### Table 1. Comparison of Hilbert and Best R-Tree Traversal Orderings

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### Table 6. Normalized energy consumption and SEM for Hilbert programs

### Table 5: Hilbert apos;s Axioms for Group III

### Table 10: Hilbert basis when D4 acts as #3 + #5.

### Table 13: Hilbert basis when D4 acts as #5 + #5.

### Table 1. Hilbert Curve State Diagram: for Mapping from One Dimension

"... In PAGE 5: ... This state diagram is then expressed in tablular form in Tables 1 and 2. Table1 contains a row for each state and is used in the mapping from one to n dimensions. Within a row, points, expressed as n-points, are ordered by sequence number, or derived-key value.... In PAGE 14: ... Our rules result in a number of states given by n2 n;1 According to Bially, this is the minimum possible. The size of a single state is determined by the number of derived-key { next-state pairs in Table1 , for example, and is given by the expression 2 n . The complexity of the mapping algorithm given in Algorithm 1 can be seen to be O(kn) and this is the same as for the algorithm given by Butz which relies on calculation alone, although the latter includes a higher constant fac- tor.... ..."