Nondeterministic algorithm - Revision history

en>Ivanvector: /* Use */ unlinking guess

2014-12-10T20:20:21Z

Use: unlinking guess

← Older revision		Revision as of 22:20, 10 December 2014
Line 1:		Line 1:
	~~Professionals a strategy~~ and also battle activation where then you must manage your hold tribe and also prevent leakages. You have to be able to build constructions which will provide protection for your main soldiers along with each of our instruction. First target on your protection and ~~simply after its recently been taken treatment. You will need to move forward now with the criminal offense process. As well as ones own Military facilities, you in addition need to keep in mind~~'s ~~eye the way your tribe is certainly going. For instance, collecting indicates as well as widening your own tribe could be the key to good improvements~~.<br><br>		My name is Ferne and I am studying Gender and Women's Studies and Modern Languages at Judenburg / Austria.<br><br>Also visit my web blog: [http://healingfactory.co.kr/qna/27233 Bookbyte textbooks Coupons]

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en>Schapel: /* Use */ the guesses in a search are not estimation -- they are blind guesses

2014-02-24T12:50:40Z

Use: the guesses in a search are not estimation -- they are blind guesses

← Older revision		Revision as of 14:50, 24 February 2014
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	~~In [[computer science]]~~, a '~~''polynomial-time approximation scheme''' ('''PTAS''')~~ is ~~a type of [[approximation algorithm]] for [[optimization problem]]s (most often~~, ~~[[NP-hard]] optimization problems)~~.		Professionals a strategy and also battle activation where then you must manage your hold tribe and also prevent leakages. You have to be able to build constructions which will provide protection for your main soldiers along with each of our instruction. First target on your protection and simply after its recently been taken treatment. You will need to move forward now with the criminal offense process. As well as ones own Military facilities, you in addition need to keep in mind's eye the way your tribe is certainly going. For instance, collecting indicates as well as widening your own tribe could be the key to good improvements.<br><br>

	~~A PTAS is~~ an ~~algorithm which takes an instance of an optimization problem~~ and ~~a parameter ε > 0~~ and, in ~~polynomial time~~, ~~produces a solution that is within a factor 1 + ε of being optimal (or 1 - ε for maximization problems)~~. ~~For example, for~~ the ~~Euclidean [[traveling salesman problem]], a PTAS would produce a tour with length at most (1 + ε)~~'~~'L'',~~ with ~~''L'' being the length of the shortest tour~~.~~<ref>[[Sanjeev Arora]]~~, ~~Polynomial-time Approximation Schemes for Euclidean TSP and other Geometric Problems, Journal of the ACM 45(5) 753–782, 1998.</ref>~~		Employees may possibly play applications to rest following an incredibly long working day at your workplace. Some like socializing by tinkering together with friends and family. If you have whichever inquiries about where and in what ways to use Clash within Clans Cheat, you makes contact with us via our web site. Other individuals perform the entire group when they're jobless combined with require something for making their brains away those scenario. No be importance reasons why you enjoy, this information will help you along to engage in in such a way which is more effectively.<br><br>For anybody who is getting a online game for your little one, look for one understanding that enables numerous [http://customers.org/ customers] to do with each other. Video gaming can regarded as a solitary action. Nevertheless, it is important if you want to motivate your youngster getting to be social, and multi-player clash of clans hack is capable executing that. They empower sisters and brothers and / or buddies to all relating to take a moment and laugh and compete alongside one another.<br><br>Ordinarily clash of clans crack tool no survey devises believe in among ones people. If you beloved this posting and you would like to obtain a lot more details relating to [http://prometeu.net hack clash of clans 2014] kindly take a look at the web page. Society is almost certainly definitely powered by fellow pressure, one of the main most powerful forces on a the planet. As long as peer pressure utilizes its power for good, clash of clans hack tool no overview will have its house in community.<br><br>Hold out for game of this particular season editions of worthwhile titles. These most of the time come out per august or higher after some of the initial headline, but feature a lot of the particular down-loadable and extra matter which was released when steps once the first headline. These ball game titles supply a huge amount more bang for this particular buck.<br><br>To defeat higher-level villages, this task aids you to use a mixture of troops reminiscent of Barbarians plus Archers and those suicide wall bombers to bust down wall spaces. Goblins can also be a useful inflexion the combo simply considering that they attack different buildings. You should understand when you're ready to begin worrying about higher troops when your family can''t win battles while having Barbarians.<br><br>Bide time until game of the 1 year versions of major bands. These often come out a yr or maybe more for the original title, but are made lots of the down loadable and extra content which had been released in stages right after the first title. Of these games offer a much bang for the cent.

	~~The running time of~~ a ~~PTAS~~ is ~~required to be polynomial in ''n'' for every fixed ε but can be different for different ε~~. ~~Thus an algorithm running in time ''[[Big O notation\|O]]''(''n''~~<~~sup~~>~~1/ε~~<~~/sup~~>~~) or even ''O''(''n''<sup>exp(1/ε)</sup>) counts as~~ a ~~PTAS.~~

	~~==Variants==~~
	~~===Deterministic===~~
	~~A practical problem with PTAS algorithms is that the exponent of the polynomial could increase dramatically as ε shrinks~~, for ~~example if the runtime is O(''n''<sup>(1~~/~~ε)!<~~/~~sup>)~~. ~~One way of addressing this is~~ to ~~define the '''efficient polynomial-time approximation scheme''' or '''EPTAS''', in which the running time is required to be ''O''(''n''<sup>''c''</sup>) for a constant ''c'' independent of ε~~. ~~This ensures that an increase in problem size has the same relative effect on runtime regardless of what ε is being used; however, the constant under the [[Big O notation\|big-O]]~~ can ~~still depend on ε arbitrarily~~. ~~Even more restrictive, and useful in practice~~, is ~~the '''fully polynomial-time approximation scheme''' or '''FPTAS''', which requires the algorithm~~ to be ~~polynomial in both the problem size ''n''~~ and ~~1/ε. All problems in FPTAS are [[fixed~~-~~parameter tractable]]. An example~~ of ~~a problem~~ that ~~has an FPTAS is the [[knapsack problem]]~~.

	~~Any [[Strongly NP-complete\|strongly NP-hard]] optimization problem with~~ a polynomially bounded objective function cannot have an FPTAS unless P=NP.<ref name="vvv"/> However, the converse fails: e.g. if P does not equal NP, [[List_of_knapsack_problems#Multiple_constraints\|knapsack with two constraints]] is not strongly NP-hard, but has no FPTAS even when the optimal objective is polynomially bounded.<ref>{{cite book\|authors= H. Kellerer and ~~U. Pferschy~~ and D. ~~Pisinger\| title = Knapsack Problems \| publisher = Springer \| year = 2004}}~~<~~/ref~~>

	~~Unless [[P = NP problem\|P = NP]], it holds that FPTAS ⊊ PTAS ⊊ [[APX]].~~<~~ref~~>~~{{citation\|first=Thomas\|last=Jansen\|contribution=Introduction to the Theory~~ of ~~Complexity~~ and Approximation Algorithms\|pages=5–28\|title=Lectures on Proof Verification and Approximation Algorithms\|editor1-first=Ernst W.\|editor1-last=Mayr\|editor2-first=Hans Jürgen\|editor2-last=Prömel\|editor3-first=Angelika\|editor3-last=Steger\|publisher=Springer\|year=1998\|isbn=9783540642015\|doi=10.1007/BFb0053011}}. See discussion following Definition 1.30 on [http://~~books~~.~~google.com/books?id=_C8Ly1ya4cgC&pg=PA20 p. 20~~].~~</ref> Consequently~~, ~~under this assumption, APX-hard problems do not have PTASs.~~

	~~Another deterministic variant~~ of the ~~PTAS is~~ the ~~'''quasi-polynomial-time approximation scheme''' or '''QPTAS'''~~. ~~A QPTAS has time complexity~~ <~~math~~>~~n^{polylog(n)}~~<~~/math~~> for ~~each fixed <math>\epsilon >0</math>~~.

	~~===Randomized===~~
	~~Some problems which do not have a PTAS may admit a [[randomized algorithm]] with similar properties~~, a ~~'''polynomial~~-~~time randomized approximation scheme''' or '''PRAS'''~~. ~~A PRAS is an algorithm which takes an instance of an optimization or counting problem and~~ a ~~parameter ε ~~>~~ 0 and~~, ~~in polynomial time, produces a solution that has~~ a ~~''high probability''~~ of ~~being within a factor ε~~ of ~~optimal. Conventionally, "high probability" means probability greater than 3/4, though as with most probabilistic complexity classes the definition is robust~~ to ~~variations in this exact value~~. ~~Like~~ a ~~PTAS, a PRAS must have running time polynomial in ''n'', but not necessarily in ε; with further restrictions on~~ the ~~running time in ε, one can define an '''efficient polynomial-time randomized approximation scheme''' or '~~'~~'EPRAS''' similar~~ to ~~the EPTAS, and a '''fully polynomial-time randomized approximation scheme''' or '''FPRAS~~''~~' similar to the FPTAS~~.<~~ref name="vvv"~~>~~{{cite book~~
	~~\| last = Vazirani~~
	~~\| first = Vijay V.~~
	~~\| title = Approximation Algorithms~~
	~~\| publisher = Springer~~
	~~\| year = 2003~~
	~~\| pages = 294–295~~
	~~\| location = Berlin~~
	~~\| isbn = 3-540-65367-8~~
	}}<~~/ref~~>

	~~==References==~~
	~~<references/>~~

	~~==External links==~~
	*Complexity Zoo: [https://complexityzoo.~~uwaterloo.ca/Complexity_Zoo:P#ptas PTAS], [https://complexityzoo.uwaterloo.ca/Complexity_Zoo:E#eptas EPTAS], [https://complexityzoo.uwaterloo.ca/Complexity_Zoo:F#fptas FPTAS]~~
	*Pierluigi Crescenzi, Viggo Kann, Magnús Halldórsson, [[Marek Karpinski]], and ~~Gerhard Woeginger, [http://www~~.~~nada~~.~~kth.se/~viggo/wwwcompendium/ ''A compendium of NP optimization problems''] – list which NP optimization problems have PTAS.~~

	~~{{DEFAULTSORT:Polynomial-Time Approximation Scheme}}~~
	~~[[Category:Approximation algorithms]]~~
	~~[[Category:Complexity classes]]~~

49.136.165.178: /* Example 2: Spanning tree */

2013-11-26T08:50:51Z

Example 2: Spanning tree

← Older revision		Revision as of 10:50, 26 November 2013
Line 1:		Line 1:
	~~Acquiring an offshore account~~ is ~~one the very best tactics~~ for ~~a person to guard their money~~, ~~and something of the greatest kinds of offshore accounts are termed no identification offshore account~~. ~~This sort~~ of ~~account doesn't need~~ a ~~person to confirm their identification when beginning the account~~, ~~as well as~~ in ~~many situations it's perfectly good~~ for a ~~person to open up the account under~~ a ~~name that~~'~~s unique~~ of ~~their very own~~. ~~There are a couple~~ of ~~issues~~ a ~~person should~~ be ~~aware of~~ a ~~few number ID offshore account including~~ the ~~means~~ of ~~opening an account~~, ~~and what such accounts are often useful~~ for.<br><br>~~How exactly~~ to ~~open a zero ID account~~<br><br>~~The procedure~~ of ~~checking a zero ID account is exceptionally simple~~. ~~In most cases~~ an ~~individual~~ can ~~basically head into a bank workplace~~, and ~~then have~~ the ~~process~~ of ~~opening~~ a ~~free account~~. ~~This usually entails having~~ an ~~individual jot down the~~ name of the ~~account~~, and ~~choosing what choices they want for your account~~. ~~An individual may then just withdraw income from your account my writing down a secret rule~~. ~~Some banks~~ that ~~provide offshore accounts will~~ not ~~perhaps require a person to visit~~ the ~~lender office~~.<br><br>~~What these accounts are used~~ for<br><br>~~These types~~ of ~~accounts are usually used by folks who want to shield their resources from things such as lawsuits~~, ~~or having them recinded with~~ a ~~government~~. ~~This really is critical~~, as it is one ~~of many techniques~~ an ~~individual may make sure that their income basically doesn~~'~~t get arrested for almost any explanation~~. ~~More~~: [http://~~noidoffshoreaccount~~.~~metroblog~~.~~com~~/~~choosing_a_no_id_prepaid_card similar webpage~~].		In [[computer science]], a '''polynomial-time approximation scheme''' ('''PTAS''') is a type of [[approximation algorithm]] for [[optimization problem]]s (most often, [[NP-hard]] optimization problems).

			A PTAS is an algorithm which takes an instance of an optimization problem and a parameter ε > 0 and, in polynomial time, produces a solution that is within a factor 1 + ε of being optimal (or 1 - ε for maximization problems). For example, for the Euclidean [[traveling salesman problem]], a PTAS would produce a tour with length at most (1 + ε)''L'', with ''L'' being the length of the shortest tour.<ref>[[Sanjeev Arora]], Polynomial-time Approximation Schemes for Euclidean TSP and other Geometric Problems, Journal of the ACM 45(5) 753–782, 1998.</ref>

			The running time of a PTAS is required to be polynomial in ''n'' for every fixed ε but can be different for different ε. Thus an algorithm running in time ''[[Big O notation\|O]]''(''n''<sup>1/ε</sup>) or even ''O''(''n''<sup>exp(1/ε)</sup>) counts as a PTAS.

			==Variants==
			===Deterministic===
			A practical problem with PTAS algorithms is that the exponent of the polynomial could increase dramatically as ε shrinks, for example if the runtime is O(''n''<sup>(1/ε)!</sup>). One way of addressing this is to define the '''efficient polynomial-time approximation scheme''' or '''EPTAS''', in which the running time is required to be ''O''(''n''<sup>''c''</sup>) for a constant ''c'' independent of ε. This ensures that an increase in problem size has the same relative effect on runtime regardless of what ε is being used; however, the constant under the [[Big O notation\|big-O]] can still depend on ε arbitrarily. Even more restrictive, and useful in practice, is the '''fully polynomial-time approximation scheme''' or '''FPTAS''', which requires the algorithm to be polynomial in both the problem size ''n'' and 1/ε. All problems in FPTAS are [[fixed-parameter tractable]]. An example of a problem that has an FPTAS is the [[knapsack problem]].

			Any [[Strongly NP-complete\|strongly NP-hard]] optimization problem with a polynomially bounded objective function cannot have an FPTAS unless P=NP.<ref name="vvv"/> However, the converse fails: e.g. if P does not equal NP, [[List_of_knapsack_problems#Multiple_constraints\|knapsack with two constraints]] is not strongly NP-hard, but has no FPTAS even when the optimal objective is polynomially bounded.<ref>{{cite book\|authors= H. Kellerer and U. Pferschy and D. Pisinger\| title = Knapsack Problems \| publisher = Springer \| year = 2004}}</ref>

			Unless [[P = NP problem\|P = NP]], it holds that FPTAS ⊊ PTAS ⊊ [[APX]].<ref>{{citation\|first=Thomas\|last=Jansen\|contribution=Introduction to the Theory of Complexity and Approximation Algorithms\|pages=5–28\|title=Lectures on Proof Verification and Approximation Algorithms\|editor1-first=Ernst W.\|editor1-last=Mayr\|editor2-first=Hans Jürgen\|editor2-last=Prömel\|editor3-first=Angelika\|editor3-last=Steger\|publisher=Springer\|year=1998\|isbn=9783540642015\|doi=10.1007/BFb0053011}}. See discussion following Definition 1.30 on [http://books.google.com/books?id=_C8Ly1ya4cgC&pg=PA20 p. 20].</ref> Consequently, under this assumption, APX-hard problems do not have PTASs.

			Another deterministic variant of the PTAS is the '''quasi-polynomial-time approximation scheme''' or '''QPTAS'''. A QPTAS has time complexity <math>n^{polylog(n)}</math> for each fixed <math>\epsilon >0</math>.

			===Randomized===
			Some problems which do not have a PTAS may admit a [[randomized algorithm]] with similar properties, a '''polynomial-time randomized approximation scheme''' or '''PRAS'''. A PRAS is an algorithm which takes an instance of an optimization or counting problem and a parameter ε > 0 and, in polynomial time, produces a solution that has a ''high probability'' of being within a factor ε of optimal. Conventionally, "high probability" means probability greater than 3/4, though as with most probabilistic complexity classes the definition is robust to variations in this exact value. Like a PTAS, a PRAS must have running time polynomial in ''n'', but not necessarily in ε; with further restrictions on the running time in ε, one can define an '''efficient polynomial-time randomized approximation scheme''' or '''EPRAS''' similar to the EPTAS, and a '''fully polynomial-time randomized approximation scheme''' or '''FPRAS''' similar to the FPTAS.<ref name="vvv">{{cite book
			\| last = Vazirani
			\| first = Vijay V.
			\| title = Approximation Algorithms
			\| publisher = Springer
			\| year = 2003
			\| pages = 294–295
			\| location = Berlin
			\| isbn = 3-540-65367-8
			}}</ref>

			==References==
			<references/>

			==External links==
			*Complexity Zoo: [https://complexityzoo.uwaterloo.ca/Complexity_Zoo:P#ptas PTAS], [https://complexityzoo.uwaterloo.ca/Complexity_Zoo:E#eptas EPTAS], [https://complexityzoo.uwaterloo.ca/Complexity_Zoo:F#fptas FPTAS]
			*Pierluigi Crescenzi, Viggo Kann, Magnús Halldórsson, [[Marek Karpinski]], and Gerhard Woeginger, [http://www.nada.kth.se/~viggo/wwwcompendium/ ''A compendium of NP optimization problems''] – list which NP optimization problems have PTAS.

			{{DEFAULTSORT:Polynomial-Time Approximation Scheme}}
			[[Category:Approximation algorithms]]
			[[Category:Complexity classes]]

188.225.178.66: /* Use */

2012-07-13T07:59:21Z

Use

New page

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