OPTIMIZATION OF LZW (LEMPEL-ZIV-WELCH) ALGORITHM TO REDUCE TIME COMPLEXITY FOR DICTIONARY CREATION IN ENCODING AND DECODING

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1 Asian Journal Of Computer Science And Information Technology 2: 5 (2012) Contents lists available at Asian Journal of Computer Science and Information Technology Journal homepage: OPTIMIZATION OF LZW (LEMPEL-ZIV-WELCH) ALGORITHM TO REDUCE TIME COMPLEXITY FOR DICTIONARY CREATION IN ENCODING AND DECODING *1 Nishad P M, 2 R. Manicka Chezian 1 Department of Computer Science, NGM College, Pollachi, India 2 Department of computer science NGM College Pollachi, Coimbatore, India. ARTICLE INFO Corresponding Author: Nishad P M* Ph.D Scholar, Department Of Computer Science, NGM College, Pollachi, India. nishadpalakka@yahoo.co.in KeyWords: Selenium RC, File Upload. ABSTRACT LZW (Lempel-Ziv-Welch) is a universal lossless data compression algorithm, which takes linear time in encoding and decoding. This paper discusses a methodology to reduce time complexity by combining binary search with LZW. The existing LZW compression algorithm takes large time for dictionary creation while encoding and decoding. By using binary search with LZW the time complexity can be reduced optimally and gradually because the comparison ratio is less while creating the dictionary. Especially while compressing the search for patterns in the table and also in the decompression algorithm for finding the pattern in the table is taking linear time for searching. Therefore, combining Enhanced LZW with binary search reduces the time complexity. The proposed methodology may be bust in data compression for communication, Maximizes the reduction of complexity in pattern identification for compression. The proposed methodology reduces the complexity in time with Binary search tree (BST). The experimental result shows % improvement on Compression and 93.34% improvement on Decompression. INTRODUCTION Data compression is a method of encoding rules that allows substantial reduction in the total number of bits to store or transmit a file. Two basic classes of data compression are applied in different areas currently that are lossy and lossless compression [l, 2]. One of the lossless data compression widely used is LZW data compression, it is a dictionary based algorithm. LZW compression is named after its developers, A. Lempel and J. Ziv, with later modifications by Terry A. Welch [3]. Lempel-Ziv-Welch (LZW) [3] this algorithm proposed by Welch in LZW compression works best for files containing lots of repetitive data. This is often the case with text and monochrome images. LZW compression is fast comparing to other algorithms. This algorithm is an improved implementation of the LZ78 algorithm published by Lempel and Ziv in 1978 (LZ78) [4]. The first algorithm of Lempel and Zive was published in 1977 and it is named as LZ77 [5]. The LZ77 [5] and LZ78 [4] are otherwise called LZ1 and LZ2 respectively like The LZW algorithm uses dictionary and index for encoding and decoding operation. It creates a dictionary and if a mach is found in the dictionary then corresponding string is replaced by the index. There are several algorithms like DEFLATE and GZIP uses the LZ family algorithms. LZW compression became the first widely used universal data compression method on computers. After the invention of LZW there are lots of improvements and enhancement done in LZW for data 2012, AJCSIT, All Right Reserved. compression that is discussed in this section. LZW compression works best for files containing lots of repetitive data especially for text and monochrome images. The LZW algorithm uses dictionary while decoding and encoding but the time taken for creating the dictionary is large, so the traditional searching method used by the LZW is replaced by the binary search, the experimental result shows massive reduction in the time complexity. LZW (Lempel-Ziv-Welch) LZW [3] compression uses a code table [6] common choice is to provide 4096 entries in the table. In this case, the LZW encoded data consists of 12 bit codes, each referring to one of the entries in the code table. Decompression is achieved by taking each code from the compressed file, and translating it through the code table to find what character or characters it represents. Codes in the code table are always assigned to represent single byte from the input file. When the LZW program starts to encode a file, the code table contains only the first 256 entries, with the remainder of the table being blank. This means that the first code in the compressed file is of single byte from the input file being converted to 12 bits. As the encoding continues, the LZW algorithm identifies repeated sequences in the data, and adds them to the code table. Compression starts the second time a sequence is encountered. The key point is that a sequence from the input file is not added to the code table until it has already 114

2 been placed in the compressed file as individual characters data table is then searched to find the variable NCODE. If a (codes 0 to 255). This is important because it allows the match in the code table is not found STRING = OCODE decompression program to reconstruct the code table +CHAR else if the NCODE is found then STRING = NCODE, directly from the compressed data, without having to then output the STRING. First Character of STRING is transmit the code table separately. assigned to CHAR, then adds entry (OCODE+ CHAR) in table The compression algorithm uses two variables: for and assigns NCODE to OCODE. This process will CHAR and STRING. The variable, CHAR, holds a single continue up to the last input. The decoding algorithm is character, (i.e.), a single byte value between 0 and 255. The shown in table-2. variable, STRING, is a variable length string, (i.e.), a group of one or more characters, with each character being a single byte. The algorithm starts by taking the first byte from the input file, and placing it in the variable, STRING. Table -1 shows this action in line 1. This is followed by the algorithm looping for each additional byte in the input file. Each time a byte is read from the input file it is stored in the variable, CHAR. The data table is then searched to determine if the concatenation of the two variables, STRING+CHAR, has already been assigned a code. If a match in the code table is not found, three actions are taken, (i), output the code for STRING, When a match in the code table is found, (ii), the concatenation of STRING+CHAR is stored in the variable, STRING, without any other action Binary search: taking place. That is, if a matching sequence is found in the A searching algorithm requires a target for which table, no action should be taken before determining to search. The list is searched until either the target is whether there is a longer matching sequence is present in located or the algorithm has determined that the target is the table or not. An example of this is shown in line 5, not in the list. Simple comparison is performed between where the sequence: STRING+CHAR = AB, is identified as the target and the data stored at each node in the list. already having a code in the table. In line 6, the next There are two forms of the binary search character from the input file, B, is added to the sequence, algorithm, both of which are designed to be applied to lists and the code table is searched for: ABB. Since this longer of sorted data. The condition that the data be sorted is a sequence is not in the table, the algorithm adds it to the constraint not present for the sequential search, and could table, outputs the code for the shorter sequence that is in mean that extra computing is required to sort the list the table (code 256), and starts over searching for before the binary search can be used. Since sorting sequences beginning with the character, B. This flow of events is continued until there are no more characters in the input file. The program is wrapped up with the code corresponding to the current value of STRING being written to the compressed file. LWZ compression algorithm is illustrated in Table-1. The Decompression algorithm uses four variables NCODE, OCODE, STRING, and CHAR. The decompression algorithm starts by taking the first byte from the input file and placing it in the variable, OCODE and output the OCODE. This action is shown in table-2 line 1. This is followed by the algorithm looping for each additional byte in the input file; each time a byte is read from the input file it is stored in the variable, NCODE. The 115 algorithms are always less efficient than searching algorithms, this could mean that binary search is much more efficient than sequential search, the combination of sorting plus binary searching may actually be less efficient than sequential search. The binary search algorithm is best used on lists that are constructed and sorted once, and then repeatedly searched. The basic idea behind binary search algorithm is to chop the list in half at each step, so that only half keys to search at each stage is one of the merits. While the more traditional targeted binary search checks at each stage to see if the target has been found, the forgetful binary search continues to chop the list in half until there is only one element left, and then checks to see if this single remaining element is the target. Though, it looks less efficient as it only checks if the target node has been found at the very end of the algorithm, the forgetful binary search is, in most cases, still more efficient than the other form of binary search. Sequential search requires a number of comparisons that is roughly proportional to the size of the list being searched, while the binary search requires only one extra comparison when the list size is doubled. Enhanced LZW Using Binary Search The time taken for Table (Dictionary) Creation in the LZW is huge. Encoding the comparison done for STRING+CHAR in the table is more, for example if the STRING +CHAR equal to ABBBD to find the availability of STRING +CHAR the algorithm have to perform search in the entire table (Shown in table-1 line number 18) and reaching the end of the table only the algorithm returns the STRING +CHAR is not available in the table so such type of

3 approach leads to increase the time complexity of LZW encoding. The same thing is happening in the LZW decoding (Decompression) also searching for the NCODE in the table taking linear time. For Example after comparing all the values in the table only it returns the presence of D is fail in the table, if D is the value for NCODE (shown in table -2 line numbers 10). So in order to reduce the time complexity of LZW encoding and decoding the binary search is used to perform the comparison to construct the table (dictionary) is shown in figure-1, to add the STRING + CHAR in encoding and OCODE+CHAR in the decoding phase to the dictionary the Binary search Tree (BST) is applied. Using the BST and Binary tree insertion the STRING + CHAR and OCODE+CHAR is updated to the table (dictionary) while encoding and decoding respectively. This BST also leads to some additional complexity for example for updating the ABBBD if STRING + CHAR, then the algorithm have to travel through the nodes AB, BC, For encoding the LZW the modification is made ABB, BA, ABBB (is shown in Figure-1 (c)). So the number using the simple binary search. Initially set the table of comparison for the insertion is reduced as comparing to contains all the possible roots (0 to 255). Then the first the earlier LZW but the comparison ratio and the byte of the input file is stored in to the STRING shown in algorithmic complexity is more. Another complexity is table-4. This is followed by the algorithm looping for each based on the root of the binary tree first created. If the first additional byte in the input file; each time a byte is read root value is not the middle value approximately menace from the input file it is stored in the variable, CHAR. (i.e.). then the possibility of creating left child or right child are Then the binary search algorithm is used to find the gradually decreases. So in such cases the comparison for position of STRING+CHAR in the table or dictionary. If the the insertion is increased leads to time complexity. For presence of STRING+CHAR in the table then the binary example in the figure-1 the root node is AB, so this is the search returns the position of the STRING+CHAR. Each time lowest value in the table (dictionary) because of the above with the comparison of MID value with the STRING+CHAR reason there is no probability of creating left child node for an additional variable also updated is called COMPARE by the root node AB so the same happens for all root node evaluating the condition if STRING+CHAR is less than key at such conditions increase the child node constructed under index MID, if yes the COMPARE variable is set in to -1 else the opposite node. This problem can be solved using the 1. So if the Matches is not found for the STRING+CHAR in self balancing binary tree but the time taken for the parent the table (dictionary) then before exiting the binary search node child node comparison for exchanging and balancing function MID is repositioned, based on the COMPARE to leads to increase for time complexity. find the exact insertion position for the STRING+CHAR, is This paper proposes a new approach using the shown in the Table -3, (i.e.), if the compare value of simple binary search to overcome the problems of child COMPARE is 1 then the MID value is incremented by 1 and node insertion using LZW with the Binary Search Tree or the MID is the insertion point for the STRING+CHAR and the Self Balanced binary tree, by using binary search, the the STRING+CHAR is added to the position of MID to the sorted table (Dictionary) is constructed. Therefore the Dictionary. Then the function returns -1. If the function complexity of using the Binary Search Tree (BST) and the returns a positive value (STRING+CHAR is available in the self balanced binary search tree gradually decreases the table) after the search then concatenated value of STRING, complexity in time. The proposed method also reduces the CHAR is assigned to the STRING. Else if the Binary search algorithmic complexity. To reduce comparison ratio using returns -1 then encode the STRING to the output file and the binary search tree the sorted table (Dictionary) is set the value of CHAR to String. The LZW encoding using generated using binary search. The BST insertion for LZW the binary search is shown in the Table-4, which has the encoding and decoding is shown in the Figure-1. sorted values. LZW decompression with binary search is also effectively implemented in the same methodology which in turn is used to update the table or dictionary instead of STRING+CHAR, the binary search for NCODE. If the NCODE is not in the table the MID value is adjusted based on the COMPARE value and find the insertion position for the OCODE+CHAR. The table-5 shows the LZW decoding after the implementation of Binary Search. Using the simple binary search to find the insertion position the LZW algorithm reduces the time complexity and algorithmic also structure can be reduces. The constructed table (Dictionary) is sorted in ascending order after each and every insertion (Shown in table-3), so the next search followed by every insertion is simplified. By comparing the Binary Search Tree (BST) the time complexity gradually reduced because the number of comparisons or the comparison ratio is reduced. If the first 116

4 node of BST (STRING+CHAR, NCODE values for LZW encoding decoding respectively) is low then the constriction of node is focused in the right child or the probability of adding child node in the left child is reduced this increases the level of the binary tree. So comparison requires for search STRING+CHAR or NCODE in the binary tree is increased. This kind of complexity can be reduced using the proposed method directly leads to reduce the time complexity. While comparing to the Self Balancing binary tree the time required for the adjusting of node for balancing leads to additional complexity, this is reduced using the Simple binary search. Merit of the above said method is by the way of constructing the dictionary each time the insertion is happening in the ascending order. This improves the efficiency of search in dictionary and leads to reduce the time complexity. The table-6, Graph-1 and Graph-2 shows the improvement of time ratio while comparing with the Existing LZW and LZW using Binary search tree (BST). Time taken for comparisons in dictionary While comparing to Existing LZW % time ratio improvement on Encoding and % for decoding, with BST % for Encoding and % improvement for Decoding. Graph-1 Time Ratio of LZW, LZW with Binary search Tree and LZW (BST_LZW) with binary Search (BS_LZW) for Encoding Graph-2 Time Ratio of LZW, LZW with Binary search Tree and LZW (BST_LZW) with binary Search (BS_LZW) for Decoding CONCLUSION LZW is a universal lossless data compression algorithm, which takes linear time in encoding. In this paper the problem of combining and summarizing LZW algorithm with binary search data compression reduces the complexity of time at the maximum is analyzed. The main focus of this paper in creating dictionary using LZW algorithm of any file with binary search comprises the efficiency of compression time and decompression time efficiently. The experimental result shows % in compressing and 93.34% decompression, comparing to other already existing algorithm, procedures and methods. The proposed work can be further enhanced and expanded for the authentication of compression and decompression techniques to obtain optimum accuracy in time. 117

5 REFERENCES [7]. Rahul Gupta, Ashutosh Gupta and Suneeta Agarwal A [1]. T. C. Bell, J. G. Cleary, and I. H. Witten, Text Novel data compression algorithm for Dynamic Compression English word C1iffs:N. J. Prentice-Hall, data IEEE REGION 8 SIBIRCON 2008 ( ) 1990 [8]. Rahul Gupta, Ashutosh Gupta and Suneeta Agarwal [2]. Rafael C. Gonzalez and Richard E. Woods, Digital A Novel Approach of Data Compression for Image Processing, Reading, Massachusetts : Dynamic Data 2008 IEEE Addison-Welsley Publishing Company, [9]. Hidetoshi Yokoo - Improved Variations Relating the [3]. WELCH, T. A A technique for highperformance Ziv Lempel and Welch-Type Algorithms for data compression. IEEE Comput. 17, 6, Sequential Data Compression IEEE Transactions on Information Theory, VOL. 38, NO. 1, JANUARY 1992 [4]. ZIV, J. AND LEMPEL, A Compression of page (73-81) individual sequences via variable-rate coding. [10]..Kinsner and R H. Greenfield The LEMPEL-ZIV-WEL IEEE Trans. Inform. Theory 24, 5, (CLHz w) Data Compression Algorithm for Packet [5]. ZIV, J. AND LEMPEL, A A universal algorithm Radio IEEE for sequential data compression. IEEE Trans. [11]. Tinku Acharya and Joseph F "Enhancing Lempel-Ziv Inform. Theory 23, 3, codes using an On-line Variable Length Binary [6]. Steven W. Smith "The Scientist and Engineer's Guide Encoding" IEEE to Digital Signal Processing " 1997 Biography * Nishad PM M.Sc., M.Phil. Seven months Worked as a project trainee in Wipro in 2005, five years experience in teaching, one and half year in JNASC and Three and half year in MES Mampad College. He has published ten papers national level/international conference and journals. He has presented three seminars at national Level. Now he is pursuing Ph.D Computer Science in Dr. Mahalingam center for research and development at NGM College Pollachi. ** Dr. R.Manicka chezian received his M.Sc., degree in Applied Science from P.S.G College of Technology, Coimbatore, India in He completed his M.S. degree in Software Systems from Birla Institute of Technology and Science, Pilani, Rajasthan, India and Ph D degree in Computer Science from School of Computer Science and Engineering, Bharathiar University, Coimbatore, India. He served as a Faculty of Maths and Computer Applications at P.S.G College of Technology, Coimbatore from 1987 to Presently, he has been working as an Associate Professor of Computer Science in N G M College (Autonomous), Pollachi under Bharathiar University, Coimbatore, India since He has published thirty papers in international/national journal and conferences: He is a recipient of many awards like Desha Mithra Award and Best Paper Award. His research focuses on Network Databases, Data Mining, Distributed Computing, Data Compression, Mobile Computing, Real Time Systems and Bio-Informatics. 118