Diode modelling - Revision history

153.19.97.133: /* Explicit solution */ Double point removed

2014-10-22T12:56:10Z

Explicit solution: Double point removed

← Older revision		Revision as of 14:56, 22 October 2014
Line 1:		Line 1:
	~~In [[constraint satisfaction]], '''backmarking''' is a variant of the [[backtracking]] algorithm.~~		Hi there, I am Andrew Berryhill. Credit authorising is how he makes money. Ohio is where his house is and his family enjoys it. To play lacross is something he would never give up.<br><br>my web-site; psychics online ([http://brazil.amor-amore.com/irboothe just click the next web page])

	Backmarking works like backtracking by iteratively evaluating variables in a given order, for example, <math>x_1,\ldots,x_n</math>. It improves over backtracking by maintaining information about the last time a variable <math>x_i</math> was instantiated to a value and information about what changed since then. In particular:

	~~[[Image:Backmarking-1.png\|thumb\|180px\|An example, in which search has reached xi=d the first time.]]~~
	# for each variable <math>x_i</math> and value <math>a</math>, the algorithm records information about the last time <math>x_i</math> has been set to <math>a</math>; in particular, it stores the minimal index <math>j<i</math> such that the assignment to <math>x_1,\ldots,x_j,x_i</math> was then [[inconsistent]];
	# for each variable <math>x_i</math>, the algorithm stores some information relative to what changed since the last time it has evaluated <math>x_i</math>; in particular, it stores the minimal index <math>k<i</math> of a variable that was changed since then.

	The first information is collected and stored every time the algorithm evaluates a variable <math>x_i</math> to <math>a</math>, and is done by simply checking consistency of the current assignments for <math>x_1,x_i</math>, for <math>x_1,x_2,x_i</math>, for <math>x_1,x_2,x_3,x_i</math>, ~~etc.~~

	~~[[Image:Backmarking-2~~.~~png\|thumb\|180px\|When search reaches xi=d for the second time, part of the path~~ is ~~the same as the first time~~.]]
	~~The second information~~ is ~~changed every time ''another'' variable~~ is ~~evaluated~~. In particular, the index of the "maximal unchanged variable since the last evaluation of <math>x_i</math>" is possibly changed every time another variable <math>x_j</math> changes value. Every time an arbitrary variable <math>x_j</math> changes, all variables <math>x_i</math> with <math>i>j</math> are considered in turn. If <math>k</math> was their previous associated index, this value is changed to <math>min(k,j)</math>.

	~~The data collected this way~~ is ~~used to avoid some consistency checks. In particular, whenever backtracking~~ would ~~set <math>x_i=a</math>, backmarking compares the two indexes relative to <math>x_i</math> and the pair <math>x_i=a</math>~~. ~~Two conditions allow to determine partial consistency or inconsistency without checking with the constraints. If <math>k~~<~~/math~~> ~~is the minimal index of a variable that changed since the last time~~ <~~math~~>x_i</math> was evaluated and <math>j</math> is the minimal index such that the evaluation of <math>x_1,\ldots,x_j,x_i</math> was consistent the last time <math>x_i</math> has been evaluated to <math>a</math>, then:

	~~# if <math>j<k</math>, the evaluation of <math>x_1,\ldots,x_j,x_i</math> is still inconsistent as it was before, as none of these variables changed so far~~; ~~as a result, no further consistency check is necessary;~~
	# if <math>j \geq k</math>, the evaluation <math>x_1,\ldots,x_k,x_i</math> is still consistent as it was before; this allows for skipping some consistency checks, but the assignment <math>x_1,\ldots,x_i</math> may still be inconsistent.

	~~Contrary to other variants to backtracking, backmarking does not reduce the search space but only possibly reduce the number of constraints that are satisfied by a partial solution.~~

	~~==References==~~
	*{{cite book
	~~\| first=Rina~~
	~~\| last=Dechter~~
	~~\| title=Constraint Processing~~
	~~\| publisher=Morgan Kaufmann~~
	~~\| year=2003~~
	~~\| url=~~http://~~www~~.~~ics~~.~~uci.edu~~/~~~dechter/books/index.html~~
	~~\| isbn=1-55860-890-7~~
	}}

	~~[[Category:Constraint programming]~~]

129.22.143.142: /* Explicit solution */

2014-02-03T23:06:35Z

Explicit solution

← Older revision		Revision as of 01:06, 4 February 2014
Line 1:		Line 1:
	~~Jayson Berryhill is how I~~'~~m called and my spouse doesn~~'t like ~~it at all~~. ~~Invoicing is~~ what ~~I do~~. ~~One of~~ the ~~very best issues~~ in the ~~world~~ for ~~him~~ is ~~doing ballet~~ and he'~~ll be starting~~ some ~~thing else along~~ with it~~. Her family members life in Ohio.~~<br><br>~~Visit my web site~~; ~~psychic readers ([~~http://www.~~weddingwall~~.~~com~~.au/~~groups~~/~~easy~~-~~advice~~-~~for~~-~~successful-personal-development-today/ weddingwall.com.au~~])		In [[constraint satisfaction]], '''backmarking''' is a variant of the [[backtracking]] algorithm.

			Backmarking works like backtracking by iteratively evaluating variables in a given order, for example, <math>x_1,\ldots,x_n</math>. It improves over backtracking by maintaining information about the last time a variable <math>x_i</math> was instantiated to a value and information about what changed since then. In particular:

			[[Image:Backmarking-1.png\|thumb\|180px\|An example, in which search has reached xi=d the first time.]]
			# for each variable <math>x_i</math> and value <math>a</math>, the algorithm records information about the last time <math>x_i</math> has been set to <math>a</math>; in particular, it stores the minimal index <math>j<i</math> such that the assignment to <math>x_1,\ldots,x_j,x_i</math> was then [[inconsistent]];
			# for each variable <math>x_i</math>, the algorithm stores some information relative to what changed since the last time it has evaluated <math>x_i</math>; in particular, it stores the minimal index <math>k<i</math> of a variable that was changed since then.

			The first information is collected and stored every time the algorithm evaluates a variable <math>x_i</math> to <math>a</math>, and is done by simply checking consistency of the current assignments for <math>x_1,x_i</math>, for <math>x_1,x_2,x_i</math>, for <math>x_1,x_2,x_3,x_i</math>, etc.

			[[Image:Backmarking-2.png\|thumb\|180px\|When search reaches xi=d for the second time, part of the path is the same as the first time.]]
			The second information is changed every time ''another'' variable is evaluated. In particular, the index of the "maximal unchanged variable since the last evaluation of <math>x_i</math>" is possibly changed every time another variable <math>x_j</math> changes value. Every time an arbitrary variable <math>x_j</math> changes, all variables <math>x_i</math> with <math>i>j</math> are considered in turn. If <math>k</math> was their previous associated index, this value is changed to <math>min(k,j)</math>.

			The data collected this way is used to avoid some consistency checks. In particular, whenever backtracking would set <math>x_i=a</math>, backmarking compares the two indexes relative to <math>x_i</math> and the pair <math>x_i=a</math>. Two conditions allow to determine partial consistency or inconsistency without checking with the constraints. If <math>k</math> is the minimal index of a variable that changed since the last time <math>x_i</math> was evaluated and <math>j</math> is the minimal index such that the evaluation of <math>x_1,\ldots,x_j,x_i</math> was consistent the last time <math>x_i</math> has been evaluated to <math>a</math>, then:

			# if <math>j<k</math>, the evaluation of <math>x_1,\ldots,x_j,x_i</math> is still inconsistent as it was before, as none of these variables changed so far; as a result, no further consistency check is necessary;
			# if <math>j \geq k</math>, the evaluation <math>x_1,\ldots,x_k,x_i</math> is still consistent as it was before; this allows for skipping some consistency checks, but the assignment <math>x_1,\ldots,x_i</math> may still be inconsistent.

			Contrary to other variants to backtracking, backmarking does not reduce the search space but only possibly reduce the number of constraints that are satisfied by a partial solution.

			==References==
			*{{cite book
			\| first=Rina
			\| last=Dechter
			\| title=Constraint Processing
			\| publisher=Morgan Kaufmann
			\| year=2003
			\| url=http://www.ics.uci.edu/~dechter/books/index.html
			\| isbn=1-55860-890-7
			}}

			[[Category:Constraint programming]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-10T16:54:14Z

ISBNs (Build KE)

New page

Jayson Berryhill is how I'm called and my spouse doesn't like it at all. Invoicing is what I do. One of the very best issues in the world for him is doing ballet and he'll be starting some thing else along with it. Her family members life in Ohio.<br><br>Visit my web site; psychic readers ([http://www.weddingwall.com.au/groups/easy-advice-for-successful-personal-development-today/ weddingwall.com.au])