show, respectively, the angle distribution and relative edge lengths for the four-element airfoil meshes. As noted previously, the angle quality degrades with mesh coarsening. Like- wise, the edge lengths for the coarser meshes do not match the desired edge lengths as closely as for the ner meshes.

1998

"... In PAGE 9: ... shows closeups of the coarse meshes at the trailing edge of the main element. A summary of size and angle quality information for these meshes is given in Table1 . The mesh quality remains good for the rst two coarse meshes, but degrades very badly for the third coarse mesh; this is an area which requires more work.... ..."

Cited by 2

### Table 1: Results of the decomposition approach for real-world instances. The forth column contains the desired edge length, the fth column gives the number of triangles (T) among the macro elements. (C) refers to the number of homogeneous components in the mesh decomposition, the number of active components is given in brackets. Templates (1), (2), and (3) are the standard templates, whereas template (4) is the general template for quadrangles. The last column gives the CPU time (seconds) to solve the minimum cost bidirected ow instances with CPLEX.

"... In PAGE 10: ...dge lengths. The results obtained by our decomposition approach are very appealing. Most remarkably, the decomposition approach always yields a feasible solution if one exists, neither some kind of \emergency quot; template is necessary nor do we leave unre ned \holes. quot; Table1 shows the distribution of realized templates for quadrangles. However, more expressive quantities for the mesh quality will be given in the following subsection.... In PAGE 10: ... We set a time limit of 300 seconds to solve a minimum cost bidirected ow instance, however, in all cases the actual solution time for a near-optimal feasible solution was less than 25 seconds. The time to compute the optimal solution for these problems is given in Table1 . The running time ranges from less than a second to 244 seconds of CPU time for the instances given there.... ..."

### Table 1: New parameterized complexity results for several NP-complete variants of Vertex Cover treated in this work. The parameter k is the size of the desired vertex cover, m denotes the number of edges, and n denotes the number of vertices.

2006

"... In PAGE 3: ... The parameter k is the size of the desired vertex cover, m denotes the number of edges, and n denotes the number of vertices. surveyed in Table1 . In our presentation, n denotes the number of vertices and m denotes the number of edges of the input graph.... In PAGE 20: ...Conclusion We extended the parameterized complexity picture for natural variants and gen- eralizations of Vertex Cover. Table1 in Section 2 summarizes our new results. Notably, whereas the fixed-parameter tractability of Vertex Cover immedi- ately follows from a simple search tree strategy, this does not appear to be the case for all of the problems studied here.... ..."

### Table 1: Statistics relative to the numerical evaluation of the quadtree meshes. globally well-shaped and conform to the desired sizes. However, the average edge length is closer to p2 than to the unit length (this is most likely due to the discrete [2:1] transition introduced during the tree decomposition). The e ciency index con rms that the elements sizes are compatible with the desired sizes. So far, the results con rm the e ciency of the algorithm, between 1.5 and 2.5 millions elements per minute are generated on a HP 9000 PA8200,

1998

Cited by 5

### Table 2: Accuracy of different classification models in an overall test. after the classification. On the right side of the same figure the analysis of errors from the same learning process are presented. Edges of each line shows the target (left) and desired output values for given case (person). Note that most slopes of the error-lines are small, meaning that a given case is not clear and can not be assigned to a single class. More over, most of these errors are not really errors because they may indeed correspond to two classes.

"... In PAGE 5: ...5 is shown. In Table2 the overall performance is presented and in Table 3 the generalization after dividing the whole set into training and testing sets for 10% + 90%and5%+95% learning. Figure 4 shows the confusion matrix (on the left).... ..."

### Table 1: Algorithms for identifying web communities. EXACT-FLOW-COMMUNITY augments the web graph in three steps: an artificial source, D7, is added with infinite capacity edges routed to all seed vertices in CB; each preexisting edge is made bidirectional and rescaled to a constant value CZ; and all vertices except the source, sink, and seed vertices are routed to the artificial sink with unit capacity. After augmenting the web graph, a residual flow graph is produced by a maximum flow procedure. All vertices accessible from D7 through non-zero positive edges form the desired result and satisfy our definition of a community. APPROXIMATE-FLOW-COMMUNITY takes a set of seed web sites as input, crawls to a fixed depth including inbound hyperlinks as well as outbound hyperlinks (with inbound hyperlinks found by querying search engines), applies EXACT-FLOW-COMMUNITY to the induced graph from the crawl, ranks the sites in the community by the number of edges each has inside of the community, adds the highest ranked non-seed sites to the seed set, and iterates the procedure. The first iteration may only identify a very small community; however, when new seeds are added, increasingly larger communities can be identified. Note that CZ is heuristically chosen.

2002

"... In PAGE 3: ... Note that CZ is heuristically chosen. our method works without an explicit sink site via graph augmentation as described in Table1 . See [4] for the corresponding theorem and proof.... In PAGE 3: ... Thus, separating the source from the sink finds a community that is strongly connected internally, but relatively disconnected externally to the rest of the graph. Table1 also shows an approximate version of the approach, APPROXIMATE-FLOW-COMMUNITY, which uses a subset of the web graph found by a fixed depth crawl that follows both inbound and out- bound hyperlinks. Results are improved on each iteration by reseeding the algorithm with additional web sites found in the earlier steps.... ..."

Cited by 76

### Table 1: Keytransformationsusedin theVHL.Manymoretransformationsareused duringcalibration(thus the skippednumbers).

1999

"... In PAGE 3: ... Some of these calibrations can be collapsed to reduce the number of transformations needed during operation of the VHL. Table1 shows the key transformations in the style of Tuceryan et al. [22].... ..."

Cited by 13

### Table 1: Algorithms for identifying web communities. EXACT-FLOW-COMMUNITY augments the web graph in three steps: an artificial source, a0 , is added with infinite capacity edges routed to all seed vertices in a72 ; each preexisting edge is made bidirectional and rescaled to a constant value a73 ; and all vertices except the source, sink, and seed vertices are routed to the artificial sink with unit capacity. After augmenting the web graph, a residual flow graph is produced by a maximum flow procedure. All vertices accessible from a0 through non-zero positive edges form the desired result and satisfy our definition of a community. APPROXIMATE-FLOW-COMMUNITY takes a set of seed web sites as input, crawls to a fixed depth including inbound hyperlinks as well as outbound hyperlinks (with inbound hyperlinks found by querying search engines), applies EXACT-FLOW-COMMUNITY to the induced graph from the crawl, ranks the sites in the community by the number of edges each has inside of the community, adds the highest ranked non-seed sites to the seed set, and iterates the procedure. The first iteration may only identify a very small community; however, when new seeds are added, increasingly larger communities can be identified. Note that a73

2002

"... In PAGE 3: ... Note that a73 is heuristically chosen. our method works without an explicit sink site via graph augmentation as described in Table1 . See [4] for the corresponding theorem and proof.... In PAGE 3: ... Thus, separating the source from the sink finds a community that is strongly connected internally, but relatively disconnected externally to the rest of the graph. Table1 also shows an approximate version of the approach, APPROXIMATE-FLOW-COMMUNITY, which uses a subset of the web graph found by a fixed depth crawl that follows both inbound and out- bound hyperlinks. Results are improved on each iteration by reseeding the algorithm with additional web sites found in the earlier steps.... ..."

Cited by 76

### Table 1 can be traversed. Eight conflguration times the six possible traversing gives 48 cases, and this is the 3! possible permutations of the visiting order of the three edges multiplied by the 23 possible signs of the three edges. Instead of conflgurations and traversing, we will talk about visiting permutations and signs, there is a one-to-one correspondence between them. Therefore the problem is to tell in constant time for each permutation, sign pattern and reality edge whether or not there are other two reality edges to the right being in the given permutation and sign pattern. Any sign pattern can be discussed in a general way, the three signs will be denoted by s1, s2 and s3 from left to right. Another observation is that it is enough to give algorithms for the 1; 2; 3, the 2; 1; 3 and 1; 3; 2 permutations since the cycle can be traversed with starting the tour on the leftmost edge in the other direction. This will cause a change in the permutation such that 3 and 1 will be swapped, and all signs will change to the other sign. For example, on Fig. 3. the cases on the right column will turn to the cases on the left column if the cycle is traversed in a reverse order.

"... In PAGE 6: ...) It is easy to show that cycle-increasing mutations act on one cycle. If three reality edges are in one cycle, they are in one of the eight possible conflgurations on Table1 . The idea of the algorithm is that for each conflguration and reality... In PAGE 7: ...onflguration transposition inv. trans. to the left inv. trans. to the right +2-c +1-c +1-c +1-c +2-c \rest quot; +1-c \rest quot; +2-c +1-c \rest quot; \rest quot; \rest quot; +1-c +1-c \rest quot; +1-c \rest quot; \rest quot; \rest quot; +1-c \rest quot; \rest quot; \rest quot; Table1 . The possible conflgurations of three reality edges in a cycle and the category of mutations acting on them.... In PAGE 7: ... Dotted arcs are not necessarily reality edges but alternating paths of reality end desire edges. Existence of mutations Each conflguration on Table1 can be traversed in... ..."