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Longest Common Subsequence
A longest common subsequence (LCS) is the longest subsequence common to all sequences in a set of sequences (often just two sequences). It differs from the longest common substring: unlike substrings, subsequences are not required to occupy consecutive positions within the original sequences. The problem of computing longest common subsequences is a classic computer science problem, the basis of data comparison programs such as the diff utility, and has applications in computational linguistics and bioinformatics. It is also widely used by revision control systems such as Git for reconciling multiple changes made to a revision-controlled collection of files. For example, consider the sequences (ABCD) and (ACBAD). They have 5 length-2 common subsequences: (AB), (AC), (AD), (BD), and (CD); 2 length-3 common subsequences: (ABD) and (ACD); and no longer common subsequences. So (ABD) and (ACD) are their longest common subsequences. Complexity For the general case of an arbitrar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Memoization
In computing, memoization or memoisation is an optimization technique used primarily to speed up computer programs by storing the results of expensive function calls and returning the cached result when the same inputs occur again. Memoization has also been used in other contexts (and for purposes other than speed gains), such as in simple mutually recursive descent parsing. Although related to caching, memoization refers to a specific case of this optimization, distinguishing it from forms of caching such as buffering or page replacement. In the context of some logic programming languages, memoization is also known as tabling. Etymology The term "memoization" was coined by Donald Michie in 1968 and is derived from the Latin word "memorandum" ("to be remembered"), usually truncated as "memo" in American English, and thus carries the meaning of "turning he results ofa function into something to be remembered". While "memoization" might be confused with "memorization" (becaus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hirschberg's Algorithm
In computer science, Hirschberg's algorithm, named after its inventor, Dan Hirschberg, is a dynamic programming algorithm that finds the optimal sequence alignment between two strings. Optimality is measured with the Levenshtein distance, defined to be the sum of the costs of insertions, replacements, deletions, and null actions needed to change one string into the other. Hirschberg's algorithm is simply described as a more space-efficient version of the Needleman–Wunsch algorithm that uses divide and conquer. Hirschberg's algorithm is commonly used in computational biology to find maximal global alignments of DNA and protein sequences. Algorithm information Hirschberg's algorithm is a generally applicable algorithm for optimal sequence alignment. BLAST and FASTA are suboptimal heuristics. If ''x'' and ''y'' are strings, where length(''x'') = ''n'' and length(''y'') = ''m'', the Needleman–Wunsch algorithm finds an optimal alignment in O(''nm'') time, using O(''nm'') space. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Collision
In computer science, a hash collision or hash clash is when two pieces of data in a hash table share the same hash value. The hash value in this case is derived from a hash function which takes a data input and returns a fixed length of bits. Although hash algorithms have been created with the intent of being collision resistant, they can still sometimes map different data to the same hash (by virtue of the pigeonhole principle). Malicious users can take advantage of this to mimic, access, or alter data. Due to the possible negative applications of hash collisions in data management and computer security (in particular, cryptographic hash functions), collision avoidance has become an important topic in computer security. Background Hash collisions can be unavoidable depending on the number of objects in a set and whether or not the bit string they are mapped to is long enough in length. When there is a set of ''n'' objects, if ''n'' is greater than , ''R'', , which in this ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Checksum
A checksum is a small-sized block of data derived from another block of digital data for the purpose of detecting errors that may have been introduced during its transmission or storage. By themselves, checksums are often used to verify data integrity but are not relied upon to verify data authenticity. The procedure which generates this checksum is called a checksum function or checksum algorithm. Depending on its design goals, a good checksum algorithm usually outputs a significantly different value, even for small changes made to the input. This is especially true of cryptographic hash functions, which may be used to detect many data corruption errors and verify overall data integrity; if the computed checksum for the current data input matches the stored value of a previously computed checksum, there is a very high probability the data has not been accidentally altered or corrupted. Checksum functions are related to hash functions, fingerprints, randomization functions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Function
A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually used to index a fixed-size table called a ''hash table''. Use of a hash function to index a hash table is called ''hashing'' or ''scatter storage addressing''. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally and storage space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys. Use of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Growth
In mathematics, a function or sequence is said to exhibit quadratic growth when its values are proportional to the square of the function argument or sequence position. "Quadratic growth" often means more generally "quadratic growth in the limit", as the argument or sequence position goes to infinity – in big Theta notation, f(x)=\Theta(x^2). This can be defined both continuously (for a real-valued function of a real variable) or discretely (for a sequence of real numbers, i.e., real-valued function of an integer or natural number variable). Examples Examples of quadratic growth include: *Any quadratic polynomial. *Certain integer sequences such as the triangular numbers. The nth triangular number has value n(n+1)/2, approximately n^2/2. For a real function of a real variable, quadratic growth is equivalent to the second derivative being constant (i.e., the third derivative being zero), and thus functions with quadratic growth are exactly the quadratic polynomials, as these a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diff
In computing, the utility diff is a data comparison tool that computes and displays the differences between the contents of files. Unlike edit distance notions used for other purposes, diff is line-oriented rather than character-oriented, but it is like Levenshtein distance in that it tries to determine the smallest set of deletions and insertions to create one file from the other. The utility displays the changes in one of several standard formats, such that both humans or computers can parse the changes, and use them for patching. Typically, ''diff'' is used to show the changes between two versions of the same file. Modern implementations also support binary files. The output is called a "diff", or a patch, since the output can be applied with the Unix program . The output of similar file comparison utilities is also called a "diff"; like the use of the word "grep" for describing the act of searching, the word ''diff'' became a generic term for calculating data difference and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backtracking
Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of ''k'' queens in the first ''k'' rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned. Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edit Distance
In computational linguistics and computer science, edit distance is a string metric, i.e. a way of quantifying how dissimilar two strings (e.g., words) are to one another, that is measured by counting the minimum number of operations required to transform one string into the other. Edit distances find applications in natural language processing, where automatic spelling correction can determine candidate corrections for a misspelled word by selecting words from a dictionary that have a low distance to the word in question. In bioinformatics, it can be used to quantify the similarity of DNA sequences, which can be viewed as strings of the letters A, C, G and T. Different definitions of an edit distance use different sets of string operations. Levenshtein distance operations are the removal, insertion, or substitution of a character in the string. Being the most common metric, the term ''Levenshtein distance'' is often used interchangeably with ''edit distance''. Types of edit dis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shortest Common Supersequence Problem
In computer science, the shortest common supersequence of two sequences X and Y is the shortest sequence which has X and Y as subsequences. This is a problem closely related to the longest common subsequence problem. Given two sequences X = and Y = , a sequence U = is a common supersequence of X and Y if items can be removed from U to produce X and Y. A shortest common supersequence (SCS) is a common supersequence of minimal length. In the shortest common supersequence problem, two sequences X and Y are given, and the task is to find a shortest possible common supersequence of these sequences. In general, an SCS is not unique. For two input sequences, an SCS can be formed from a longest common subsequence (LCS) easily. For example, the longest common subsequence of X ..m= abcbdab and Y ..n= bdcaba is Z ..L= bcba. By inserting the non-LCS symbols into Z while preserving their original order, we obtain a shortest common supersequence U ..S= abdcabdab. In particular, the equatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Stein
Clifford Seth Stein (born December 14, 1965), a computer scientist, is a professor of industrial engineering and operations research at Columbia University in New York, NY, where he also holds an appointment in the Department of Computer Science. Stein is chair of the Industrial Engineering and Operations Research Department at Columbia University. Prior to joining Columbia, Stein was a professor at Dartmouth College in New Hampshire. Stein's research interests include the design and analysis of algorithms, combinatorial optimization, operations research, network algorithms, scheduling, algorithm engineering and computational biology. Stein has published many influential papers in the leading conferences and journals in his fields of research, and has occupied a variety of editorial positions including in the journals ''ACM Transactions on Algorithms'', ''Mathematical Programming'', ''Journal of Algorithms'', ''SIAM Journal on Discrete Mathematics'' and ''Operations Resear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
