diagram for P complexity P , NP complexity NP , NP complete , and NPhard set of problems NPhardNP complexity non deterministic polynomial time hard , in computational complexity theory , is a class of problems that are, informally, at least as hard as the hardest problems in NP . A problem H is NPhard if and only if there is an NP complete problem L that is polynomial time Turing reduction ... call takes only one step to compute. NPhard problems may be of any type decision problem ... L Since L is NP complete, and hence the hardest in class NP, also problem H is at least as hard ... If there is a polynomial algorithm for any NPhard problem, then there are polynomial algorithms for all problems in NP, and hence P NP If P NP, then NPhard problems have no solutions in polynomial time, while P NP does not resolve whether the NPhard problems can be solved in polynomial time If an optimization problem H has an NP complete decision version L , then H is NPhard. A common mistake is to think that the NP in NPhard stands for non polynomial . Although it is widely suspected that there are no polynomial time algorithms for NPhard problems, this has never been proven. Moreover, the class ... An example of an NPhard problem is the decision subset sum problem , which is this given a set of integers ... to be NP complete. Another example of an NPhard problem is the optimization problem of finding the least ... salesman problem . There are decision problems that are NPhard but not NP complete, for example ... problem is NPhard but not NP complete . For example, the Boolean satisfiability problem can be reduced ..., is not. There are also NPhard problems that are neither NP complete nor Recursive language undecidable ... definition of NPhard that is often used restricts NPhard to decision problem s and then uses ... is NPhard if L sup sup NP, L sup sup L. If it is also the case that L is in NP , then L is called NP complete . NP naming convention The NP family naming system is confusing NPhard problems are not all ... more details
tocright NP may refer to Locations NP postcode area , Newport, United Kingdom NP, country code for Nepal ISO 3166 1 alpha 2 country code .np , the country code top level domain ccTLD for Nepal NP, anabbreviation for Ngee Ann Polytechnic , Singapore N.P The an abbreviation for Nichols Point , Australia Health, science, technology and mathematics NP complexity , Nondeterministic Polynomial, a computational complexity class NP complete , a class of decision problems NPhard , a class of problems in computational complexity Co NP , a complexity class Np, or Neper , a dimensionless unit N sub p sub , Power number , a dimensionless number Np, the chemical symbol for Neptunium Nasopharyngeal airway , an adjunct to airway management NP lemma, or Neyman Pearson lemma NP or Norma Portuguesa , a Portuguese technical standard Nucleoside phosphorylase , an enzyme p n junction NP junction or PN junction , the simplest electronic device, used to make diodes and transistors Number Portability , the ability to retain one s phone number when changing telecommunication carriers in Europe Nurse practitioner , a registered nurse who has completed advanced nursing education New Proposal or new work item proposal , a stage in standardization process used by International Organization for Standardization Language, literature, magazines, and games NP novel NP novel , a book by Japanese author Banana Yoshimoto Noun phrase in grammar Nintendo Power , a magazine published by Future US in North America. Transportation AAR reporting mark for the Northern Pacific Railway Disambiguation cs NP de NP es NP eo Np fa NP fr NP ko NP it NP he NP sw NP lv NP lt NP nl NP ja NP no NP pl Np pt NP ro NP ru NP sr Np fi Np th NP vi NP zh NP ... more details
Infobox Top level domain name .np background CCF image Image Dotnp.jpg .NP registration for your life, for your business 240px introduced 1995 type Country code top level domain status Active registry Mercantile Communications Pvt. Ltd. sponsor Mercantile Communications Pvt. Ltd. intendeduse Entities connected with NEP actualuse Used in Nepal restrictions Local presence requirement names must be based on company organization or brand name structure Registrations are made at the third level beneath various second level names document http www.register.com.np terms and conditions.asp Terms and conditions disputepolicy website http www.register.com.np .np domain registration .np is the Internet country code top level domain ccTLD for Nepal . Second level domains .com.np .edu.np .gov.np .mil.np .net.np .org.np Registrations require a local presence in Nepal for registration. Registrations are also expected to be for names based directly on a company or organization name, or a product brand name. http register.mos.com.np cctlds.asp External links http www.iana.org root whois np.htm IANA .np whois information http www.register.com.np .np domain registration website CcTLD DEFAULTSORT NP Category Country code top level domains Category Nepalese media Category Communications in Nepal Compu domain stub af .np ar .np ast .np az .np be .np be x old .np bs .np bg .np cv .np cs .np cy .np da .np et .np el .np es .np eo .np eu .np fa .np fr .np xal .np ko .np hy .np hr .np bpy . id .np is .np it .np krc .np ka .np lv .np lb .np hu .np ms .np nl .np ja .np ce .np no .np oc .np uz .np nds .np pl .np pt .np ro .np ru .np sah .np sq .np sk .np sr .np sh .np fi .np sv Toppdom n N tl .np tt .np th .np tg .np tr .np tk .np uk .np ur Np. vi .np fiu vro .np war .np yo .np diq .np zh .np ... more details
File P npnp complete np hard.svg thumb 300px right Euler diagram for P complexity P , NP complexity NP , NP complete, and NPhard set of problems In computational complexity theory , the complexity class NP complete abbreviated NP C or NPC is a class of decision problem s. A decision problem L is NP complete if it is in the set of NP complexity NP problems so that any given solution to the decision problem can be verified in polynomial time , and also in the set of NPhard problems so that any NP ... 2 is said to be NPhard , whether or not it satisfies condition 1. A consequence of this definition ... that is thought to be hard , but isn t thought to be NP complete. The easiest way to prove that some ... . On the other hand, there are NP problems with at most one solution that are NPhard under randomized ... problem NPhard References Reflist Cite book last Garey first M.R. authorlink Michael Garey coauthors ... a solution in the first place indeed, the most notable characteristic of NP complete problems is that no fast ..., determining whether or not it is possible to solve these problems quickly, called the P versus NP ... science today. While a method for computing the solutions to NP complete problems using a reasonable ... s still frequently encounter NP complete problems. NP complete problems are often addressed by using approximation algorithm s. Formal overview NP complete is a subset of NP complexity NP , the set of all decision problems whose solutions can be verified in polynomial time NP may be equivalently defined ... machine . A problem p in NP is also in NPC if and only if every other problem in NP can be transformed into p in polynomial time. NP complete can also be used as an adjective problems in the class NP complete are known as NP complete problems. NP complete problems are studied because the ability to quickly verify solutions to a problem NP seems to correlate with the ability to quickly solve that problem P complexity P . It is not known whether every problem in NP can be quickly solved this is called ... more details
Abbreviations date December 2007 In computational complexity theory , the complexity class NP equivalent is the set of function problem s that are both NP easy and NPhard . ref harvtxt Garey Johnson 1979 , p. 117, 120. ref NP equivalent is the analogue of NP complete for function problem s. For example, the problem FIND SUBSET SUM is in NP equivalent. Given a set of integer s, FIND SUBSET SUM is the problem of finding some nonempty subset of the integers that adds up to zero or returning the empty set if there is no such subset . This optimization problem is similar to the decision problem subset sum problem SUBSET SUM . Given a set of integers, SUBSET SUM is the problem of finding whether there exists a subset summing to zero. SUBSET SUM is NP complete. To show that FIND SUBSET SUM is NP equivalent, we must show that it is both NPhard and NP easy. Clearly it is NPhard. If we had a Black box systems black box that solved FIND SUBSET SUM in unit time, then it would be easy to solve SUBSET SUM. Simply ask the black box to find the subset that sums to zero, then check whether it returned a nonempty set. It is also NP easy. If we had a black box that solved SUBSET SUM in unit time, then we could use it to solve FIND SUBSET SUM. If it returns false , we immediately return the empty set. Otherwise, we visit each element in order and remove it provided that SUBSET SUM would still return true after we remove it. Once we ve visited every element, we will no longer be able to remove any element without changing the answer from true to false at this point the remaining subset of the original elements must sum to zero. This requires us to note that later removals of elements do not alter ... return S Another well known NP equivalent problem is the traveling salesman problem . Notes reflist References Garey Johnson . DEFAULTSORT Np Equivalent Category Complexity classes de NP quivalenz pt NP equivalente ... more details
Why some NP problems are hard to solve Because of the many important problems in this class, there have ...Image Complexity classes.svg thumb 250px Diagram of complexity classes provided that P NP . The existence of problems within NP but outside both P and NP complete, under this assumption, was Ladner s theorem ... &CFID 15151515&CFTOKEN 6184618 ACM site . ref In computational complexity theory , NP is one of the most fundamental complexity class es. The abbreviation NP refers to Nondeterministic algorithm nondeterministic polynomial time . Intuitively, NP is the set of all decision problem s for which the instances ... Turing machine . In an equivalent formal definition, NP is the set of decision problem s where the yes ...&f false p. 283 ref The complexity class P complexity P is contained in NP , but NP contains many important problems, the hardest of which are called NP complete NP complete problems, for which no polynomial ... in complexity theory, the P NP problem P NP problem , asks whether such algorithms actually exist for NP complete, and by corollary, all NP problems. It is widely believed that this is not the case. ref name poll cite journal author William I. Gasarch title The P ?NP poll. journal SIGACT News volume ... 1052796.1052804 format PDF accessdate 2008 12 29 ref Formal definition The complexity class NP can be defined in terms of NTIME as follows math mbox NP bigcup k in mathbb N mbox NTIME n k . math Alternatively, NP can be defined using deterministic Turing machines as verifiers. A formal language language L is in NP if and only if there exist polynomials p and q , and a deterministic Turing machine ... q x , M x,y 0 Introduction Many natural computer science problems are covered by the class NP . In particular ... in NP . Verifier based definition In order to explain the verifier based definition of NP ..., and in fact the subset sum problem is NP complete. However, notice that, if we are given a particular ... whether a given subset has sum zero is called verifier . A problem is said to be in NP if and only ... more details
lowercase unsolved computer science Is NP co NP ? In computational complexity theory , co NP is a complexity class . A problem math mathcal X math is a member of co NP if and only if its complement complexity complement math overline mathcal X math is in the complexity class NP complexity NP . In simple terms, co NP is the class of problems for which efficiently verifiable proofs of no instances, sometimes called counterexamples, exist. An example of an NP complete problem is the subset sum problem ... is in co NP and asks given a finite set of integers, does every non empty subset have a nonzero sum ... is easily verified. P , the class of polynomial time solvable problems, is a subset of both NP and co NP. P is thought to be a strict subset in both cases and demonstrably cannot be strict in one case but not the other . NP and co NP are also thought to be unequal citation needed date October 2011 . If so, then no NP complete problem can be in co NP and no co NP complete problem can be in NP. This can be shown as follows. Assume that there is an NP complete problem that is in co NP. Since all problems in NP can be reduced to this problem it follows that for all problems in NP we can construct ..., i.e., NP is a subset of co NP. From this it follows that the set of complements of the problems in NP is a subset of the set of complements of the problems in co NP, i.e., co NP is a subset of NP. Since we already knew that NP is a subset of co NP it follows that they are the same. The proof for the fact that no co NP complete problem can be in NP is symmetrical. If a problem can be shown to be in both NP and co NP, that is generally accepted as strong evidence that the problem is probably not NP complete since otherwise NP co NP . An example of a problem which is known to be in NP and in co NP is integer factorization given positive integers m and n determine if m has a factor less than n and greater than one. Membership in NP is clear if m does have such a factor then the factor itself ... more details
In computational complexity theory complexity theory , the complexity class NP easy is the set of function problem s that are solvable in polynomial time by a deterministic Turing machine with an oracle machine oracle for some decision problem in NP complexity NP . In other words, a problem X is NP easy if and only if there exists some problem Y in NP such that X is polynomial time Turing reduction polynomial time Turing reducible to Y. ref harvtxt Garey Johnson 1979 , p. 117, 120. ref This means that given an oracle machine oracle for Y, there exists an algorithm that solves X in polynomial time possibly by repeatedly using that oracle . NP easy is another name for FP sup NP sup see the function problem article or for F sub 2 sub P see the polynomial hierarchy article . An example of an NP easy problem is the problem of sorting a list of strings. The decision problem is string A greater than string B is in NP. There are algorithms such as Quicksort that can sort the list using only a polynomial number of calls to the comparison routine, plus a polynomial amount of additional work. Therefore, sorting is NP easy. There are also more difficult problems that are NP easy. See NP equivalent for an example. The definition of NP easy uses a Turing reduction rather than a many one reduction because the answers to problem Y are only TRUE or FALSE, but the answers to problem X can be more general. Therefore, there is no general way to translate an instance of X to an instance of Y with the same answer. Notes reflist References Garey Johnson . DEFAULTSORT Np Easy Category Complexity classes de NP leicht pt NP f cil zh NP ... more details
In computational complexity , problems that are in the complexity class NP complexity NP but are neither in the class P complexity P nor NP complete are called NP intermediate , and the class of such problems is called NPI . Ladner s theorem , shown in 1975 by Richard Ladner, ref cite journal first Richard last Ladner title On the Structure of Polynomial Time Reducibility journal Journal of the ACM JACM volume 22 issue 1 year 1975 pages 155 171 doi 10.1145 321864.321877 ref is a result asserting that, if P NP problem P &ne NP , then NPI is not empty that is, NP contains problems that are neither in P nor NP complete . Since the other direction is trivial, we can say that P NP if and only if NPI is empty. Under the assumption that P &ne NP, Ladner explicitly constructs a problem in NPI, however this problem is artificial and otherwise uninteresting. It is an open question whether any natural problem has the same property. Some problems that are considered good candidates for being NP intermediate are the graph isomorphism problem , integer factorization factoring , and computing the discrete logarithm . Another problem in NP that is not known to be in P or NP complete is the circuit minimization minimum circuit size problem MCSP . Unlike the above problems, MCSP is believed to be in NP complete. However, proving as much via a many one reduction will imply circuit lower bounds for E complexity E unless NP is contained in SUBEXP, which is a violation of the exponential time hypothesis . Therefore, proving that MCSP is in NP complete is considered outside of current techniques. ref ... section5.ps Basic structure, Turing reducibility and NP hardness Lance Fortnow, http oldblog.computationalcomplexity.org ... 16 Ladner s Theorem . Accessed 17 09 2009 http www.cs.umd.edu jkatz complexity lecture2.pdf NP completeness Dead link date September 2011 ComplexityZoo Class NPI N npi DEFAULTSORT Np Intermediate Category Complexity classes de Ladner Theorem it NP Intermedio pl Problem NP po redni ... more details
Lowercase Infobox control chart name np chart proposer Walter A. Shewhart subgroupsize n 1 measurementtype Number nonconforming per unit qualitycharacteristictype Attributes data distribution Binomial distribution sizeofshift 1.5 meanchart Np control chart.svg meancenter math n bar p frac sum i 1 m sum j 1 n begin cases 1 & mbox if x ij mbox defective 0 & mbox otherwise end cases m math meanlimits math n bar p pm 3 sqrt n bar p 1 bar p math meanstatistic math n bar p i sum j 1 n begin cases 1 & mbox if x ij mbox defective 0 & mbox otherwise end cases math In statistical process control statistical quality control , the np chart is a type of control chart used to monitor the number of Nonconformity quality nonconforming units in a Sample statistics sample . It is an adaptation of the p chart and used in situations where personnel find it easier to interpret process performance in terms of concrete numbers of units rather than the somewhat more abstract proportion. ref cite book last Montgomery first Douglas title Introduction to Statistical Quality Control publisher John Wiley & Sons , Inc. year 2005 location Hoboken, New Jersey pages 279 url http www.eas.asu.edu masmlab montgomery isbn 9780471656319 oclc 56729567 ref The np chart differs from the p chart in only the three following aspects The control limits are math n bar p pm 3 sqrt n bar p 1 bar p math , where n is the sample size and math bar p math is the estimate of the long term process mean established during control chart setup. The number nonconforming np , rather than the fraction nonconforming p , is plotted against the control limits. The sample size, math n math , is constant. See also p chart References reflist DEFAULTSORT Np Chart Category Quality control tools Category Statistical charts and diagrams ... more details
Infobox Book name NP title orig translator Ann Sherif image Image Banana yoshimoto npusa1.jpg 200px image caption 1st edition Japanese author Banana Yoshimoto illustrator cover artist country Japan language Japanese language Japanese series genre Novel publisher Kadokawa Shoten release date 1990 in literature 1990 english release date 1994 in literature 1994 media type Print Hardcover Hardback pages 194 pp isbn 0 8021 1545 4 dewey 895.6 35 20 congress PL865.O7138 N713 1994 oclc 29255351 preceded by English Kitchen novel followed by English Lizard novel NP is a novel written by Japan Japanese author Banana Yoshimoto in 1990 in literature 1990 and translated into English language English in 1994 in literature 1994 by Ann Sherif . Plot summary spoiler this content was copied over from Kitchen, and has been commented out to be replaced subsequently with specific content about this novel. Literary significance & criticism Although one may notice a certain Western influence in Yoshimoto s style, Kitchen is still critically recognised as an example of contemporary Japanese literature The Independent , The Times and the New Yorker have all reviewed the novel favourably. Book information NP English edition by Banana Yoshimoto Hardcover ISBN 0 8021 1545 4, published by Grove Press Paperback ISBN 0 671 89826 4, published by Washington Square Press References references Category 1990 novels Category Novels by Banana Yoshimoto 1990s novel stub ko N P ja N P it N.P. ... more details
cleanup date March 2011 no footnotes date March 2011 CD NP chimeric natriuretic peptide is a novel natriuretic peptide developed by the Mayo Clinic as a potential treatment for heart failure . ref name McKie McKie et al. 2010 CD NP An innovative designer natriuretic peptide activator of particulate guanylyl cyclase receptors for cardiorenal disease. Curr Heart Fail Rep. 7 93 99 ref ref name Lisy Lisy et al. 2008 Design, synthesis and actions of a novel chimeric natriuretic peptide CD NP. J Am Coll Cardiol 52 60 68 ref ref name Dickey Dickey et al. 2008 Novel bifuncitonal natriuretic peptides as potential therapeutics. J Biol Chem 283 35003 35009 ref CD NP is created by the fusion of the 15 amino acid C terminus of Dendroaspis natriuretic peptide DNP with the full C type Natriuretic Peptide CNP structure ref name Lisy both peptide which are endogenous to humans. This peptide chimera is a dual activator of the natriuretic peptide receptors NPR A and NPR B and therefore exhibits the natriuresis natriuretic and diuretic properties of DNP, as well as the antiproliferative and antifibrotic properties of CNP. ref name McKie ref name Dickey Molecular Problem Fibrosis When faced with pressure overload, the heart attempts to compensate with a number of structural alterations including hypertrophy of cardiomyocytes and increase of extracellular matrix ECM proteins. ref Bonnin et al 1981 Collagen synthesis and content in right ventricular hypertrophy in the dog. Am J Physiol 10 703 13 ref ... Mechanism of CD NP As CD NP interacts with both NRP A and NRP B, this drug has antifibrotic potential. ref name McKie Binding of CD NP to NRP B elicits an antifibrotic response by catalyzing ..., in vitro study of human fibroblasts demonstrates that CD NP reduces TGF beta 1 induced ... peptide CD NP suppresses TGF beta 1 induced collagen type I production in human cardiac fibroblasts ... and DNP, CD NP treatment results in a reduction in stress on the heart through natriuresis diuresis ... more details
wiktionarypar hard hardness Hard or Hardness may refer to Hardness , resistance of physical materials to change under force Hard water , water with a high mineral content NPhard , a term used in Computational complexity theory Hard, Austria , a town in Austria Hard Z rich , a quarter in Z rich Hard tennis , a type of tennis court Hard music festival , concerts and live events Hard, or hard on, a slang term for an erection Hard nautical , a firm or paved beach or slope convenient for hauling vessels out of the water Hayward Area Recreation and Park District , abbreviated H.A.R.D. Music Hard band , a Hungarian hard rock supergroup Hard Brainpower album Hard Brainpower album Hard Gang of Four album Hard Gang of Four album Hard Jagged Edge album Hard Jagged Edge album Hard song Hard song , by Rihanna Disambig cs Tvrdost de Hard Begriffskl rung fr Hard it Hard nl Hard no Hardhet pt Hard ro Hard uk Hard ... more details
Infobox Album See Wikipedia WikiProject Albums Name Hard For It Type Studio Artist Cutty Ranks Cover Cutty Ranks Hard For It.jpg Released 2006 ref name vibes cite web url http www.reggae vibes.com rev sin hardfori.htm title Cutty Ranks Hard for It Review accessdate 2007 12 30 work Reggae Vibes.com ref Recorded Genre Length Label Walboomers Records ref name vibes Producer Reviews Last album This album Hard For It Next album Hard For It is an album by Cutty Ranks . The song 20 Inch was recorded in several versions, including a version with vocals by Master P . Track listing Talli Talli Remix feat. Kobra Khan What Dem Fighting For Dirty Mind Hard For It 20 Inch Mega Mix feat. Kobra Khan Head Mistress Dem A Eat Gal Strange Feeling Who Give Di Orders Wise Up Better Day Holiday Take Me Away feat. Emereld Guilty feat. A20 Turn Me On feat. Flave I Congratulate You Move To The Gal Dem 20 Inch References references http www.reggae vibes.com rev sin hardfori.htm Reggae Vibes review http www.juno.co.uk products 259011 01.htm entry at Juno.uk.co Category 2006 albums Category Cutty Ranks albums ... more details
Use British English date May 2011 Use dmy dates date May 2011 Infobox album Name It s Hard Type studio Artist The Who Cover The who its hard album.jpg Released 4 September 1982 Recorded June 1982, Turn Up Down Studio at Glyn Johns home in Surrey , England Genre Rock music Rock Length 46 29 Language English language English Label Polydor Records Polydor UK br Warner Bros. Records Warner Bros. Original ... It s Hard br 1982 Next album Endless Wire The Who album Endless Wire br 2006 Misc Singles Name It s Hard ... date 1982 Single 3 It s Hard Single 3 date 1983 Album reviews rev1 Allmusic rev1score Rating 2 5 ref ... music reviews album 3045 22014 ref noprose yes It s Hard is the tenth studio album by English ... It s Hard . Live performances Just over half of this album has been played live over the course ... performance of Athena . It s Hard was played the entire 1982 tour and regularly featured a short ... Horizon in Chicago , in place of It s Hard . This was because the song was written by Townshend ... John Entwistle 3 39 Cooks County 3 51 It s Hard 3 47 Dangerous Entwistle 3 36 Eminence Front 5 39 ... digitally remastered reissue of It s Hard added four live tracks recorded on the last show of The Who s The Who Tour 1982 1982 tour , on 17 December in Toronto . li value 13 It s Hard 4 56 Eminence Front ... Moon It s Hard Bot generated title ref align center 28 UK Singles Chart ref name chart align center ... align center 5 It s Hard Billboard Mainstream Rock ref name multiple align center 39 class wikitable ... title It s Hard artist The Who award Gold autocat yes region United States type album certification ... linernotes It sHard.htm It s Hard Liner Notes The Who Category 1982 albums Category Albums ... Records albums Category The Who albums Category Warner Bros. Records albums cs It s Hard de It s Hard es It s Hard fr It s Hard it It s Hard nl It s Hard nn It s Hard pt It s Hard ro It s Hard fi It s Hard sv It s Hard ... more details
lowercase In Computational complexity theory complexity theory , computational problems that are co NP complete are those that are the hardest problems in co NP , in the sense that they are the ones most likely not to be in P complexity P . If there exists a way to solve a co NP complete problem quickly, then that algorithm can be used to solve all co NP problems quickly. Each Co NP complete problem is the complement complexity complement of an NP complete problem. There are some problems in both NP and co NP , however it is not known if the sets are equal, although inequality is thought more likely. See co NP and NP complete for more details. Fortune showed in 1979 that if any sparse language is co NP complete or even just co NPhard , then nowrap P NP problem P NP , ref S. Fortune. A note on sparse complete sets. SIAM Journal on Computing , volume 8, issue 3, pp.431 433. 1979. ref a critical foundation for Mahaney s theorem . Formal definition A decision problem C is co NP complete if it is in co NP and if every problem in co NP is polynomial time many one reduction polynomial time many one reducible to it. This means that for every Co NP problem L , there exists a polynomial time algorithm which can transform any instance of L into an instance of C with the same truth value . As a consequence, if we had a polynomial time algorithm for C , we could solve all co NP problems in polynomial time. Example One simple example of a co NP complete problem is Tautology logic tautology , the problem of determining whether a given Boolean algebra logic Boolean formula is a tautology that is, whether every possible assignment of true false values to variables yields a true statement ... NP complete, even though the satisfiability problem is trivial, as every positive Boolean formula is satisfiable. References references ComplexityClasses Category Complexity classes es Co NP completo fr Co NP complet ko Co NP pl Klasa Co NPC pt Co NP completo ... more details
is said to be strongly NPhard if a strongly NP complete problem has a polynomial reduction to it in combinatorial optimization, particularly, the phrase strongly NPhard is reserved for problems that are not known to have a polynomial reduction to another strongly NP complete problem. Normally numerical ... does not equal NP, List of knapsack problems Multiple constraints knapsack with two constraints is not strongly NPhard, but has no FPTAS even when the optimal objective is polynomially bounded ref ...In computational complexity , strong NP completeness is a property of computational problems that is a special case of NP complete NP completeness . A general computational problem may have numerical parameters ... parameters. A problem is said to be strongly NP complete strongly NP complete in the strong sense , if it remains ... first2 D. S. authorlink2 David S. Johnson title Strong NP Completeness Results Motivation, Examples ... by the input size. Thus strong NP completeness or NP hardness may also be defined as the NP completeness or NP hardness of this unary version of the problem. For example, bin packing is strongly NP complete while the 0 1 Knapsack problem is only weakly NP complete . Thus the version of bin packing where the object and bin sizes are integers bounded by a polynomial remains NP complete, while ... . While weakly NP complete problems may admit efficient solutions in practice as long as their inputs are of relatively small magnitude, strongly NP complete problems do not admit efficient solutions in these cases. From a theoretical perspective any strongly NPhard optimization problem with a polynomially bounded objective function cannot have an FPTAS unless P NP ref name vvv ... year 2004 ref . Some strongly NP complete problems may still be easy to solve on average , but it s more likely that difficult instances will be encountered in practice. Unless P NP problem P NP , there is no fully polynomial time approximation scheme or FPTAS for the strongly NP complete ... more details
In computational complexity , an NP complete or NPhard problem is weakly NP complete or weakly NPhard , if there is an algorithm for the problem whose running time is polynomial in the dimension of the problem and the magnitudes of the data involved provided these are given as integers , rather than the base two logarithms of their magnitudes. Such algorithms are technically exponential functions of their input size and are therefore not considered polynomial. For example, the NPhard knapsack problem can be solved by a dynamic programming algorithm requiring a number of steps polynomial in the size of the knapsack and the number of items assuming that all data are scaled to be integers . This algorithm is exponential time since the input sizes of the objects and knapsack are logarithmic in their magnitudes. However, as Garey and Johnson 1979 observed, A pseudo polynomial time pseudo polynomial time algorithm will display exponential behavior only when confronted with instances containing exponentially large numbers, which might be rare for the application we are interested in. If so, this type of algorithm might serve our purposes almost as well as a polynomial time algorithm . The related term strongly NP complete or unary NP complete refers to those problems that remain NP complete even if the data are encoded in unary numeral system unary that is, if the data are small relative to the overall input size . References M. R. Garey and D. S. Johnson. Computers and Intractability a Guide to the Theory of NP Completeness . W.H. Freeman, New York, 1979. L. Hall. http www.esi2.us.es mbilbao complexi.htm Computational Complexity . The Johns Hopkins University. Category Weakly NP complete problems Category Computational complexity theory Category Complexity classes ... more details
Euler diagram for P complexity P , NP complexity NP , NP complete, and NPhard set of problems Main ... as tough as any other problem in NP . NPhard problems are those at least as hard as NP complete problems, i.e., all NP problems can be reduced in polynomial time to them. NPhard problems need not be in NP ... doi 10.2307 2580891 ref Also P NP still leaves open the average case complexity of hard problems in NP ... in all instances, to Cryptomania , where P NP and generating hard instances of problems outside P ... over instances of NPhard problems. The world where P NP but all problems in NP are tractable ...pp move indef unsolved computer science Is P NP ? Millennium Problems File Complexity classes.svg thumb 250px Diagram of complexity classes provided that P NP . The existence of problems within NP but outside both P and NP complete, under that assumption, was established by NP intermediate Ladner s theorem ... &CFID 15151515&CFTOKEN 6184618 ACM site . ref The P versus NP problem is a major List of unsolved ... Fortnow , http www.cs.uchicago.edu fortnow papers pnp cacm.pdf The status of the P versus NP problem ... a US 1,000,000 prize for the first correct solution. In essence, the P NP problem can be restated ... an answer can be verified in polynomial time is called NP complexity NP . Consider the subset sum ... hence this problem is in NP quickly checkable but not necessarily in P quickly solvable . An answer to the P NP question would determine whether problems like the subset sum problem ... that P does not equal NP , it would mean that there are problems in NP such as NP complete problems ... could be verified in polynomial time. Context The relation between the complexity class es P and NP ... decision problem s defined Formal definitions for P and NP below that can be solved on a deterministic ... NP complexity NP consists of all those decision problems whose positive solutions can be verified in polynomial ... Technology, 2006. Definition 7.19 and Theorem 7.20. ref Clearly, P NP . Arguably the biggest open ... more details
NotMovedToCommons File Np ox st .jpg reason not certain that it is a PD image Non free use rationale Article Neptunium Description Neptunium ions in solution Source http www.chemie master.de FrameHandler.php?loc http www.chemie master.de pse pse.php?modul Np Portion Entire image. Low resolution Purpose To depict the subject of the article Replaceability The only image found of solution of Np ions ... more details
programming NPhard in some cases, P if convex Cost parametric linear programming Feasible basis extension ... is NPhard. Comput. Geom. Theory Appl., 9 1 2 3&ndash 24, 1998 ref Many motion planning among polygonal obstacles in the plane are NPhard. Planar partitioning into connected subassemblies ...Here are some of the more commonly known problems that are NP complete when expressed as decision problem s. This list is in no way comprehensive there are more than 3000 known NP complete problems . Most ... A Guide to the Theory of NP Completeness , and are here presented in the same order and organization ... number ref harvtxt Garey Johnson 1979 GT2 ref NP complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP complete variants include ... Set ref NP complete special cases include the minimum maximal matching problem, ref harvtxt Garey ... Citation needed reason harvtxt Garey Johnson date November 2010 only mentions NP hardness, not NP ... Garey Johnson date November 2010 only mentions NP hardness, not NP completeness date March 2009 ... title The hardness of the lemmings game, or Oh no, more NP completeness proofs url http dimacs.rutgers.edu ... S and A S are connected. ref Assembly Into Two Connected Parts Is NP Complete , Inf. Proc. Letters ... Is NP Complete , SIAM News, Vol 33, No 6. ref See also Karp s 21 NP complete problems List of PSPACE ... is a classic, developing the theory, then cataloguing many NP Complete problems. cite conference ... list of selected NP complete problems publisher COMP202, Dept. of Computer Science, University .... Woeginger, G title A compendium of NP optimization problems publisher KTH NADA, Stockholm url http ... K title NP complete problems work Math Reference Project url http www.mathreference.com lan cx np,intro.html accessdate 2008 06 21 cite web first E last Friedman title Pearl puzzles are NP complete year ... 10.1007 BF03025367 last Kaye first Richard year 2000 title Minesweeper is NP complete journal Mathematical ... more details
main ISO 3166 2 ISO 3166 2 NP is the entry for Nepal in ISO 3166 2 , part of the ISO 3166 standardization standard published by the International Organization for Standardization ISO , which defines code s for the names of the principal country subdivision subdivision s e.g., province s or state administrative division state s of all country countries coded in ISO 3166 1 . Currently for Nepal, ISO ... of Nepal 14 zones Each code consists of two parts, separated by a hyphen. The first part is tt NP tt ... name English language en tt NP 1 tt Madhyamanchal Central tt NP 2 tt sort MadhyaPashchimanchal Madhya Pashchimanchal Mid Western tt NP 3 tt Pashchimanchal Western tt NP 4 tt Purwanchal Eastern tt NP 5 tt Sudur Pashchimanchal Far Western Zones class wikitable sortable Code Subdivision name Nepalese language ne In development region tt NP BA tt Bagmati Zone Bagmati Madhyamanchal tt 1 tt tt NP BH tt Bheri Zone Bheri Madhya Pashchimanchal tt 2 tt tt NP DH tt Dhawalagiri Zone Dhawalagiri Pashchimanchal tt 3 tt tt NP GA tt Gandaki Zone Gandaki Pashchimanchal tt 3 tt tt NP JA tt Janakpur Zone Janakpur Madhyamanchal tt 1 tt tt NP KA tt Karnali Zone Karnali Madhya Pashchimanchal tt 2 tt tt NP KO tt Kosi Zone Kosi Koshi Purwanchal tt 4 tt tt NP LU tt Lumbini Zone Lumbini Pashchimanchal tt 3 tt tt NP MA tt Mahakali Zone Mahakali Sudur Pashchimanchal tt 5 tt tt NP ME tt Mechi Zone Mechi Purwanchal tt 4 tt tt NP NA tt Narayani Zone Narayani Madhyamanchal tt 1 tt tt NP RA tt Rapti Zone Rapti Madhya Pashchimanchal tt 2 tt tt NP SA tt Sagarmatha Zone Sagarmatha Purwanchal tt 4 tt tt NP SE tt Seti ... codes M O NP Nepal FIPS region codes of Nepal External links http www.statoids.com unp.html Regions of Nepal , Statoids.com ISO 3166 Category ISO 3166 2 NP Category Regions of Nepal ISO 3166 2 Category Zones of Nepal ISO 3166 2 Category Nepal related lists cs ISO 3166 2 NP de ISO 3166 2 NP it ISO 3166 2 NP nl ISO 3166 2 NP sk ISO 3166 2 NP roa tara ISO 3166 2 NP yo ISO 3166 2 NP ... more details
8290 1992 NP is a asteroid belt main belt minor planet . It was discovered by Eleanor F. Helin and L. Lee at the Palomar Observatory in San Diego County, California San Diego County , California, on July 2, 1992. ref cite web url http ssd.jpl.nasa.gov sbdb.cgi?sstr 8290 title JPL Small Body Database Browser 8290 1992 NP work Jet Propulsion Laboratory JPL Small Body Database publisher NASA accessdate November 15, 2011 ref See also List of minor planets 8001 9000 References reflist beltasteroid stub MinorPlanets Navigator 8289 An Eefje 8291 Bingham Small Solar System bodies DEFAULTSORT 1992 NP Category Astronomical objects discovered in 1992 Category Discoveries by Eleanor F. Helin Category Main Belt asteroids vi 8290 1992 NP ... more details
coord 41 15 44 N 96 02 55 W display title Infobox Company company name NP Dodge Company company logo Image NP Dodge Color.png 180px N.P. Dodge Company company type Privately held company Private foundation Council Bluffs, IA br 1855 as N.P. Dodge location Omaha, Nebraska key people N.P. Dodge Jr, President ... http www.npdodge.com www.npdodge.com The NP Dodge Company is based in Omaha , Nebraska . Established in 1855 as a small land office in Council Bluffs , Iowa , NP Dodge is now the largest full service ... aboutus.cfm About Us . NP Dodge Company. Retrieved 2006 04 30. ref NP Dodge Company is the oldest ... 2008. ref About Subsidiaries of the NP Dodge company include NP Dodge Residential Sales and Land Development. Other areas of the company include http www.neirelo.com NEI Global Relocation , NP Dodge Property Management, NAI NP Dodge , NP Dodge Condo Sales, NP Dodge Title Services, and NP Dodge Builder ... Street of Dreams. ref http www.npdodge.com pressrelease.cfm?dt 20060623163342 NP Dodge Company . Retrieved ... high school and come join him. N.P. worked his way out on a surveying crew in 1853 and together ..., leaving the business management to his brother, N.P. Nathan Phillips Dodge II 1872 1950 joined NP Dodge Company in the early 1900s. His plan was to offer lots as his father did, making it affordable ... development brought the NP Dodge Company to a nationwide status with more than 200 subdivisions .... ref br br N.P. Dodge III 1910 2004 , called Phil, took over the NP Dodge Company in 1950. Eventually, NP Dodge refocused on the Omaha area. Phil expanded the company offerings to include residential ... Legislature , Metropolitan Utilities District Board, and Omaha City Council . br br N.P. Dodge IV 1937 , called Sandy, has taken up the work of his father, maintaining NP Dodge as the oldest ... Foundation Board . ref http www.npdodge.com NPDodge,Jr,CPM NP Dodge Company . Retrieved 4 9 08. ref br br N.P. Dodge V , or Nate, is the 5th generation of the Dodge family. Nate earned his Bachelor ... more details
Heavy NP shift is a particular manifestation of shifting linguistics shifting where a heavy noun phrase NP appears in a position to the right of its canonical position under certain circumstances. Although the term is coined according to the tradition of transformational grammar , which describes the process to be done by movement of the NP, the term is also used by linguists who do not believe in transformational grammar. Heaviness is determined by the grammatical complexity, such as a noun modified by a relative clause , but length is also correlated to complexity. The following pair shows a a sentence without heavy NP shift and b the same sentence after the operation has applied 1. a I gave the books which my uncle left to me as part of his inheritance to Bill 1. b I gave to Bill the books which my uncle left to me as part of his inheritance The operation cannot usually apply to smaller ... In the preceding examples, heavy NP shift has inverted the order of the Object grammar The object ... model of ideal gasses presented by Prof. Smith John R. Ross observed that heavy NP shift obeys a right roof constraint that is, an NP cannot be shifted outside of its containing clause, as shown ... the books which my uncle left to me Analyses of heavy NP shift There have been a number of different analyses of heavy NP shift within generative syntax. The traditional assumption was that there is a rightward ... NP to the right edge of the Verb phrase in which it occurs. In an alternative formulation, heavy NP shift may apply freely to any NP regardless of weight, but light NPs which undergo shifting are filtered ... Kayne s theory of Antisymmetry . Larson s analysis of heavy NP shift has been criticized by Ray ... ref see also Simpler Syntax . Jackendoff argues that heavy NP shift does not result from movement ... of heavy NP shift is that, in the case of ditransitive verbs, a shifted direct object prevents extraction ... be unexpected if heavy NP shift merely resulted from optionality in complement ordering, or from ... more details
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