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The '''List Update''' or the '''List Access''' problem is a simple model used in the study of [[Competitive analysis (online algorithm)|competitive analysis]] of [[online algorithms]]. Given a set of items in a list where the cost of accessing an item is proportional to its distance from the head of the list, e.g. a [[Linked List]], and a request sequence of accesses, the problem is to come up with a strategy of reordering the list so that the total cost of accesses is minimized. The reordering can be done at any time but incurs a cost, and the standard cost model includes a free transposition of the item being accessed anywhere ahead of its current position and a paid transposition of a unit cost for exchanging any two items in the list. Performance of algorithms depend on the construction of request sequences by adversaries under various [[Adversary model]]s
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An online algorithm for this problem has to reorder the elements and serve requests based only on the knowledge of previously requested items and hence its strategy may not have the optimum cost as compared to an offline algorithm that gets to see the entire request sequence and devise a complete strategy before serving the first request.
 
==Adversary Models==
An adversary is an entity that gets to choose the request sequence <math>\sigma</math> for an algorithm ''ALG''. Depending of whether <math>\sigma</math> can be changed based on the strategy of ''ALG'', adversaries are given various powers, and the performance of ''ALG'' is measured against these adversaries.  
 
An '''oblivious adversary''' has to construct the entire request sequence <math>\sigma</math> before running ''ALG'', and pays the optimal offline price, <math>OPT(\sigma)</math> which is compared against <math>ALG(\sigma)</math>
 
An '''adaptive online adversary''' gets to make the next request based on the previous results of the online algorithm, but pays for the request optimally and online.  
 
An '''adaptive offline adversary''' gets to make the next request based on the previous results of the online algorithm, but pays the optimal offline cost.
 
==Offline algorithms==
Competitive analysis for many list update problems were carried out without any specific knowledge of the exact nature of the optimum offline algorithm (OPT). The best known algorithm runs in O(''n''2<sup>''l''</sup>(''l''-1)!) time and O(''l''!) space where ''n'' is the length of the request sequence and ''l'' is the length of the list.<ref>N. Reingold and J. Westbrook. Optimum Offline algorithms for the list update and paging rules. Technical Report YALE/DcS/TR-805, Yale University, New Haven, Conn, August 1990</ref>
 
It is interesting to note that paid transpositions are in general necessary for optimum algorithms. Consider a list (''a'',''b'',''c'') where ''a'' is at the head of the list, and a request sequence ''c'',''b'',''c'',''b''. An optimal offline algorithm using only free exchanges would cost 9 (3+3+2+1), whereas an optimal offline algorithm using only paid exchanges would cost 7 (Swap ''c'' and ''a'' in the beginning = 1+(1+2+1+2)). So, we cannot get away with just using free transpositions for the optimum offline algorithm.
 
The optimum list update problem was proven to be [[NP-Hard]] by {{harv|Ambühl|2000}}.
 
==Online algorithm==
An online algorithm ''ALG'' has a competitive ratio ''c'' if for any input it performs at least as good as ''c'' times worse than OPT. i.e. if there exists an <math>\alpha\geq0</math> such that for all finite length request sequences <math>\sigma</math>, <math> ALG(\sigma)-c.OPT(\sigma)\leq\alpha</math>. Online algorithms can either be deterministic or randomized and it turns out that randomization in this case can truly help against oblivious adversaries.
 
===Deterministic===
Most deterministic algorithms are variants of these three algorithms :
; MTF (Move to front) : After accessing an item move it to the front of the list without changing the order of other items
; TRANS (Transpose) : After accessing an item, transpose it with the immediately preceding item.
; FC (Frequency Count) : For each item maintain a frequency count of the number of accesses to it - when an element is accessed increase its frequency count and reorder the list in the decreasing order of frequencies.
 
Observe that all these use just free transpositions. It turns out that both TRANS and FC are not competitive. In a classic result using [[Potential method]] analysis {{harv|Sleator|Tarjan|1985}} proved that MTF is 2-competitive. The proof does not require the explicit knowledge of OPT but instead counts the number of inversions i.e. elements occurring in opposite order in the lists of MTF and OPT.  
 
Any deterministic algorithm has a lower bound of <math>2-\frac{2}{l+1}</math> for a list of length ''l'', and MTF is actually the optimum deterministic list update algorithm. The type of adversary doesn't matter in the case of deterministic algorithms, because the adversary can run a copy of the deterministic algorithm on his own to precompute the most disastrous sequence.
 
===Randomized===
Consider the following simple randomized algorithm :
; BIT : For every item in the list, maintain a bit. Initialize all the bits uniformly and randomly to 0 or 1. When an item is accessed, flip the bit, and if it is 1 move it to the front, else don't.
 
This algorithm is barely random - it makes all its random choices in the beginning and not during the run. It turns out that BIT breaks the deterministic bound - it is '''better''' than MTF against oblivious adversaries. It is 7/4-competitive. There are other randomized algorithms, like COMB, that perform better than BIT. Boris Teia proved a lower bound of 1.5 for any randomized list update algorithm.<ref>Teia, Boris, A lower bound for randomized list update algorithms, Inf. Process. Lett. (1993), pp. 5--9</ref>
 
==Related Problems==
The list update problem where elements maybe inserted and deleted is called the dynamic list update problem, as opposed to the static list update problem where only accessing list elements are allowed. The upper bound of <math>2-\frac{2}{l+1}</math> holds for the dynamic model as well.
 
There are different cost models as well. In the usual full cost model, an access to an element located at a position ''i'' costs ''i'', but the last comparison is inevitable for any algorithm, i.e. there are ''i-1'' elements standing in the way of ''i''. In the partial cost model, these final comparison costs totaling to the number of elements in the request sequence are ignored. For the costs of paid transpositions other than unity, '''P'''<sup>'''d'''</sup> models are used.
 
==See also==
* [[Online algorithm]]
* [[Competitive analysis (online algorithm)|Competitive analysis]]
* [[Cache algorithms]]
 
==Notes==
{{Reflist}}
 
== References ==
*{{citation|title=Amortized efficiency of list update and paging rules|first1=D.|last1=Sleator|author1-link=Daniel Sleator|first2=R.|last2=Tarjan|author2-link=Robert Tarjan|journal=Communications of the ACM|year=1985|doi=10.1145/2786.2793|volume=28|issue=2|pages=202–208}}.
 
*{{cite book
| authorlink = Allan Borodin
| author = Borodin, A.
  | coauthors = El-Yaniv, R.
| url = http://www.cs.technion.ac.il/~rani/book.html
| title = Online Computation and Competitive Analysis
| publisher = Cambridge University Press
| year = 1998
| isbn = 0-521-56392-5}}
 
*{{Citation
| authorlink = Christoph Ambühl
| author = Ambühl, C.
| title = Offline list update is np-hard
| publisher = Springer
| year = 2000
| pages = 42–51 }}
 
[[Category:Analysis of algorithms]]
[[Category:Online algorithms]]
[[Category:Randomized algorithms]]

Latest revision as of 18:57, 18 April 2014



Knives are classified as becoming either a folding knife or fixed blade knife. No series of kitchen knife evaluations would be comprehensive without the need of reviewing the finest Japanese kitchen knives. Which type of knife to purchase is the one question that each and every severe cook need to ask. Mainly because a cook's knife (whether it be a classic Western chef's knife or a santoku) is the single most essential buy that a burgeoning chef will make. Each and every other knife and each and every other cooking item is just an accessory (except probably the skillet and the Dutch oven). If not, I recommend that you stick with type of knife you have.

The judging criteria integrated knife skills, security, santitation, organization, cooking tactics and clean-up, as well as the temperature, taste, texture, portion size and presentation of the finished dish. The Art Institutes Ideal Teen Chef Competitors, now in its twelfth year, is an chance for high school seniors in the U.S. and Canada interested in pursuing a culinary profession to encounter the excitement and discipline of the market.

I ate a lot of steak ahead of, but I go out of my way to eat steak Japanese Chef Knives Usuba now due to the fact I have an incredible kitchen cutlery set. My set has been amazing and I cannot look to stay out of the kitchen now. I assume the material utilised for the grips on the knife have to not be of higher quality. I've had an certainly excellent knowledge with this fantastic kitchen cutlery set. Just bought two (and got a third set no cost) at my neighborhood Kroger. Two of my favored items in the globe: Disney and Coffee.

A chef controls the knife's leverage by holding the blade in between her thumb and forefinger, with the rest of her hand gripping the closer her hand is to the knife's tip, the additional manage she has over the blade. Santoku knives get heavy use in Japan, though a lot of American chefs have adopted them as a replacement for the standard chef's knife. This is your general goal knife you will use it for almost almost everything.

They are serrated on one side and beveled on the other, and if they are detachable, the beveled side can be honed with your steel or along with the serrated side sharpened with a knife sharpener developed for both serrated and non-serrated blades! I would propose, practicing your honing skill on a knife you happen to be not as concerned about ruining. I was provided a set of Global knives last year and I am in knife heaven!

Moreover, it is constructed by creating use of a forge mechanism which creates a unbiased knife. This is extra expensive as compared to block knife. It is also crucial to consider the materials that are composed of the Japanese chef knives. Majority of the chefs in the East choose this kind of knife blade. Japanese chef knives also come in many knife handles. The AccuSharp is a excellent example of the very best compact knife sharpeners.

Finding excellent knives has often been an concern with me. You have a good write-up on how to pick the correct knife. I am not considerably of an amateur chef myself, but I know a man who is.. I'm going to pass this on to him. If you have any sort of questions relating to where and just how to make use of Japanese Chef Knives Go, you could contact us at the web site. There's a museum and workshop combined in the town and you can see a totally operating knife that fits inside a cherry stone. I was use to broke a tiny kitchen knife by cutting big bone.I feel this lens will aid me to use proper knife. Wow, that is a lot of knife facts.

This 14-piece set stocks a kitchen with most cutlery requires, and packs all knives in a modern black hardwood storage block. The set incorporates: an eight-inch chef's knife, an eight-inch slicer, an eight-inch bread knife, a 5-inch boning knife, a four-1/two-inch utility knife, a three-1/two-inch paring knife, and six four-1/2-inch steak knives, plus a pair of shears. The second season of Top Chef began airing in October 2006.

Ping Knife (Square Head) Item # SLKF018 7" x 12.5" x four.25" Wan Woo Knife (Square Head).. Copyright © 2008-2009 Thunder Group®. This Greatest Selling - Steak Knife Set, six Piece Stainless Steel Case Pack 36 Tends to SELL OUT Quite Rapid! Involves is alot of planned relating to Steak Knife Set, 6 Piece Stainless Steel Case Pack 36. Basically all knife sets contain a chefs knife, regardless of the good quality of the knives.