### Table 18: Results of LBN+/LBP+ for TSP graphs and preprocessed versions of these

2004

### Table 8: Upper bounds and results of MMD and MMD+ for TSP graphs and preprocessed versions of these

2004

Cited by 17

### Table 1 Now suppose edges e and f are both in the 2TSP graph G1, and G2 is any other 2TSP graph. Graphs Gs and Gp are as de ned above. Table 2 relates the class of e and f in G1 to their class in Gs and Gp.

"... In PAGE 14: ... Suppose e is an edge in G1 and f is an edge in G2. Table1 shows the relation between the class of edge e in G1, edge f in G2 and the pair e; f in Gs and Gp. For example, if edges e and f are cut edges in G1 and G2 respectively, then e and f must be an s; t-separating pair in Gp.... In PAGE 16: ... Since H is a least constituent graph, H must be formed by composing two 2TSP graphs H1 and H2 such that H1 contains e and H2 contains f. According to Table1 , e and f cannot be an s; t-non-separating pair in H. Therefore they must be cut edges for H, as claimed.... ..."

### Table 1 Now suppose edges e and f are both in the 2TSP graph G1, and G2 is any other 2TSP graph. Graphs Gs and Gp are as defined above. Table 2 relates the class of e and f in G1 to their class in Gs and Gp.

"... In PAGE 13: ... Suppose e is an edge in G1 and f is an edge in G2. Table1 shows the relation between the class of edge e in G1, edge f in G2 and the pair e; f in Gs and Gp. For example, if edges e and f are cut edges in G1 and G2 respectively, then e and f must be an s; t-separating pair in Gp.... ..."

### Table 1: Dimensions of graphs generated from TSP library instances.

2003

Cited by 28

### Table 2 Let z be a non-leaf node in decomposition tree T and let Tz denote the subtree of T rooted at z. The 2TSP graph H that has Tz as a decomposition tree is a constituent graph for G with respect to T . If e and f are edges in G then the least constituent graph containing e and f is the smallest constituent graph of G that contains both e and f. This graph has as a decomposition tree Tz where z is the least common ancestor of ^ e and ^ f in T . Let G be a 2TSP graph containing edges e and f and let H be the least constituent graph of G that contains e and f. Table 3 gives the relation between the class of an edge in a 2TSP graph and its class in a constituent of that graph.

"... In PAGE 14: ... Graphs Gs and Gp are as de ned above. Table2 relates the class of e and f in G1 to their class in Gs and Gp.... ..."

### Table 2: Runtime of the TSP program with 14{node graph as input. Di erent system con gurations and memory consistency are used.

"... In PAGE 21: ... Hence, the run time of the program depends on this ordering when the machines are not the same. Table2 present results of running this program with the same input but with di erent con gu- rations. In this table, slow means the slowest machine and fast means one of the faster machines.... ..."

### Table 2: Pair of nodes t[sc, G] and t[sp, G] associated to a triple t in a graph G.

"... In PAGE 7: ... The set t[sc, G] will contain pairs of nodes in the graph G[sc] and the set t[sp, G] will contain pairs of nodes in G[sp]. Formally, we denote by t[sc, G] the pairs of nodes (u, v), u, v nodes in G[sc] as described in Table2 (second column). Analogously, we define t[sp, G] using Table 2 (third column).... In PAGE 7: ... Formally, we denote by t[sc, G] the pairs of nodes (u, v), u, v nodes in G[sc] as described in Table 2 (second column). Analogously, we define t[sp, G] using Table2 (third column). As an example, for a triple of the form (a, sc, b) in a graph G, (a, b, c)[sc, G] contains the single pair of nodes (na, nb), where both nodes na, nb belong to G[sc].... ..."