Bubble sort - Revision history

en>Glrx: Undid revision 641681563 by Ravindra5337 (talk) if list is sorted, then swapped is false, not swapped is true, and until exits

2015-01-11T23:11:02Z

Undid revision 641681563 by Ravindra5337 (talk) if list is sorted, then swapped is false, not swapped is true, and until exits

← Older revision		Revision as of 01:11, 12 January 2015
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135.23.49.20: /* Rabbis and turtles */ Rabbis -> Rabbits

2014-03-03T21:31:12Z

Rabbis and turtles: Rabbis -> Rabbits

← Older revision		Revision as of 23:31, 3 March 2014
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	~~In [[game theory]], a '''job scheduling game'''~~ is a ~~game that models a scenario in which multiple selfish users wish~~ to ~~utilize multiple processing machines~~. ~~Each user has~~ a ~~single job~~, and ~~he needs to choose a single machine to process it~~. The ~~incentive of each user~~ is ~~to have his job run as fast as possible~~.		The Jacksonville Farmers Market is held year round from 7 a.m. to 7 p.m. onrr a daily basis. This permanent market is preferred destination for residents looking for organic ingredients, specialty goods and seasonal foods. The Jacksonville Farmers Market is held at 1810 West Beaver Street. Call (904) 354-2821 for more information.<br><br>The indisputable fact Kevin Nash beat Goldberg for the title because of a cattle prod and afterwards Nash handed the belt back to hogan without the pain . finger poke of doom is the main promises catalyst that started WCW's downfall. Once Goldberg was defeated, he was never the incredibly. He also holds the notoriety as being the man who ended Bret Hart's career, by using a legitimate kick to the head that caused a concussion, which helped lead to Bret's seizure.<br><br>Just as hogan shoes delivered for followers at Wrestlemania 1, the Mavericks delivered for enthusiasts and sent the Heat back to your locker looking to next every 12 months.<br><br>It was time much more for Hulk Hogan to leave out the WWE, this a person to head to World Championship Wrestling. Vince McMahon wanted Hulk Hogan to lose the title to Bret Hart as a way of passing the torch but Hulk Hogan refused. Instead Hulk Hogan defended the WWE World Heavyweight Title against Yokozuna. Yokozuna kicked out of Hulk Hogan's leg drop and then did a leg drop of the to win the the WWE World Heavyweight Trophy. Yokozuna then gave one final Banzai Drop to Hulk Hogan to stop Hulkamania.<br><br>Watch those eyes - Visual contact is a legitimate critical invest conversation, so make sure you create it for her. Pay attention how she makes utilization of her eyes, when she looks to you hogan outlet the whole period you can be talking then she is keen on what you in order to express especially basically offering you particular concentration. Furthermore, when seated across a table, see if she looks up swiftly in order to catch some kind of glimpse of you, in case she does then this is a good sign. When she has roaming eyes, then maybe it's time you wander your eyes to an unique girl and cut your losses!<br><br>Wrestlemania V saw the collision of the Mega Powers, Randy Savage and hogan shoes. The feud one of the two started after Randy Savage became suspicious of Hogan's intentions with Savage's valet, Miss Elizabeth. The feud between Randy Savage and hogan shoes assists you to showcase wrestling at its best.<br><br>April 5, 2009, at Reliant Stadium in Houston Wrestlemania XXV, the silver anniversary of Wrestlemania will broadcast live via pay-per-view. Keep a on Jeff Hardy, in which has never won an event at Wrestlemania. His the come. Expect a grand entrance from John Cena and a tough match. Triple H is arising to Wrestlemania XV for you to fight. He's got more enemies than as well as family hasn't won a Wrestlemania match since 2003. Is he going to be able to keep his smart aleck comments to himself long enough to win a title at Wrestlemania XXV?<br><br>When you adored this short article as well as you wish to be given details with regards to [http://www.medicalgroup-cerro.it/scarpe-hogan/ hogan scarpe] generously go to the website.

	~~== Definition ==~~

	~~'''Job scheduling games''' are the following set of problems: given <math> M </math> machines and <math>N</math> jobs. Each job <math>i</math> is associated with a vector <math>p_i =~~ (~~p_i^1,...,p_i^m~~) ~~</math>, corresponding to its size on each machine (i~~.~~e., <math> p_i^j~~ <~~/math~~> ~~is the processing time of job~~ <~~math~~>~~i</math> on machine <math>j</math>). Players correspond to jobs.~~ The ~~strategy set of each player is the set of machines. Given a strategy~~ for ~~each player,~~ the ~~total load on each machine is the sum of processing times~~ of the jobs that chose that machine. Usually each player seeks to minimize the total load on its chosen machine. The standard objective function is minimizing the total load on the most-loaded machine (this objective is called [[makespan minimization]]).

	~~For example: given game with 2 machines M1 and M2 and 2 jobs J1 and J2. The rows represent the strategies job J1 can choose and the columns represent the strategies job J2 can choose.~~
	~~{\| class="wikitable" style="text-align:center; width:150px; height:150px" border="1"~~
	\|+
	\|-
	~~! J1/J2!! M1 !! M2~~
	\|-
	~~! M1~~
	~~\| (1,10) \|\| (10,10)~~
	\|-
	~~! M2~~
	~~\| (1,1) \|\| (10,1)~~
	\|}

	~~== Motivation ==~~

	~~The problem of dividing several jobs among several machines in~~ a ~~way that optimizes some global objective function is well known~~ and ~~has been widely studied in [[computer science]]. In this type of problems there is a '''central designer''' that determines~~ the ~~allocation of jobs into machines and all the participating entities are assumed~~ to ~~obey~~ the ~~protocol~~. ~~However, since the emergence~~ of the Internet, problems in '''distributed settings''' has been studied as well. In this type of problems, different machines and jobs may be owned by different strategic entities, who will typically attempt to optimize their own objective rather than the global objective.

	~~== Main Properties ==~~

	~~The price of stability is used to measure inefficiency. It differentiates between games in which all equlibria are inefficient and those in which there exists an equilibrium~~ that ~~is inefficient~~

	~~=== For every job scheduling game price of stability is equal to 1 ===~~

	''~~'proof''': [[Price of stability]] is equal to best [[Nash equilibrium]] divided by OPTimum~~. ~~Therefore~~, ~~in order to prove that Price of stability = 1 it is sufficient to prove that the optimum is equal to~~ the ~~best Nash equilibrium~~. ~~In order to proof that, it is sufficient to proof that there is an OPTimum solution which is in Nash equilibrium, since if the OPTimum is~~ also ~~Nash equilibrium it is especially best Nash equilibrium.~~

	~~The optimum state is when~~ the ~~most loaded machine is~~ the ~~less loaded it can be. Assuming each job which was scheduled~~ to the ~~most loaded machine will not aspire to move to another machine. In addition, each job~~ that ~~was scheduled to~~ a ~~machine~~ which ~~is not the most loaded one, will not aspire~~ to ~~move to the most loaded machine~~. ~~Given a game with in the optimum state with~~ <~~math~~> M <~~/math~~> ~~machines~~. ~~Assuming there is a job~~ <~~math~~> x <~~/math~~> ~~that aspire~~ to ~~be scheduled on machine <math> M_i </math> instead of being scheduled on~~ the ~~most loaded machine - <math> M_d</math>. In that case~~, ~~there exist~~ a ~~machine that after job <math>x</math> was transfer, its load is less than the load of the machine <math> M_d</math> before job <math>x</math> changed~~. ~~This is in contradiction~~ to the ~~assumption that~~ the ~~game is in the OPTimum state~~. ~~Therefore, job will not be reassigned from and to~~ the ~~most loaded machine~~.
	~~We will now observe the scheduling~~ of ~~the <math> M-1 </math> machines left~~ and ~~the amount~~ of ~~jobs left (with out the jobs that was scheduled on machine <math> M_d</math>). For~~ the ~~same reasons that were mention earlier, there is no job that would like~~ to ~~move from~~ the ~~(new) most load machine or to~~ the ~~(new) most load machine~~. ~~By passing all <math> M </math> machines in inductive steps we will get n jobs scheduled~~ to <~~math~~> M <~~/math~~>~~.This jobs will not aspire to move from their own machine. Meaning~~, for ~~each job~~, ~~its strategy is its best response~~ to the ~~profile. In other words we have got an OPTimum state which~~ is ~~also~~ in ~~Nash equilibrium~~.
	~~Thus~~, ~~price~~ of ~~stability = 1.~~

	~~----~~

	~~The price~~ of ~~anarchy~~ is a ~~concept from game theory that describes the difference in maximum social utility~~ and the ~~utility~~ of ~~an equilibrium point~~ of the ~~game.~~

	~~=== There exist job scheduling game where Price~~ of ~~anarchy is not bounded ===~~

	''~~' claim: '''[[Price of anarchy]] = <math>\infty </math>~~.

	~~'''proof: '''Given a game with 2 machines <math>M_1</math>~~ and <~~math~~>~~M_2~~<~~/math~~> ~~and 2 jobs <math>J_1 = 1~~,~~K </math> and <math>J_2 = K~~,~~1 </math> for any natural <math> K >1 </math>~~. ~~In this game, job <math>J_1 </math> cost 1 on machine <math>M_1 </math> and <math>K</math>~~ on ~~machine <math>M_2 </math>~~, ~~and job <math>J_2 </math> cost <math>K</math> on machine <math>M_1 </math> and 1 on machine <math>M_2 </math>~~. ~~Therefore,~~ the ~~OPTimum state is when <math>J_1 </math> is scheduled to <math>M_1 </math>~~ and ~~<math>J_2 </math> scheduled to <math>M_2 </math> since the objective function is 1~~. ~~Moreover, the worst [[Nash equilibrium]] is when <math>J_1 </math>~~ is ~~scheduled~~ to ~~<math>M_2 </math> and <math>J_2 </math> scheduled~~ to ~~<math>M_1 </math>~~ since ~~the objective function is <math>K</math>~~. ~~It is a [[Nash equilibrium]] because if job <math>J_1</math> will~~ be ~~scheduled~~ to ~~machine~~ <~~math~~> ~~M_2~~ <~~/math~~> ~~the total load of~~ this ~~machine will raise from <math>K</math>~~ to ~~<math>K+1</math>, and likewise for job <math> J_2 </math>. Since [[Price of anarchy]] is equal~~ to ~~worst~~ [~~[Nash equilibrium]] divided by Optimum, price of anarchy = <math>K </math>. This is true for any natural <math>K </math> and thus price of anarchy is not bounded as claimed.~~

	~~== External links ==~~
	*http://www.~~faculty~~.~~idc.ac.il/tami/Papers/approxSE.pdf~~
	*http://www.aicit.org/jcit/paper_detail.html?q=56
	*http://www.computer.org/portal/web/csdl/doi?doc=doi/10.1109/~~WETICE.2007.109~~
	*http://www.computer.org/csdl/proceedings/compeng/2010/3974/00/3974a124-~~abs.html~~
	*http:/~~/rd~~.~~springer.com/chapter/10.1007/978-3-642-31724-8_65~~

	~~[[Category:Game theory]]~~

en>Nick Levine: Reverted edits by 198.97.41.12 (talk) to last version by Glrx

2014-01-30T18:21:55Z

Reverted edits by 198.97.41.12 (talk) to last version by Glrx

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76.6.165.10: Reverted animated GIF at the top of the page to the image used previously: This GIF's depiction of bubblesort is totally inaccurate (the other two animations on the page are just fine, however)

2012-08-31T13:13:00Z

Reverted animated GIF at the top of the page to the image used previously: This GIF's depiction of bubblesort is totally inaccurate (the other two animations on the page are just fine, however)

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