This document proposes a new approach to speed up combinatorial search strategies using stack and hash table data structures. The method uses a temporary array to help generate combinations in each iteration. A stack is created to push the first parameter, and the algorithm iterates popping values from the stack until it is empty. Indexes of a combination array are set to the stack length and popped values. Hashing provides a more reliable and flexible method of data retrieval than other structures, and is faster than searching arrays or lists. This approach could speed up generation and search processes for combinatorial approaches.

1. ANewApproach to Speed up Combinatorial
Search Strategies Using Stack and Hash Table
Data Engineering and Cloud Computing Department
Reva University
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2. Outline
o Abstract
o Stack
o Algorithm of insertion in Stack :(PUSH)
o Algorithm of deletion in Stack :(POP)
o Hash Table
o Method
o Advantage
o Conclusion
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3. Abstract
Owing to the significance of combinatorial search strategies both for academia and
industry, the introduction of new techniques is a fast growing research field these
days. Nonetheless, despite the kind of problem these approaches solve, they are
heavy computation with the number of combinations and growing search space
dimensions. This paper presents a new approach to speed up the generation and
search processes using a combination of stack and hash table data structures. This
approach could be put to practice for the combinatorial approaches to speed up the
generation of combinations and search process in the search space.
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4. Stack
• A stack is a Last In, First Out (LIFO) data structure, objects inserted last are the
first to come out of the stack
• Anything added to the stack goes on the “top "of the stack
• Anything removed from the stack is taken from the “top” of the stack
• Things are removed in the reverse order from that in which they were inserted
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5. ALGORITHM
OF
INSERTION
IN STACK:
(PUSH)
Procedure pushes an ITEM onto the stack
Step:1 [Stack already filled?]
If top=max, then: Print: OVERFLOW and Return.
Step:2[Increase TOP by 1]
Set Top=Top+1
Step:3 [Insert ITEM in new TOP position.]
Set STACK[TOP]:=ITEM
Step :4 Return
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6. ALGORITHM
OF I
DELETION
IN STACK:
(POP)
Procedure deletes or popes an ITEM from the stack
Step 1: [Stack has an item to be removed?]
If top=0, then: Print: UNDERFLOW and Return.
Step 2: Set ITEM:=STACK [TOP].
Step 3:[Decrease TOP by 1]
Set TOP =TOP-1
Step 4: Return
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7. Hash Table
 A hash table is a data structure that stores elements and allows insertions, lookups,
and deletions to be performed
 A hash table is an alternative method for representing a dictionary
 In a hash table, a hash function is used to map keys into positions in a table. This
act is called hashing
 Hash Table Operations
 Search: compute f(k) and see if a pair exists
 Insert: compute f(k) and place it in that position
 Delete: compute f(k) and delete the pair in that position
 In ideal situation, hash table search, insert or delete
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8. Example
Let's see the following numbers or keys that you wanted to map into an array of 10
elements:
123456
123467
123450
To apply the division method, you could divide the number by 10 (or the maximum
number of elements in the array) and use the remainder (the modulo) as an index. The
following would result:
123456 % 10 = 6 (the remainder is 6 when dividing by 10)
123467 % 10 = 7 (the remainder is 7)
123450 % 10 = 0 (the remainder is 0)
These numbers would be inserted into the array at positions 6, 7, and 0 respectively. It
might look something like this:
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9. Method
I. Additionally, a temporary array was created with index i to help the generated
combinations in each iteration (Steps 1-2).
II. A stack data structure (S) was created and the first parameter (0) was pushed
inside (Steps 3-4).
III. The algorithm continued to iterate until the stack became empty (Step 5).
IV. The index number i of the Comb array was set to length of S - 1 and the value v
of this index i was set to the top value in the stack (i.e. pop) until the v was less
than k (Steps 6-9).
V. Furthermore, the algorithm continued to increment the i and v then push the value
of v into S until the index number was equal to the length of the required
interaction strength t (Steps 9-15).
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10. Method
Input: Input-parameters k and combination strength t
Output: All t-combinations of k where
k = k1, k2, k3, kn
1 Let Comb be an array of length t;
2 Let i be the index of Comb array;
3 Create a stack S;
4 S ← 0;
5 while S = null do
6 i =(the length of S - 1);
7 v = pop the stack value;
8 while pop value < k do
9 set Comb of index (i) to v;
10 i ← i + 1;
11 v ← v + 1;
12 push v to stack;
13 if i = t then
14 Add Comb to final array;
15 break;
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11. Advantage
• Hashing provides a more reliable and flexible method of data retrieval than any
other data structure.
• It is faster than searching arrays and lists.
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12. Conclusion
In this paper, we have presented our proposed approach to generate and search for the
interaction elements of the input parameters of the combinatorial search strategies.
Based on our experience with these strategies, the generation of input parameters
combinations and search for the interaction elements for the fitness function will
slow down the generation process of the final test suite of the interaction.
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13. Thank you!
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