Tree annotation of the proposed method includes both labeling and mapping schemes that work together to transform the XML tree into RDB storage. This approach adopted the node indexing of range labeling and prefix-based labeling as the initial annotation. Subsequently, we adopted the ORDPath ¹⁴ labeling scheme for any dynamic update operations. Henceforth, the proposed approach is named as ORD-GAP.

This labeling is in the format of ( s-e) l. The s denotes the start range while the e denotes the end range. The l expresses the level of each node position. These values for s and e are generated based on the gap g. The value g is calculated based on the formula: g= Σ (max _fan-out+max _depth).

Figure 2 illustrates the snippet view of the SIGMOD Record dataset ¹⁵ labelled with the ORD-GAP scheme. This dataset is commonly used for benchmarking purpose. It was chosen as it contains various fan-outs (number of children each node has) and many levels to better demonstrate how our proposed approach works. Firstly, we need to find out the value for g, whereby we need to know the max _fan-out and max _depth From the dataset, we observed that the maximum fan-out and maximum level is 4 and 6 respectively. As such, the gap value calculated by our algorithm (see Figure 3(a)) is 10. The root will always start with s as 1. The value of the following node is allocated from the gap value and the previous node’s value. In this case, since the gap is 10 and the value on the previous node’s is 1 (the root node), so, the node “issue” is assigned with 11 and tailed by node “author” with 21 for the s. The e value on node tree will be assigned once the s has reached the leaf node. In this case, if the s label is 31 and is a leaf node, then the e label will be assigned with 41 (by adding the s value with the gap value, such as 31+11), followed by the node “issue” with 51 as the e.

Figure 3 shows the pseudocode for ORD-GAP. Figure 3(a) shows the calculation of g which is formulated based on Σ (max _fan-out + max _depth) of the tree while Figure 3(b) shows the algorithm to assign a label. In Function GetGap, parent node and next level of current node is an input used to obtain g. The max _fan-out is the maximum number of child while max _depth is the deepest level of the tree.

Mapping schemes of ORG-GAP contain two tables to map the XML data in RDB. The two tables are internal table and text table. The internal table is called iTable, which is used for storing the node that does not contain a text value. A text table is called tTable, and is used to store the leaf nodes. The attributes of both tables consists of Start, End, Level, PStart, Value; Start node keeps the s value of node, End node keeps the e value of node, and Level node keeps the depth of a node from the root. Tables 1 and 2 are the partial view of iTable and tTable based on outcome after the labeling scheme (see Figure 2).

ORD-GAP supports all structural relationships which are level, P-C, A-D and sibling. A-D relationship is determined based on the following conditions:

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if (A(s) < D(s) < A(e)) and (D (level) – A (level) > 1).

Example: Let node1 be volume (21-51)2 and node2 be SigmodRecord (1-811)0, (SigmodRecord (1) < volume (21) < SigmodRecord (811) and volume (2) – SigmodRecord (0) > 1). As such, node1 and node2 has A-D relationship.

For P-C relationship, it is determined based on the following conditions:

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if (P(s) < C(s) < P(e)) and (C (level) – P (level) = 1)

The level difference should be equal to one since the parent would be only one level higher than the child. Another condition is the PStart value should be equal to P value.

Example: Let node1 be article (111-341)3 and node2 be authors (241-331)4, (article (111) < authors (241) < article (341) and authors (4) – article (3)=1). As such, node1 and node2 have P-C relationship.

Lastly for Siblings, if the nodes have the same PStart from the table, they are siblings.

Example: Let node1 be endPage (201-231)4 and node2 be authors (241-331)4. From iTable, both have PStart ‘6’. As such, node1 is a sibling of node2.

The insertion consists of left-most, right-most and in-between insertion. Each insertion includes an additional node known as medium node which represents the insertion of dynamic update. Thus, this method creates an unlimited insertion on XML tree which avoids node relabeling.

Figure 4 shows dynamic updates of left-most, in-between, and right-most insertion. The nodes represent the left-most insertion (21.1), in-between insertion (641.1), and right-most insertion (831.1). The insertion contains internal node and leaf node that will be mapped in the iTable (internal table) and tTtable (leaf node) as depicted in Tables 3 and 4, respectively.

We have implemented ORD-GAP using Java Development Kit (JDK) 8.0.510.16 on Netbean IDE 8.0.2 compile. Experimental evaluations were conducted to measure the performance of ORD-GAP as compared to ORDPath ¹⁴ and ME Labeling ¹⁶ approaches. These two existing approaches were taken for comparison because the technique does not require node re-labeling.

In the first part of the evaluation, the XML document is stored and transformed into RDB storage. The data insertion time and database storage size are recorded for all three approaches. After the storage is completed, we performed query retrieval to measure the performance of ORD-GAP, ORDPath and ME Labeling.

Lastly, our proposed approach ORD-GAP is put into evaluation to test for the dynamic update operations. All the experiments are performed on i7-3770 @3.4 processor with 16GB of RAM running on Windows 7. In the subsequence evaluations, we used the DBLP dataset ¹⁷ to demonstrate the possibility of supporting larger dataset.

In this evaluation, insertion time was recorded four times. We discarded the first reading to omit the buffering effect for consistency of execution time. The results recorded are the average time of the three consecutive times. Table 5 shows the insertion time of ORD-GAP, ORDPath ¹⁴ and ME labeling. ¹⁶ ORD-GAP is the fastest followed by ME Labeling and ORDPath.

Database storage consumption was evaluated to determine the storage space using ORD-GAP, ORDPath and ME Labeling approaches. From our experimental observation (see Table 6), we observed that ME Labeling requires higher storage space volume as compared to ORD-GAP and ORDPath due to the larger labeling size required as the depth of the XML tree increases.

As depicted, ORD-GAP reserved a gap between nodes, which delaying the initial node labelling, as ORD-GAP requires some calculation on retrieving the initial nodes. While ORDPath uses dot separated component byte-by-byte, that assigning node label is taken from the parent’s nodes toward the depth of XML tree. Whereas ME Labeling uses multiplication that causes the increases of size labels. The multiplication requires more time on the computation as the size label increase. Thus, both ORDPath and ME Labeling take less time for node labeling.

Table 7 displays the query node in tree representation and XPath notation for each query.

Figure 5 shows the query execution performance on various approaches. ORD-GAP is leading, followed by ME labeling and ORDPath. ORDPath require more time as compared to ORD-GAP and ME Labeling due to the number of elements in a node in DBLP. Although DBLP tree contains only three levels, it has multiple siblings in a node. Thus, the data model grows horizontally. ORDPath is prefix-based labeling that traverses using breadth-first search traversal. Likewise, ORDPath did not perform well. As the sibling’s node increases, the size label is increased. Hence, it requires more time to retrieve data in the database.

SIGMOD Record dataset available from: http://aiweb.cs.washington.edu/research/projects/xmltk/xmldata/www/repository.html#sigmod-record. ¹⁵

DBLP dataset available from:

http://aiweb.cs.washington.edu/research/projects/xmltk/xmldata/www/repository.html#dblp. ¹⁷