A NEW FREQUENT SIMILAR TREE ALGORITHM
MOTIVATED BY DOM MINING
Using RTDM and its New Variant — SiSTeR
Barkol Omer, Bergman Ruth and Golan Shahar
HP Labs, Technion City, Haifa, Israel
Keywords:
Frequent trees, Tree edit distance, RTDM, DOM, Web mining, Web data records.
Abstract:
The importance of recognizing repeating structures in web applications has generated a large body of work
on algorithms for mining the HTML Document Object Model (DOM). A restricted tree edit distance metric,
called the Restricted Top Down Metric (RTDM), is most suitable for DOM mining as well as less computa-
tionally expensive than the general tree edit distance. Given two trees with input size n
1
and n
2
, the current
methods take time O(n
1
· n
2
) to compute RTDM. Consider, however, looking for patterns that form subtrees
within a web page with n elements. The RTDM must be computed for all subtrees, and the running time
becomes O(n
4
). This paper proposes a new algorithm which computes the distance between all the subtrees
in a tree in time O(n
2
), which enables us to obtain better quality as well as better performance, on a DOM
mining task. In addition, we propose a new tree edit-distance — SiSTeR (Similar Sibling Trees aware RTDM).
This variant of RTDM allows considering the case were repetitious (very similar) subtrees of different quantity
appear in two trees which are supposed to be considered as similar.
1 INTRODUCTION
There is a growing interest in discovering knowledge
from complex data, which is organized as trees, rather
than as a single relational table. This research is
motivated by applications that manipulate molecular
data, XML data and Web content. We are partic-
ularly motivated by modern web applications. The
content of these applications is, invariably, automat-
ically generated using templates, whose content is
filled from databases, or web toolkits, such as Google
Web Toolkit. Such HTML documents are incredi-
bly complex. For example, the Google search page,
which presents a simple form, which a user perceives
as a few interface objects, contains about 100 objects
and its maximal depth is 12. While automatically gen-
erated content tends to be complex, it also tends to
be consistent. Thus, the same functional components
will tend to have similar DOM (Document Object
Model) structure. A key aspect of of understanding
DOM structures is, therefore, finding repeating DOM
structures. To find such structures, we propose a new
algorithm for finding frequent trees, which are simi-
lar, but not necessarily identical.
Frequent tree mining algorithms search for repeat-
ing subtree structures in an input collection of trees.
These algorithms vary in the restrictions that the re-
peating structure must adhere to, and in the type of
trees that are searched. These types include bottom-
up subtrees in ordered, labeled trees (Luccio et al.,
2001), induced subtrees, (Abe et al., 2002; Zaki,
2002), unordered trees (Luccio et al., 2004; Zaki,
2004) and embedded subtrees (Zaki, 2004). A good
overview of frequent tree mining may be found in
(Chi et al., 2005). For DOM structure mining, we are
interested in a particular tree mining scenario. The
trees are rooted, labeled and ordered. Unlike the al-
gorithm in (Luccio et al., 2001) the patterns we seek
are similar, but not identical.
There is also extensive prior research on similar-
ity between trees and on tree edit distance algorithms.
The prevalent definition of edit distance for labelled
ordered trees was proposed by (Tai, 1979). For un-
ordered trees the problem is known to be NP-hard
(Bille, 2005). For ordered trees, on the other hand,
polynomial algorithms exist (Tai, 1979; Zhang and
Shasha, 1989). Several researchers have identified re-
strictions to this definition of edit distance. One ex-
ample is the constrained edit distance, that was stud-
ied for ordered trees in (Zhang, 1995) and for un-
ordered trees (Zhang, 1996). In (Lu, 1984), a distance
metric based on node splitting and merging is defined.
238
Omer B., Ruth B. and Shahar G..
A NEW FREQUENT SIMILAR TREE ALGORITHM MOTIVATED BY DOM MINING - Using RTDM and its New Variant — SiSTeR.
DOI: 10.5220/0003658102300235
In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval (KDIR-2011), pages 230-235
ISBN: 978-989-8425-79-9
Copyright
c
 2011 SCITEPRESS (Science and Technology Publications, Lda.)

A better notion of tree distance for mining the web is
the top-down edit distance (Selkow, 1977), in which
insertions and deletions are restricted to the leaves of
the trees. A variant of this definition, the restricted
top-down distance (Reis et al., 2004), is even more
suitable for web mining, because it captures the pro-
cess of building web pages.
The setting of DOM mining prescribes the type
of trees we are working with. The repeating sub-
trees should include the actual content of the Web
page. The internal nodes are often a collection of DIV
and SPAN elements that can be aligned fortuitously.
Thus, the subtrees are bottom-up, in principle, but
small differences between trees are acceptable. The
acceptable differences, or edit operations, are also re-
stricted. The prevalent notion of edit distance does
not match our intuition about the differences between
HTML structures. For example, consider a complex
control embedded in a container element. The edit
distance between the control and its container is very
small. That is, it is quite difficult to isolate the con-
trol from its container. This distinction is enabled by
the Restricted Top-Down edit Metric (RTDM) (Reis
et al., 2004), because of the restrictions it places on
the permitted edit operations.
Given a collection of trees, we aim to find all the
repeating subtrees. A na¨ıve algorithm for finding such
repeating structure may be
1. For each pair of nodes in all input trees, compute
the RTDM of the subtrees rooted at these nodes
2. Cluster subtrees based on the computed distances
3. Output significant clusters
Unfortunately, step (1) is computationally expensive.
Given two trees with input size n
1
and n
2
, the running
time is O(n
1
2
· n
2
2
), i.e., squared in the size of the in-
put trees. Note that if we look for repeating structures
on a single tree with n nodes, e.g., one web page, the
running time is O(n
4
).
Our first main contribution is a new algorithm that
given two trees, computes the RTDM distances be-
tween all the subtrees in the first tree and all the sub-
trees in the second tree in time O(n
1
· n
2
). To find
the repeating subtrees in a single input tree with this
algorithm would take time O(n
2
), rather than O(n
4
).
We further present a variant of RTDM. We con-
sider the case where we want to be less sensitive to the
number of similar sibling subtrees within two trees we
compare. We present SiSTeR (Similar Sibling Trees
aware RTDM), which is a variant of RTDM. This
variant allows two trees to be considered as similar to
each other, even when they differ with regards to the
number of similar sibling subtrees within them (see a
schematic example in Figure 1). For example, con-
Figure 1: In some settings one would like to consider these
two trees as very similar as they differ only with regards to
the number of similar sibling subtrees within them.
sider a citation of an article site. Each entry has the
“Cited by” section. This subtree will have different
number of child-subtrees (the cites) for each article.
Regardless of their number, we would like to identify
two “Cited by” subtrees as similar.
1.1 Organization
We formally define the restricted edit distance mea-
sure in section 2. The dynamic programming algo-
rithm is presented in Section 3.1. We embed this al-
gorithm in the context of a frequent tree mining al-
gorithm in 3.3. In Section 3.2 we present and dis-
cuss our new RTDM variant, SiSTeR. We discuss
two DOM mining applications, DOM structure min-
ing and DOM pattern search, in Section 4. Section 5
provides experimental results, assessing the quality of
our algorithm and the SiSTeR metric.
2 PRELIMINARIES
This section lays the formal infrastructure for our dis-
cussion. We consider rooted-ordered-labelled trees.
Within our framework some manipulations are al-
lowed on trees. The allowed edit operations are some-
what different than that of standard operations and
best suit our setting. The operations allowed in our
framework are delete, insert and replace for subtrees.
For two trees T
1
= (V
1
,E
1
,L) and T
2
= (V
2
,E
2
,L) and
two vertices v
1
∈ V
1
and v
2
∈ V
2
we define the re-
place operation by T
1
(T
1
(v
1
) → T
2
(v
2
)) to be the tree
T
1
, when taking out the subtree T
1
(v
1
) and replacing
it with the subtree T
2
(v
2
), where the order of v
2
as
a child is the same order that v
1
had and the labels
given by L remain. When the context is clear we will
write T
1
(v
1
) → T
2
(v
2
), for short. The delete opera-
tion, then, is defined to be T
1
(v
1
) → λ and the insert
operation is defined to be λ → T
2
(v
2
), where λ de-
notes the empty tree. See Figure 2 for an illustration
of these edit operations.
Similar to other edit schemes, here too, we define
a sequence of edit operations S = s
1
,... , s
k
. The S-
derivation of T
1
is defined to be the sequence of trees
A NEW FREQUENT SIMILAR TREE ALGORITHM MOTIVATED BY DOM MINING - Using RTDM and its New
Variant — SiSTeR
239

Figure 2: Consider the three trees T
1
, T
2
and T
3
, such that
the white area is exactly the same in all. Then, T
2
is ac-
cepted from T
1
by removing the subtree rooted at u, i.e., by
the delete operation T
1
(T
1
(u) → λ) = T
2
. Respectively, T
3
is accepted from T
2
by insert operation λ → T
4
(w) and from
T
1
by replacing operation T
1
(u) → T
4
(w).
accepted by T
1
(s
1
)(s
2
)... (s
k
). If the resulting tree is
T
2
we say that S is a derivation from T
1
to T
2
and we
denote it by T
1
S
→ T
2
.
We define a cost function γ, which assigns a real
number to each edit operation. This cost function is
constrained in our framework to be a distance met-
ric. The cost for a sequence S is simply defined to
be γ(S) =
∑
k
i=1
γ(s). We then define the edit distance
between two trees T
1
and T
2
to be the lowest-cost S-
derivation from T
1
to T
2
. That is
D(T
1
,T
2
) = min
S : T
1
S
→T
2
{γ(S)}. (1)
In order to proceed, we broaden our definition to
(directed-ordered-labelled) forests. A forest is a set
of trees. The forests we are interested in are ordered
forests, which means that the set of trees is ordered.
All our definitions generalize naturally from trees to
forests (including those of S-derivation, γ, and D, al-
though the operations are still only defined for a single
connected tree at a time). Given a tree T = (V,E,L),
for any v ∈ V denote F (v) to be the forest which con-
sists all the subtrees of T with the children of v as
their roots, with the order of the trees in the forest re-
mains as the order of their roots as children of v.
Whereas prior top-down edit distance metrics are
defined as operations on nodes, we define the edit dis-
tance in terms of operations on subtrees. Nonetheless,
this definition differs from the top-down edit distance
definition in (Selkow, 1977) only in the relabel oper-
ation, and it is identical to RTDM (Reis et al., 2004).
3 SCIENTIFIC CONTRIBUTION
3.1 An All-Subtree Edit Distance
Algorithm
The following is straightforward:
Lemma 1. For any two non empty trees T
1
=
(V
1
,E
1
,L) and T
2
= (V
2
,E
2
,L) and two vertices
within v
1
∈ V
1
and v
2
∈ V
2
it holds that:
D(T
1
(v
1
),T
2
(v
2
)) =
(
γ(T
1
(v
1
) → T
2
(v
2
)) L(v
1
) 6= L(v
2
)
D(F
1
(v
1
),F
2
(v
2
)) otherwise
(2)
where, the distance between two forests is defined as
follows. For h ∈ {1,2} let F
h
be a forest whose roots
are v
1
h
,v
2
h
,... , v
ℓ
h
h
, and for each h denote by F
i→
h
the
forest whose roots are v
i
h
,... , v
ℓ
h
h
, then
D(F
1
,λ) =
∑
ℓ
1
k=1
γ(T
1
(v
k
1
) → λ)
D(λ,F
2
) =
∑
ℓ
2
k=1
γ(λ → T
2
(v
k
2
))
D(F
1
,F
2
) = min











γ(T
1
(v
1
1
) → λ)+D(F
2→
1
,F
2
)
γ(λ → T
2
(v
1
2
))+D(F
1
,F
2→
2
)
D(T
1
(v
1
1
),T
2
(v
1
2
))+
D(F
2→
1
,F
2→
2
)
(3)
To compute the edit distance of every pair of sub-
trees in two input trees efficiently, we adopt a dynamic
programming approach. Prior algorithms (Selkow,
1977; Reis et al., 2004) begin at the root of the tree
and follow the structure of the tree down. Our algo-
rithm, on the other hand, uses a bottom-up approach.
The challenge in the bottom up approach is that we
do not know which subtrees to match. We, therefore,
must match all subtrees to each other, which forms
the basis of the all-subtree computation. As the com-
putation moves up the tree, the constraints due to tree
structure are enforced.
To compute the edit distance we consider, for any
vertex in the tree T , the subtree rooted at this vertex
as a reversed pre-order sequence of vertices. (Note
that this is not equal to post-order as the right-most
child will appear first in our case.) Let v
i
be the ith
vertex in that order (i ≥ 1).
Given two trees T
1
and T
2
, for any h ∈ {1, 2} de-
note the index of the first child by
C
h
(i) =
(
i− 1 if v
i
of T
h
has children
0 otherwise
(4)
and the index of the previous sibling by,
I
h
(i) = i− |T
h
(v
i
)| (5)
We then define the two following matrices of di-
mensions (n
1
+ 1) × (n
2
+ 1), where the first, M
V
, is
aimed to capture the required distances between each
two subtrees, and the second, M
F
, assists the com-
putation of the first by holding the distance between
the forests that precedes the relevant trees. We define
M
V
(0,0) = M
F
(0,0) = 0, and:
KDIR 2011 - International Conference on Knowledge Discovery and Information Retrieval
240

i > 0 M
V
(i, 0) = γ(T
1
(v
i
) → λ)
j > 0 M
V
(0, j) = γ(λ → T
2
(v
j
))
i, j > 0 M
V
(i, j) =
(
γ(T
1
(v
i
) → T
2
(v
j
) L(v
i
) 6= L(v
j
)
M
F
(C
1
(i),C
2
( j)) otherwise
and
i > 0 M
F
(i, 0) = M
V
(i, 0) +M
F
(I
1
(i), 0)
j > 0 M
F
(0, j) = M
V
(0, j) + M
F
(0,I
2
( j))
i, j > 0 M
F
(i, j) = min





M
V
(i, 0) +M
F
(I
1
(i), j)
M
V
(0, j) + M
F
(i, I
2
( j))
M
V
(i, j) + M
F
(I
1
(i), I
2
( j))
(6)
Our algorithm will be standard dynamic program-
ming. For each i ≥ 0 - fill the ith row and column
in M
V
and M
F
. We claim the following:
Lemma 2. Given two directed-ordered-labelled trees
T
1
= (V
1
,E
1
,L) and T
2
= (V
2
,E
2
,L), the algorithm
above computes D(T
1
(v),T
2
(u)) for every v ∈ V
1
and
u ∈ V
2
(and in particular D(T
1
,T
2
)) correctly with
computation complexity O(n
1
· n
2
).
3.2 SiSTeR: A Similar Sibling Aware
Tree Metric Variant of RTDM
We present a variant of RTDM that makes our mea-
sure even more compatible with DOM applications.
Our Similar Sibling-Trees-aware RTDM (SiSTeR) is
a variant in which multiple subtrees are handled as a
set regardless of their number. In many websites sib-
ling subtrees might be very similar, and do not impact
similarity to other trees. Forum threads are a good
example. In forums, the number of posts in a thread
should not influence the similarity to other threads.
SiSTeR presents two additional operations to the
standard edit operations: one-to-many-replace and
many-to-one-replace. The semantics of these oper-
ations, is to allow a series of consecutive replaces
of one subtree with many subtrees (rather than re-
place and then a row of inserts or deletes in stan-
dard RTDM). For these operations, the cost is defined
to be the sum of the many replaces occurred. Note
that the replace operation is a special case of many-
to-one-replace and one-to-many-replace. Thinking of
strings, this allows distance 0 between the string a
and the string aaaaa, unlike the standard edit-distance
which requires 4 insert-operations. Here a one-to-
many-replace operation with cost-0 for each of the re-
place operation allows“similar-sibling awareness”. A
page in an article citation site on some paper will have
different number of “Cited by” entries. Still, the sub-
tree representing this “Cited by” part should be con-
sidered as similar to the same parts in different pages
where this number might be completely different. We
denote the SiSTeR edit distance by D
′
.
We revised our all-subtree distance algorithm to
use SiSTeR. In addition to M
F
and M
V
we will also
calculate M
OTM
and M
MTO
in the following way
i, j > 0 M
OTM
(i, j) = M
V
(i, j) + min
(
M
F
(I
1
(i), I
2
( j))
M
OTM
(i, I
2
( j))
(7)
i, j > 0 M
MTO
(i, j) = M
V
(i, j) + min
(
M
F
(I
1
(i), I
2
( j))
M
MTO
(I
1
(i), j)
(8)
In Equation 6 we insert the following change:
i, j > 0 M
F
(i, j) = min













M
V
(i, 0) +M
F
(I
1
(i), j)
M
V
(0, j) + M
F
(i, I
2
( j))
M
MTO
(i, j)
M
OTM
(i, j)
(9)
We have the following version of Lemma 2
Lemma 3. Given two directed-ordered-labelled trees
T
1
= (V
1
,E
1
,L) and T
2
= (V
2
,E
2
,L), the algorithm
above computes D
′
(T
1
(v),T
2
(u)) for every v ∈ V
1
and
u ∈ V
2
(and in particular D
′
(T
1
,T
2
)) correctly with
computation complexity O(n
1
· n
2
).
3.3 A Frequent Tree Algorithm for
Similar Occurrences
We propose an algorithm for finding sets of sub-
trees, such that each set contains a number of subtrees
which are similar to each other. Thus, the required
output is a meaningful clustering of bottom-up sub-
trees, in which the similarity measure is the RTDM.
Given the All-Subtree Edit Distance Algorithm pre-
sented in Section 3.1 the frequent tree algorithm is
straightforward.
Given the input tree perform the following:
1. Run the All-Subtree Edit Distance Algorithm as
appears in Section 3.1 getting the distance matrix
between every two subtrees in the input tree.
2. Based on this matrix, cluster the subtrees. We use
a clustering approach from (Koontz et al., 1976).
3. Using thresholds, output the significant clusters.
A NEW FREQUENT SIMILAR TREE ALGORITHM MOTIVATED BY DOM MINING - Using RTDM and its New
Variant — SiSTeR
241

4 APPLICATIONS
We discuss two applications for DOM mining.
4.1 DOM Structure Mining
The ability to efficiently find repeating structure in
trees has immediate applications for mining Web ap-
plications. Several classes of constructs common to
Web applications manifest as repeating DOM struc-
tures, including controls (e.g., the video controls com-
mon to YouTube.com site), records (e.g., search re-
sults in Google, items for purchase in Amazon and
videos in YouTube) and containers (For example, in
YouTube the Videos Being Watched Now and Most
Popular are containers.)
The algorithm was activated on the YouTube.com
site. Our experiment demonstrates that the algorithm
can be used to find all three types of structures. Con-
trols are easy to find, since the distance between the
entire cluster of subtrees is 0. Records can be found
by allowing clusters with some dissimilarity. We typ-
ically use 20% of the combined length of the subtrees
as a distance threshold. Containers are the most diffi-
cult to identify. Nevertheless, our algorithm can often
find containers using a higher distance threshold, e.g.,
60% of the subtree sizes. Another approach for find-
ing containers is to use the headers, which are more
similar, and identify the container from the header.
In YouTube, for which we used a threshold of 20%
one gets the container’s headers to be clustered to-
gether. The best method might combine information
from headers and complete subtrees.
4.2 DOM Structure Search
The All-Subtree Edit Distance algorithm is further ap-
plicable to the problem of searching the web for a pre-
defined DOM structure. In this use case, the user, or
an application, seeks a known DOM structure, i.e.,
a pattern, in a collection of web pages. However, the
pattern may be inexact. Applications that benefit from
efficient search for inexact patterns include mashups,
article extraction, and web automation.
It is straightforward to return the desired search
results. The time for this algorithm is O(n· k), where
n is the size of the page and k is the size of the pattern.
Assuming that the size of the pattern is small and in-
dependent of n, the algorithm is linear in the size of
the input tree.
5 RESULTS
5.1 Performance of the All-subtree Edit
Distance Algorithm
In this section, we assess the computation time re-
quired to compute a complete distance matrix for
DOM structures on a single web page. We compare
the proposed all-subtree edit distance algorithm from
Section 3.1, with applying the top-down algorithm
(RTDM) (Reis et al., 2004) for all subtrees. The re-
sults are presented in Table 1. Times shown are in
seconds. With the exception of the Amazon page, we
used the home page of the application. On Amazon,
the page we used is the results of searching for the
keyword “spectrum”.
Table 1: All-Subtree edit distance performance.
Site Size RTDM All-Subtree
YouTube.com 1809 9.2495856 0.781215
Marriott.com 2180 12.2494512 1.4530599
Amazon.com 3848 45.3417186 3.4842189
Google.com 669 0.7968393 0.1093701
iGoogle.com 1000 2.7655011 0.2187402
5.2 Results for DOM Record Mining
This section evaluates our system as a tool for DOM
record mining. In our test we chose pages that con-
tained both lists and tables of items, mainly from
previous works (Liu et al., 2003; Park and Barbosa,
2007; Zhai and Liu, 2005). We compared the preci-
sion and recall of our algorithm to DEPTA (Zhai and
Liu, 2005). We refer the reader to that work for com-
parison to other alternatives. Table 2 shows a sum-
mary of the set of pages in our experiment.
In Table 2, the Cnt column specifies the ground
truth about the number of records on the page. Corr
columns give the number of these items retrieved
by our Frequent Similar Trees and by DEPTA. The
DEPTA system frequently partitioned the records to
several sets. In this case, the the number of different
sets they are divided to is specified in brackets. al-
gorithm and by DEPTA. Due to space limitations, we
omit the columns showing the false positives for both
algorithms. For our Frequent Similar the precision is
100%. The DEPTA system has only two false posi-
tive giving a precision of 99.5%. We conducted ad-
ditional experiments on 30 more complex web pages.
With recall of 99% and precision of 100%, our perfor-
mance is superior to that of (Park and Barbosa, 2007),
which reported 85.7% recall and 100% precision. The
DEPTA system failed to run on these examples.
KDIR 2011 - International Conference on Knowledge Discovery and Information Retrieval
242

In general, one can say our results improve upon
prior systems in all respects. The main advantages of
our results are better recall in the harder cases, and no
over segmentation of the different sets.
Table 2: Experimental Results for Record Retrieving.
URL Tree Cnt Frequent DEPTA
Size Similar Trees
Corr Time Corr
www.amazon.com 3589 16 16 5.67 0
forums.gentoo.org 2833 25 25 4.24 18(4)
forums.sun.com 1729 15 15 0.97 15(3)
shoutwire.com 3543 20 20 4.6 20
messages.yahoo.com 2017 38 38 1.25 37
www.gateway.com 1461 6 6 1.14 0
shop.ebay.com 3664 50 50 4.53 40
www.google.com 848 11 8 0.17 0
www.abt.com 5408 40 40 10.62 40(9)
www.alibris.com 3225 25 25 3.73 25
bobsdiscountmarine 1318 16 16 1.69 0
www.cameraworld. 2115 25 25 1.47 25
www.compusa.com 2884 18 16 2.99 18(5)
www.cooking.com 2199 23 23 1.67 23
www.dealtime.com 1388 11 11 0.51 11(3)
www.drugstore.com 1572 42 42 0.67 42(14)
magazinesofamerica 759 6 6 2.2 6(2)
www.nextag.com 5351 30 30 8.72 30
nothingbutsoftware 3047 24 24 4.25 24(6)
www.refurbdepot.com 2890 15 15 4.81 10(5)
rochesterclothing.c 1820 16 16 0.98 16(4)
www.smartbargains.c 3095 24 24 3.06 0
www.tigerdirect.c 1527 20 20 0.93 20(5)
Sum / Average 2534 516 511 3.08 420
Recall 99% 81%
Only for successful 95%
5.3 Results for SiSTeR to Allow Detect
Similarity of Forums
This section evaluate the SiSTeR variant of RTDM
to allow to be aware to similar sibling subtrees when
computing the similarity between DOM trees. In
particular, when looking on forums’ DOM trees the
amount of lines or quotes in different posts create
a big difference between different posts. Here, the
posts each of which might have very different number
of lines or different number of quotes of other posts,
should be discovered as similar. We have tested our
algorithm using SiSTeR in comparison with the same
algorithm using RTDM. We have checked the simi-
larity between different posts in all of the following
forums: forums13.itrc.hp.com, forums.oracle.com,
hackquest.com, fdt.powerflasher.com/forum, and fo-
rum.projecteuler.net. In all these examples we no-
ticed a significant reduction in the number of clusters
that were discovered by using our similarity measure
as a distance metric. For example, in the forum pro-
jecteuler.net the RTDM-based algorithm outputed 10
different clusters of posts and another 20% of posts
that were in no cluster, while the SiSTeR-based algo-
rithm reduced it to 4 clusters and 10% un-clustered
posts.
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A NEW FREQUENT SIMILAR TREE ALGORITHM MOTIVATED BY DOM MINING - Using RTDM and its New
Variant — SiSTeR
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