Roll forming - Revision history

en>Monkbot: /* Bibliography */Task 5: Fix CS1 deprecated coauthor parameter errors

2014-07-24T04:12:47Z

Bibliography: Task 5: Fix CS1 deprecated coauthor parameter errors

← Older revision		Revision as of 06:12, 24 July 2014
Line 1:		Line 1:
	~~[[File:Stirling permutation Euler tour.svg\|thumb\|240px\|Euler tour of a tree~~, ~~with edges labeled to show the order in which they~~ are ~~traversed by~~ the ~~tour]]~~		Chef's knives, also identified as French knives or cook's knives, are the [http://workhorses.com/ workhorses] of the kitchen. Do you have [http://www.google.co.uk/search?hl=en&gl=us&tbm=nws&q=kitchen+scissors&gs_l=news kitchen scissors] that make you glad to use them? Should you beloved this post and you want to be given more information with regards to [http://www.thebestkitchenknivesreviews.com/best-cutting-boards-reviews-guide-and-comparison/ most effective cutting board size] i implore you to check out our own web-site. A straight three" paring knife: A utility knife. It runs by way of the middle of the deal with and not only delivers a way to attach the handle, but it helps give the knife a excellent balance. While each and every knife has a use, most persons never will need so lots of of the more specialized knives. If you never have any other knife, you require a paring knife. It really is a modest knife with a straight, sharp blade. This tiny knife is simple to deal with and use. Every kitchen really should have at least 1 good paring knife. Sharpen your kitchen knives on a sharpener.<br><br><br><br>As well frequently individuals who don't cook finally set out to make dinner and choose the healthiest, most punishing recipe imaginable mainly because they are on a diet program or squeamish about producing anything with fat (how else are boneless, skinless chicken breasts so preferred?) This is completely the incorrect way to go about it. When you cook, particularly if you are a newbie, you need to make items that are over the leading scrumptious. Gourmet Cutlery Set with Wood Block.<br><br>Pretty nicely presented - knives are component of the toolbox each and every fantastic cook or chef needs to generate excellent meals. I have a knife set that is not Calphalon but appreciate the info for down the road. Without the need of a doubt, a very best chef knife is undoubtedly regarded as a very very good investment for moms offered that it is the a single of the most considerable kitchen utensils that moms usually use when they are cooking.<br><br>For these who are seriously committed to the art of cooking, when it comes to browsing for that perfect chef knife bag remember that there are devoted web-sites out there for your perusal. Furthermore, when contemplating what goes into a chef knife bag or kitchen block set keep in mind that there are a complete lots of unique kindsknives that you want to familiarize your self with prior to choosing the correct one particular for you. This is a guide for Chef's knife utilities.<br><br>Worldwide recommends periodically sharpening your knives employing either a whetstone or ceramic stone, but even the wheel sharpener is stated to deliver very good benefits. MinoSharp are hand held ceramic sharpeners and no knowledge or talent is needed to use them - merely fill the reservoir with water and run your knife backwards and forwards a handful of instances. Even with the finest knife on the marketplace, it's no excellent unless it is sharp.<br><br>In contrast, the Classic line has a conventional French knife handle, with a heavy rounded butt and square edges on the handle. On the other hand, a heavy bolster that extends down to the heel of the knife gives the blade a further function: cracking and crushing. If you only purchase a single excellent item in your kitchen it ought to be a excellent chef's knife. This will outcome is a sharper edge for longer, and less put on and tear on your knife.<br><br>Presuming The purchaser concerned as a way for choose up a bit of a Steak Knife Set, six Piece Stainless Steel Case Pack 36 to a meeting savings, The person could also sample to observe upwards of crown of object particulars , specification or even verbal description. Understand specifically the review really should grant you to appreciate of the Steak Knife Set, 6 Piece Stainless Steel Case Pack 36 difficulties or even specialists. The other style is Japanese, and well-liked brands include things like Global and Shun.<br><br>Announcement of remedy in 2014 was a surprise and a boost to analysis and information-seeking. The planet has only a single entertainer with a Paul McCartney marionette and quite a few sets of Beatles puppets. Tomatoes land in unexpected locations amongst tasty globe cuisines, including Tomato Juice Cakes from Girl Scout pot lucks - they are fairly good. The DIA practically lost its 100 art collections to settle the bankruptcy of the City of Detroit. A serrated knife has a extended jagged edge.<br><br>Block knife sets are a terrific investment for your kitchen. Pick from the 14-Piece Knife Set with Organic Wood Block or the Ginsu eight-Piece Stainless Steel Knife Set with Bamboo Block. The eight piece forged knife set includes a 3-1/2-inch paring knife, 5-inch utility knife, five-inch serrated knife, 7-inch santoku knife, an eight-inch chef's knife, shears, sharpening rod and bamboo storage block. A Chef's Knife is a versatile knife used to peel, trim, pare, slice, dice and chop.
	~~The '''Euler tour technique (ETT)''', named after~~ [~~[Leonhard Euler]], is a method in [[graph theory]] for representing [[tree (graph theory)\|trees]]~~. ~~The tree is viewed as a [[directed graph~~]~~] that contains two directed edges for each edge in~~ the ~~tree~~. ~~The tree can then be represented as a~~ [~~[Eulerian circuit]] of the directed graph, known as the '''Euler tour representation''' (ETR) of the tree~~. ~~The ETT allows for efficient, [[parallel computation~~]~~] of solutions~~ to ~~common problems in [[algorithmic graph theory]]. It was introduced by Tarjan~~ and ~~Vishkin in 1984.<ref name="Tarjan">R.E. Tarjan, U. Vishkin:~~ [http://www.~~mpi-inf.mpg~~.de/~~departments/d1/teaching/ws10/models_of_computation/Tarjan,%20Vishkin%20~~-~~%201984%20~~-~~%20Finding%20biconnected%20components%20and%20computing%20tree%20functions%20in%20logarithmic%20parallel%20time.pdf "Finding biconnected components~~ and ~~computing tree functions in logarithmic parallel time"~~]. ~~Proceedings of FOCS 1984, 12–20~~.~~</ref>~~

	~~==Construction==~~
	~~Given an undirected tree presented as a set~~ of ~~edges,~~ the ~~Euler tour representation (ETR) can be constructed in parallel as follows:~~
	* We construct a symmetric list of ~~directed edges:~~
	** For each undirected edge {''u'',''v''} in the ~~tree, insert (''u'',''v'')~~ and ~~(''v'',''u'') in the edge list.~~
	* Sort the edge list [[Lexicographical order\|lexicographically]]. (Here we assume that the nodes of the ~~tree are ordered~~, ~~and that~~ the ~~root is the first element in this order~~.)
	* Construct adjacency lists for each ~~node (called ''next'')~~ and a ~~map from nodes to the first entries~~ of the ~~adjacency lists (called ''first''):~~
	** For each edge (''u'',''v'') in the list, do in parallel:
	~~***~~ If ~~the previous edge (''x''~~,~~''y'') has ''x'' ≠ ''u''~~, i.e. ~~starts from~~ a ~~different node,~~ set ~~first(''u'') = (''u'',''v'')~~
	*** Else if ''x'' = ''u'', i.e. starts from the ~~same node~~, ~~set next~~(~~''x''~~,~~''y''~~)~~ = (''u''~~,~~''v'')~~

	~~Construct an edge list (called ''succ'') in Euler tour order by setting pointers succ(''u''~~,~~''v'') for all edges (''u'',''v'') in parallel according~~ to the ~~following rule:~~

	: <~~math~~>~~\mathrm{succ}(u,v)=\begin{cases}~~
	~~\mathrm{next}(v,u) & \mathrm{next}(v,u)\neq \mathrm{nil} \\~~
	~~\mathrm{first}(v)&\text{otherwise}.~~
	~~\end{cases}~~
	<~~/math~~>

	~~The resulting list ''succ'' will be circular~~.

	~~The overall construction takes work ''W''(''n'') = O(sort(''n'')) (~~the ~~time it takes to sort ''n'' items in parallel) if~~ the ~~tree has ''n'' nodes~~, as ~~in trees~~ the ~~number~~ of ~~edges is one less than~~ the ~~number of nodes~~.

	~~== Roots, advance and retreat edges ==~~
	If the ~~tree has a root~~, ~~we can split the circular list ''succ'' at~~ that ~~root~~. In that ~~case, we can speak~~ of ~~''advance'' and ''retreat'' edges: given~~ a ~~pair of nodes~~ '~~'u'',''v'', the first occurrence of~~ either ~~(''u'',''v'')~~ or ~~(''v''~~,~~''u'') in~~ the ~~ETR~~ is ~~called the ''advance edge'',~~ and ~~the second occurrence~~ is ~~called~~ the ~~''retreat edge''~~. ~~This appeals to~~ the ~~intuition that~~ the ~~first time such an edge~~ is ~~traversed~~ the ~~distance to the root is increased~~, ~~while the second time~~ the ~~distance decreases~~.

	~~==Applications==~~
	~~Rerooting~~ the ~~tree can be done in constant time O(1) by splitting the circular list ''succ'' at~~ the ~~new root.~~

	~~All~~ of the ~~following problems can be solved in O(Prefix sum(''n'')) (the time it takes to solve~~ the ~~[[prefix sum]] problem in parallel for~~ a ~~list of ''n'' items)~~:
	~~# Classifying advance~~ and ~~retreat edges: Do list ranking on the ETR and save the result~~ in a ~~two-dimensional array ''A'~~'. ~~Then (''u'',''v'')~~ is ~~an advance~~ edge ~~iff ''A''(''u''~~,~~''v'') ~~<~~ ''A''(''v''~~,~~''u'')~~, ~~and a retreat edge otherwise~~.
	~~# Determine~~ the ~~level~~ of ~~each node: Do a prefix sum on~~ the ~~ETR~~, ~~where every advance edge counts as 1~~, and ~~every retreat edge counts as −1~~. ~~Then~~ the ~~value at~~ the ~~advance~~ edge ~~(''u'',''v'') is~~ the ~~level of ''v''~~.
	~~# Number of nodes in~~ a ~~subtree rooted at ''v'': determine advance edge (''u''~~,~~''v'')~~, ~~and the retreat edge (''u''~~,'~~'v'') in parallel~~, ~~and then count the number of advance edges between (''u''~~,~~''v'')~~ and ('~~'u'',''v'') using prefix sum.~~
	~~# The [[depth-first search]] index of~~ a ~~node ''v'': count the number of advance edges up~~ to and ~~including (''u'',''v'')~~.

	~~== References ==~~
	~~{{Reflist}}~~

	~~[[Category:Graph algorithms]]~~
	~~[[Category:Parallel computing]]~~

en>Addbot: Bot: Migrating 6 interwiki links, now provided by Wikidata on d:q1155749 (Report Errors)

2013-02-26T19:07:12Z

Bot: Migrating 6 interwiki links, now provided by Wikidata on d:q1155749 (Report Errors)

← Older revision		Revision as of 21:07, 26 February 2013
Line 1:		Line 1:
	The ~~writer~~'~~s name~~ is ~~Sebrina Zoll~~. ~~In her professional lifestyle she~~ is a ~~people manager~~. ~~Ohio is~~ the ~~only place she~~'~~s been residing~~ in. ~~What she really enjoys doing is to ice skate~~ and ~~now she is attempting to make cash with it~~. ~~She's not good at style but you might want to check her website~~: http://~~Willbleaumhxsu~~.~~Wordpress~~.~~com~~/<br><br>~~Also visit my blog~~ [~~http~~:~~//Willbleaumhxsu~~.~~Wordpress~~.~~com/ Boca Raton CPA jobs~~ in ~~louisiana~~]		[[File:Stirling permutation Euler tour.svg\|thumb\|240px\|Euler tour of a tree, with edges labeled to show the order in which they are traversed by the tour]]
			The '''Euler tour technique (ETT)''', named after [[Leonhard Euler]], is a method in [[graph theory]] for representing [[tree (graph theory)\|trees]]. The tree is viewed as a [[directed graph]] that contains two directed edges for each edge in the tree. The tree can then be represented as a [[Eulerian circuit]] of the directed graph, known as the '''Euler tour representation''' (ETR) of the tree. The ETT allows for efficient, [[parallel computation]] of solutions to common problems in [[algorithmic graph theory]]. It was introduced by Tarjan and Vishkin in 1984.<ref name="Tarjan">R.E. Tarjan, U. Vishkin: [http://www.mpi-inf.mpg.de/departments/d1/teaching/ws10/models_of_computation/Tarjan,%20Vishkin%20-%201984%20-%20Finding%20biconnected%20components%20and%20computing%20tree%20functions%20in%20logarithmic%20parallel%20time.pdf "Finding biconnected components and computing tree functions in logarithmic parallel time"]. Proceedings of FOCS 1984, 12–20.</ref>

			==Construction==
			Given an undirected tree presented as a set of edges, the Euler tour representation (ETR) can be constructed in parallel as follows:
			* We construct a symmetric list of directed edges:
			** For each undirected edge {''u'',''v''} in the tree, insert (''u'',''v'') and (''v'',''u'') in the edge list.
			* Sort the edge list [[Lexicographical order\|lexicographically]]. (Here we assume that the nodes of the tree are ordered, and that the root is the first element in this order.)
			* Construct adjacency lists for each node (called ''next'') and a map from nodes to the first entries of the adjacency lists (called ''first''):
			** For each edge (''u'',''v'') in the list, do in parallel:
			*** If the previous edge (''x'',''y'') has ''x'' ≠ ''u'', i.e. starts from a different node, set first(''u'') = (''u'',''v'')
			*** Else if ''x'' = ''u'', i.e. starts from the same node, set next(''x'',''y'') = (''u'',''v'')

			Construct an edge list (called ''succ'') in Euler tour order by setting pointers succ(''u'',''v'') for all edges (''u'',''v'') in parallel according to the following rule:

			: <math>\mathrm{succ}(u,v)=\begin{cases}
			\mathrm{next}(v,u) & \mathrm{next}(v,u)\neq \mathrm{nil} \\
			\mathrm{first}(v)&\text{otherwise}.
			\end{cases}
			</math>

			The resulting list ''succ'' will be circular.

			The overall construction takes work ''W''(''n'') = O(sort(''n'')) (the time it takes to sort ''n'' items in parallel) if the tree has ''n'' nodes, as in trees the number of edges is one less than the number of nodes.

			== Roots, advance and retreat edges ==
			If the tree has a root, we can split the circular list ''succ'' at that root. In that case, we can speak of ''advance'' and ''retreat'' edges: given a pair of nodes ''u'',''v'', the first occurrence of either (''u'',''v'') or (''v'',''u'') in the ETR is called the ''advance edge'', and the second occurrence is called the ''retreat edge''. This appeals to the intuition that the first time such an edge is traversed the distance to the root is increased, while the second time the distance decreases.

			==Applications==
			Rerooting the tree can be done in constant time O(1) by splitting the circular list ''succ'' at the new root.

			All of the following problems can be solved in O(Prefix sum(''n'')) (the time it takes to solve the [[prefix sum]] problem in parallel for a list of ''n'' items):
			# Classifying advance and retreat edges: Do list ranking on the ETR and save the result in a two-dimensional array ''A''. Then (''u'',''v'') is an advance edge iff ''A''(''u'',''v'') < ''A''(''v'',''u''), and a retreat edge otherwise.
			# Determine the level of each node: Do a prefix sum on the ETR, where every advance edge counts as 1, and every retreat edge counts as −1. Then the value at the advance edge (''u'',''v'') is the level of ''v''.
			# Number of nodes in a subtree rooted at ''v'': determine advance edge (''u'',''v''), and the retreat edge (''u'',''v'') in parallel, and then count the number of advance edges between (''u'',''v'') and (''u'',''v'') using prefix sum.
			# The [[depth-first search]] index of a node ''v'': count the number of advance edges up to and including (''u'',''v'').

			== References ==
			{{Reflist}}

			[[Category:Graph algorithms]]
			[[Category:Parallel computing]]

en>Srleffler: /* Overview */ rm bad link.

2012-07-25T03:06:53Z

Overview: rm bad link.

New page

The writer's name is Sebrina Zoll. In her professional lifestyle she is a people manager. Ohio is the only place she's been residing in. What she really enjoys doing is to ice skate and now she is attempting to make cash with it. She's not good at style but you might want to check her website: http://Willbleaumhxsu.Wordpress.com/<br><br>Also visit my blog [http://Willbleaumhxsu.Wordpress.com/ Boca Raton CPA jobs in louisiana]