HD-Tree: An Efficient High-Dimensional Virtual Index Structure Using a Half Decomposition Strategy

Round 1

Reviewer 1 Report

The article ‘HD-tree: an efficient high-dimensional virtual index structure using a half decomposition strategy’ presents an improvement over the existing data structure called ‘D-Tree’. The authors follow a different decomposition strategy that ensures fewer nodes and better performing range queries and repeated insertion. The proposed approach was also tested on a synthetic dataset which demonstrates the improved performance.

 

The authors have presented a brief introduction of various algorithms and covered D-Tree in detail, since it is being improved in the article. The listings related to the four algorithms and the associated description briefly describes the main aspects of HD-Tree. The experiments presented afterwards, demonstrate the improvement using these proposed algorithms.

 

Though the article is globally well written, it needs significant modifications. There are several places where clarifications/corrections are required; some of them I indicate below.

 

In section 2

• Lines 91-95 are not very clear. This part presents the D-tree. However, a mix of the term ‘binary’ and the use of decimal values makes it difficult to understand.
• Line 110: “The node number of a full” What is Node number?

I think the the Section 2 ‘Background’ need to introduce all the important terms used in the article. I cited here just two examples. The terms related to D-Tree, if used by HD-Tree need to be defined and compared.

 

In section 3

• Discussion on hashmap is missing in the article, especially while explaining D-Tree and HD-Tree using an example in Lines 159-166.
• Lines 213-216 and Figure 4 need to be homogenized. dimen is used in the text and dimension in the Figure. Are they same? Or are they different?
• Definitions of rectangle and basic rectangle are needed before the lines 213-216
• Line 258: that the encoding and its prefix encodings have one in the hash table. What does one mean here?

 

Same comment as above, a brief description of key terms is needed.

 

In section 4:

1. Figure 5 and the text description in Lines 294-303 are not coherent. Are there three different datasets? or Figure 5 is just a projection of the same dataset. Why did the authors choose these datasets and not some existing benchmark datasets?
2. Figures 6 (a-e) not clear, what are the differences between the three images? I am lost with the three sets of images and the legends are not very clear. The textual description is not helpful.

 

The article needs proofreading. The figures and the algorithms need to be explained in detail. Since comments are missing in the algorithms, a better approach would be to explain the key parts of the algorithm using line numbers. It will be equally interesting to see other approaches that have extended the D-Tree algorithm.

Minor errors

• Line 61: One of the most advanced method-> One of the most advanced methods
• Line 92-93 binary codes of 100, 101, 102, 103 (binary).: Not clear, either use the binary values or remove (binary)
• Figure 2: Example of four-dimensiona -> Example of four-dimensions
• Line 111: it only need to -> it only needs to
• Lines 126-127: which is the suffix code of one of it and its upper codes: Not clear
• Lines 135: we proposes a -> we propose a
• Figure 5 : Unifrom -> Uniform

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

This manuscript falls within the scope of the journal Algorithms and deals with a very interesting field. This paper presents an improvement, called HD-tree, of a previous indexing method for multidimensional point data, called D-tree. which the new one has faster I/O and better time performance when constructing and when querying the new structure. They have tried to prove the usefulness and contributions of the proposed topic. The authors made an effort to write good paper. It is interesting and can be useful for other researchers, so it can be very useful for the wider scientific community.

• Abstract is concise with all necessary elements: with showed methodology, and results, but should be additionally improved. Please add aims of the study better than it. Specially try to bold that HD-tree has better time performance and other advantages. 
• You should apply a character distance before citations!! Line 47, change "KD-tree[9]" to "KD-tree [9]". And do it for other references. 
• Lines 79, 81, change "section" to "Section". 
• The methods are adequately described. The authors show algorithms in one well way, so this can help readers to better understanding the important tasks of paper and the author's proposal.
• Lines 98, 108, and many others, please change "Fig.1" to "Fig. 1" and do it for others. 
• In Line 225, change "Eq.1" to "Eq. 1" and do it for other cases. 
• Apply dot or comma signs after equations.
• The results are clearly presented. The authors put in the effort that explains in one understand way all obtained results. Their comments are supported by results. 
• The conclusions are supported by the results. In Line 358, please change "introduce" to "introduced". At the end of the conclusion write guidelines for future research.
• Update the reference list. I believe that you can apply new and recent papers. 

I propose a minor revision. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have provided an updated version of their article, for which I would like to thank them. They have incorporated all my comments in the new version.

 

The abstract has been updated and it is clearer about their proposed changes to the existing D-tree algorithm. In section 2, they have introduced the key concepts and presented their definitions. They may need to add the definition of point object (Line 105). They can also cite some existing works to help the readers find these concepts in the literature.

 

Step numbers have been added to explain the steps proposed by their algorithm. They have also provided a detailed explanation of the datasets and their characteristics, which may help the readers understand the updated subfigures in Figure 6.

 

The newly added line 429 In the conclusion is not very clear. I think the authors want to compare their proposed approach to the D-Tree. They also need to compare their proposed approach to the existing extensions of D-Tree.

 

Minor comments

1. Line 96: is also the rectangle mentioned above -> is a rectangle described above?
2. Line 101: 0x165 can get 0x16 and -> 0x165 can give 0x16 and?
3. Line 363: does’n occupy many nodes -> doesn’t occupy many nodes

Author Response

Please see the attachment.

Author Response File: Author Response.pdf