|
Inapproximability
In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems. Scope Hardness of approximation complements the study of approximation algorithms by proving, for certain problems, a limit on the factors with which their solution can be efficiently approximated. Typically such limits show a factor of approximation beyond which a problem becomes NP-hard, implying that finding a polynomial time approximation for the problem is impossible unless NP=P. Some hardness of approximation results, however, are based on other hypotheses, a notable one among which is the unique games conjecture. History Since the early 1970s it was known that many optimization problems could not be solved in polynomial time unless P = NP, but in many of these problems the optimal solution could be efficiently approximated to a certain degree. In the 1970s, Teofilo F. Gonzalez and Sartaj Sahni began the study of h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Cover
The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 1972. Given a set of elements (called the universe) and a collection of sets whose union equals the universe, the set cover problem is to identify the smallest sub-collection of whose union equals the universe. For example, consider the universe and the collection of sets Clearly the union of is . However, we can cover all of the elements with the following, smaller number of sets: More formally, given a universe \mathcal and a family \mathcal of subsets of \mathcal, a ''cover'' is a subfamily \mathcal\subseteq\mathcal of sets whose union is \mathcal. In the set covering decision problem, the input is a pair (\mathcal,\mathcal) and an integer k; the question is whether there is a set covering of size k or less. In the set covering optimization problem, the input is a pair (\ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unique Games Conjecture
In computational complexity theory, the unique games conjecture (often referred to as UGC) is a conjecture made by Subhash Khot in 2002. The conjecture postulates that the problem of determining the approximate ''value'' of a certain type of game, known as a ''unique game'', has NP-hard computational complexity. It has broad applications in the theory of hardness of approximation. If the unique games conjecture is true and P ≠ NP, then for many important problems it is not only impossible to get an exact solution in polynomial time (as postulated by the P versus NP problem), but also impossible to get a good polynomial-time approximation. The problems for which such an inapproximability result would hold include constraint satisfaction problems, which crop up in a wide variety of disciplines. The conjecture is unusual in that the academic world seems about evenly divided on whether it is true or not. Formulations The unique games conjecture can be stated in a numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Algorithms
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time. The field of approximation algorithms, therefore, tries to understand how closely it is possible to approximate optimal solutions to such problems in polynomial time. In an overwhelming majority of the cases, the guarantee of such algorithms is a multiplicative one expressed as an approximation ratio or approximation factor i.e., the optimal solution is always guaranteed to be within a (predetermined) multiplicative factor of the returned solution. However, there are a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Algorithm
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the field of theoretical computer science as a consequence of the widely believed P ≠ NP conjecture. Under this conjecture, a wide class of optimization problems cannot be solved exactly in polynomial time. The field of approximation algorithms, therefore, tries to understand how closely it is possible to approximate optimal solutions to such problems in polynomial time. In an overwhelming majority of the cases, the guarantee of such algorithms is a multiplicative one expressed as an approximation ratio or approximation factor i.e., the optimal solution is always guaranteed to be within a (predetermined) multiplicative factor of the returned solution. However, there are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximation Ratio
An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ''ad-'' (''ad-'' before ''p'' becomes ap- by assimilation) meaning ''to''. Words like ''approximate'', ''approximately'' and ''approximation'' are used especially in technical or scientific contexts. In everyday English, words such as ''roughly'' or ''around'' are used with a similar meaning. It is often found abbreviated as ''approx.'' The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock). Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. In science, approximation can refer to u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Venkatesan Guruswami
Venkatesan Guruswami (born 1976) is a senior scientist at the Simons Institute for the Theory of Computing and Professor of EECS and Mathematics at the University of California, Berkeley. He did his high schooling at Padma Seshadri Bala Bhavan in Chennai, India. He completed his undergraduate in Computer Science from IIT Madras and his doctorate from Massachusetts Institute of Technology under the supervision of Madhu Sudan in 2001. After receiving his PhD, he spent a year at UC Berkeley as a Miller Fellow, and then was a member of the faculty at the University of Washington from 2002 to 2009. His primary area of research is computer science, and in particular on error-correcting codes. During 2007–2008, he visited the Institute for Advanced Study as a Member of School of Mathematics. He also visited SCS at Carnegie Mellon University during 2008–09 as a visiting faculty. From July 2009 through December 2020 he was a faculty member in the Computer Science Department in the Sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Washington
The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle approximately a decade after the city's founding. The university has a 703 acre main campus located in the city's University District, as well as campuses in Tacoma and Bothell. Overall, UW encompasses over 500 buildings and over 20 million gross square footage of space, including one of the largest library systems in the world with more than 26 university libraries, art centers, museums, laboratories, lecture halls, and stadiums. The university offers degrees through 140 departments, and functions on a quarter system. Washington is the flagship institution of the six public universities in Washington state. It is known for its medical, engineering, and scientific research. Washington is a member of the Association of American Universiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PCP (complexity)
In computational complexity theory, a probabilistically checkable proof (PCP) is a type of proof that can be checked by a randomized algorithm using a bounded amount of randomness and reading a bounded number of bits of the proof. The algorithm is then required to accept correct proofs and reject incorrect proofs with very high probability. A standard proof (or certificate), as used in the verifier-based definition of the complexity class NP, also satisfies these requirements, since the checking procedure deterministically reads the whole proof, always accepts correct proofs and rejects incorrect proofs. However, what makes them interesting is the existence of probabilistically checkable proofs that can be checked by reading only a few bits of the proof using randomness in an essential way. Probabilistically checkable proofs give rise to many complexity classes depending on the number of queries required and the amount of randomness used. The class PCP 'r''(''n''),''q''(''n'')r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The ACM
The ''Journal of the ACM'' is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects. It is an official journal of the Association for Computing Machinery. Its current editor-in-chief is Venkatesan Guruswami. The journal was established in 1954 and "computer scientists universally hold the ''Journal of the ACM'' in high esteem". See also * ''Communications of the ACM ''Communications of the ACM'' is the monthly journal of the Association for Computing Machinery (ACM). It was established in 1958, with Saul Rosen as its first managing editor. It is sent to all ACM members. Articles are intended for readers with ...'' References External links * Publications established in 1954 Computer science journals Association for Computing Machinery academic journals Bimonthly journals English-language journals {{compu-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sartaj Sahni
Professor Sartaj Kumar Sahni (born July 22, 1949, in Pune, India) is a computer scientist based in the United States, and is one of the pioneers in the field of data structures. He is a distinguished professor in the Department of Computer and Information Science and Engineering at the University of Florida. Education Sahni received his BTech degree in electrical engineering from the Indian Institute of Technology Kanpur. Following this, he undertook his graduate studies at Cornell University in the USA, earning a PhD degree in 1973, under the supervision of Ellis Horowitz. Research and publications Sahni has published over 280 research papers and written 15 textbooks. His research publications are on the design and analysis of efficient algorithms, data structures, parallel computing, interconnection networks, design automation, and medical algorithms. With his advisor Ellis Horowitz, Sahni wrote two widely used textbooks, ''Fundamentals of Computer Algorithms'' and ''Fundamen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
