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Pagh's Problem
Pagh's problem is a datastructure problem often used when studying lower bounds in computer science named after Rasmus Pagh Rasmus Pagh is a Danish computer scientist and a professor of computer science at the University of Copenhagen. His main work is in algorithms and data structures, and he is particularly known for the cuckoo hashing algorithm and for co-founding .... Mihai Pătrașcu was the first to give lower bounds for the problem. In 2021 it was shown that, given popular conjectures, the naive linear time algorithm is optimal.Henzinger, Monika, et al. "Unifying and strengthening hardness for dynamic problems via the online matrix-vector multiplication conjecture." Proceedings of the forty-seventh annual ACM symposium on Theory of computing. 2015. Definition We are given as inputs k subsets X_1, X_2, \dots, X_k over a universe U=\. We must accept updates of the following kind: Given a pointer to two subsets X_1 and X_2, create a new subset X_1\cap X_2. After e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Datastructure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, relational databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upper And Lower Bounds
In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is greater than or equal to every element of . Dually, a lower bound or minorant of is defined to be an element of that is less than or equal to every element of . A set with an upper (respectively, lower) bound is said to be bounded from above or majorized (respectively bounded from below or minorized) by that bound. The terms bounded above (bounded below) are also used in the mathematical literature for sets that have upper (respectively lower) bounds. Examples For example, is a lower bound for the set (as a subset of the integers or of the real numbers, etc.), and so is . On the other hand, is not a lower bound for since it is not smaller than every element in . The set has as both an upper bound and a lower bound; all other numbers are either an upper bound or a lower bound for that . Every subset of the natural numbers has a lowe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rasmus Pagh
Rasmus Pagh is a Danish computer scientist and a professor of computer science at the University of Copenhagen. His main work is in algorithms and data structures, and he is particularly known for the cuckoo hashing algorithm and for co-founding the Basic Algorithms Research Center, BARC, in Copenhagen. Early life and education Rasmus Pagh was born in Copenhagen, but soon after his family moved to Esbjerg in western Denmark. He went to high school at Rødkilde Amtsgymnasium where he participated in the "JP Forsker" science competition, and in the "Georg Mohr" mathematics competition. After graduating in 1994, he went to study mathematics and computer science at Aarhus University. In 1998 he started his PhD with Peter Bro Miltersen and started writing articles about hashing and efficient dictionaries, culminating in his work on cuckoo hashing. Soon after his thesis defence was in the fall of 2002 he became an assistant professor at the recently founded IT University of Copenhag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mihai Pătrașcu (computer Scientist)
Mihai Pătrașcu (17 July 1982 – 5 June 2012) was a Romanian-American computer scientist at AT&T Labs in Florham Park, New Jersey, USA. Pătrașcu attended Carol I National College in Craiova. As a high school student, he won 2 gold medals and 1 silver medal at the International Olympiad in Informatics. He completed his undergraduate and graduate studies in Computer Science at Massachusetts Institute of Technology, completing his thesis under the supervision of Erik Demaine in 2008. Pătrașcu’s work was concerned with fundamental questions about basic data structures. Pătrașcu received the Machtey Award for the best student paper at the Symposium on Foundations of Computer Science in 2008, and the Presburger Award from the European Association for Theoretical Computer Science in 2012, for breaking "many old barriers on fundamental data structure problems, not only revitalizing but also revolutionizing a field that was almost silent for over a decade." Pătrașcu d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
