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- Element_distinctness_problem abstract "In computational complexity theory, the element distinctness problem or element uniqueness problem is the problem of determining whether all the elements of a list are distinct. It is a well studied problem in many different models of computation. The problem may be solved by sorting the list and then checking if there are any consecutive equal elements; it may also be solved in linear expected time by a randomized algorithm that inserts each item into a hash table and compares only those elements that are placed in the same hash table cell.It is known that, for lists of numbers, the problem's time complexity is Θ(n log n), i.e., both the upper and lower bounds on its time complexity are of order of the linearithmic function in the algebraic decision tree model of computation, a model of computation in which the elements may not be used to index the computer's memory (as in the hash table solution) but may only be accessed by computing and comparing simple algebraic functions of their values. In other words, an asymptotically optimal algorithm of linearithmic time complexity is known for this model. The algebraic computation tree model basically means that the allowable algorithms are only the ones that can perform polynomial operations of bounded degree on the input data and comparisons of the results of these computations. The same lower bound was later proved for the randomized algebraic decision tree model.It is also known that quantum algorithms can solve this problem faster in queries. The optimal algorithm is by Andris Ambainis. Scott Aaronson and Yaoyun Shi first proved a tight lower bound for a large but restricted class of functions. Ambainis and Kutin independently (and via different proofs) extended their work to obtain the lower bound for all functions.Several lower bounds in computational complexity are proved by reducing the element distinctness problem to the problem in question, i.e., by demonstrating that the solution of the element uniqueness problem may be quickly found after solving the problem in question.".
- Element_distinctness_problem wikiPageID "9312350".
- Element_distinctness_problem wikiPageRevisionID "585400262".
- Element_distinctness_problem hasPhotoCollection Element_distinctness_problem.
- Element_distinctness_problem subject Category:Articles_with_inconsistent_citation_formats.
- Element_distinctness_problem subject Category:Polynomial-time_problems.
- Element_distinctness_problem type Abstraction100002137.
- Element_distinctness_problem type Attribute100024264.
- Element_distinctness_problem type Condition113920835.
- Element_distinctness_problem type Difficulty114408086.
- Element_distinctness_problem type Polynomial-timeProblems.
- Element_distinctness_problem type Problem114410605.
- Element_distinctness_problem type State100024720.
- Element_distinctness_problem comment "In computational complexity theory, the element distinctness problem or element uniqueness problem is the problem of determining whether all the elements of a list are distinct. It is a well studied problem in many different models of computation.".
- Element_distinctness_problem label "Element distinctness problem".
- Element_distinctness_problem sameAs m.02843n2.
- Element_distinctness_problem sameAs Q5358843.
- Element_distinctness_problem sameAs Q5358843.
- Element_distinctness_problem sameAs Element_distinctness_problem.
- Element_distinctness_problem wasDerivedFrom Element_distinctness_problem?oldid=585400262.
- Element_distinctness_problem isPrimaryTopicOf Element_distinctness_problem.