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		<title>en&gt;Rjwilmsi: /* Other Algorithms */Journal cites, Added 1 doi to a journal cite using AWB (10331)</title>
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		<updated>2014-08-06T20:02:56Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Other Algorithms: &lt;/span&gt;Journal cites, Added 1 doi to a journal cite using &lt;a href=&quot;/index.php?title=Testwiki:AWB&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Testwiki:AWB (page does not exist)&quot;&gt;AWB&lt;/a&gt; (10331)&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 22:02, 6 August 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PPP&#039;&#039;&#039; is a &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[complexity class&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;], standing &lt;/del&gt;for &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot;&#039;&#039;&#039;Polynomial Pigeonhole Principle&#039;&#039;&#039;&quot;&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Introduced by [[Christos Papadimitriou]] in 1994&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ref&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{cite journal | author = Christos Papadimitriou | year = 1994 | title = On &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;complexity of the parity argument and other inefficient proofs of existence | journal = &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[Journal of Computer and System Sciences]] | volume = 48 | issue = 3 | pages = 498–532 | url = http&lt;/del&gt;://&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;www&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cs&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;berkeley.edu&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;~christos&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;papers&lt;/del&gt;/&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;On%20the%20Complexity&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pdf | doi = 10.1016/S0022-0000(05)80063-7}}&amp;lt;/ref&amp;gt; (page 528), PPP is &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;subclass &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[TFNP]]&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;It &lt;/del&gt;is a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;class of search problems &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;can &lt;/del&gt;be &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;shown &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be total by an application of &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[pigeonhole principle]].&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;We&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;re here to help you analysis the most effective pocket knife and get the most for your funds. Use our charts to browse the finest pocket knives from the leading companies. Just place, we&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;re the ultimate on the internet buyer&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s guide with tons of &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://Dallaskoreans.com/index.php?document_srl=374868&amp;amp;mid=Test valuable data&lt;/ins&gt;] for &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;each knife enthusiasts and newbies alike. Suggested ideal pocket knives for 2014&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&amp;gt;&amp;lt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The tremor offers a substantially more comfortable really feel with a very large ergonomic curved deal with. I really feel this provides a good grip even with gloves on, creating it a really strong and sturdy outdoor knife. The blade feels sturdy as nicely. I&#039;ve been hooked on Kershaw folding knives for a few years now. Their cost point and top quality is about appropriate IMO and I really like &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;speed assisted &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;https&lt;/ins&gt;://&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Projects&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;boblycat&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;org&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;blimp&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ticket&lt;/ins&gt;/&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;55719 deployment]&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I need to have a dozen or so now all more than the place with &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;couple &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;other brands mixed in&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This &lt;/ins&gt;is a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;terrific little knife. I carried it for over 5 years before I lost it and it held up good during &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;time. Just got my replacement in, this one with a black blade so it will &lt;/ins&gt;be &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;interesting &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;see how properly that holds up. Spring steel clips Or Cut Spring Steel Clips Spyderco Sage 1 Overview&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;For &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;list, I wanted &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;hold &lt;/ins&gt;it to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;mainstream production knives below about $100&lt;/ins&gt;, which &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is why you won&#039;t see larger finish brands like Zero Tolerance on &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;list. All are locking except where I gave &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;nod &lt;/ins&gt;to the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Victorinox due &lt;/ins&gt;to the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fact so several individuals carry it, and locking knives aren&#039;t normally legal&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;# Make Model Pros Cons 1 Spyderco Delica four - Fantastic VG-10 Steel Now this recommendation primarily has to do with personal preference and &lt;/ins&gt;it is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;not a deal breaker if &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;knife does not have this potential. From private knowledge and experimentation, I have discovered &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;carrying &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;knife tip up enables the quickest achievable draw, from &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;time you determine to pull out your knife&lt;/ins&gt;, to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the time &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it really is deployed&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;3.6 Carbon steel three.75 8.5 $$$$ 4. If you beloved this article and you would like to be given more info relating to &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://www.thebestpocketknifereviews.com/kershaw-leek-review/ Kershaw Leek Folding Knife&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;generously visit our own web page&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;5 Iain Sinclair Cardsharp2&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;The exterior dimensions of the knife when it &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;in &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;closed position. We assume slimmer is improved&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;in particular for pocket carry. But &lt;/ins&gt;as &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;well smaller and it will get lost in your palm&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;creating it unusable as &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tool. The target is &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;obtain a balance that fits your pockets and your hand&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Have a ruler handy if you are looking to pick up a knife on the web&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;as &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;solution photographs can in some cases &lt;/ins&gt;be &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a bit misleading &lt;/ins&gt;for &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;correct scale. The weight &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the knife &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tremendously dependent on the weight of its blade. You would select &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lighter blade for day to day tasks and a heavier a single for much more intense tasks. This implies &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you have to select your knife on primarily based on what you want to use &lt;/ins&gt;it &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;for. 8.25&quot; three.75&quot; 7.2 oz 420HC Stainless Steel $ four.9 Benchmade Griptillian Thumb Knife&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Mora Clipper Companion. 9&quot; overall. four&quot; carbon steel blade. Thick blade (.125&quot;) a lot stronger than standard Mora knives. Quite difficult steel that holds an edge that made Mora knives renowned. OD green composition handle with a smooth black rubberized overlay with Morakniv logo. Olive green molded belt sheath with water drain hole. Wonderful design and perfect size for use as an all-about camp and hunting knife. $16.95 Nite Ize S-Biner #five Black Titanium Finish.Pack. 4 three/8&quot; x 1 15/16&quot;. Load limit 100lbs. $five.95 Smith &amp;amp; Wesson Handcuff Essential for S&amp;amp;W Model 100, 300, 1850, 1900. Sturdy stainless steel important, 1 3/four&quot; extended, five/eight&quot; wide at &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;ring. Fits on essential rings or A&amp;amp;P cable important rings. $4.95 KNIFE ONLY ZOMBIE SLAUGHTER - SOG ★ Call &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Duty Zombies (Zombie Games)&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;This is my preferred knife on the list&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;I like &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;effortless opening &lt;/ins&gt;of the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;blade and &lt;/ins&gt;the way &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the knife feels in my hand. The Tenacious characteristics a 3.338 inch, 8Cr13MoV steel, combo blade, &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;locks in spot with a liner lock. The deal with &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;four.37 inches long and created from &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;robust G-ten material that has an incredibly fantastic feel in your hand. One &lt;/ins&gt;of the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;functions &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;makes any item wonderful is the potential &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;set it for person preference. SpyderCo nailed this with their Tenaciou by incorporating four placement possibilities for the pocket clip&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;At &lt;/ins&gt;an open &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;length of 7.75 inches this folding tactical knife makes an exceptional EDC.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;A further amazing function about the 710 &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;that it attributes the patented Benchmade AXIS lock &lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;which in my opinion &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the easiest lock to release with a single hand. &lt;/ins&gt;The &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;710 McHenry Williams also presents an ambidextrous design with 420J stainless steel liners with black, Nyrol GTX grips and &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;reversible steel pocket clip. Overall, I adore this knife, it is hands down my preferred EDC knife. &amp;gt;&amp;gt;Click right here for the most up-to-date pricing and testimonials on the Benchmade 710 McHenry &amp;amp; Williams. SOG Flash II(FSA8-CP) Folding Knife&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This is a knife &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;can take some abuse. From the solid RotoLock mechanism to the high good quality Elmax PM 170 steel on the four.5mm thick blade, you can trust this knife to come via for you. The handles are CNC machined perpendicular to the blades length to assure a good strong grip on the knife. I chose this knife for best designs for obvious causes. The knife has functions that each and every single person appears for in a knife. The 1 factor that may not suffice to some is the dual thumb lugs. Nevertheless, they do have a model that has that feature. If you choice is not here, drop us an e-mail ( bvoyles@ ) &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;let us know about your favorite EDC you can also post a photo of your favourite on our Facebook web page. Primary-Function of knife (blade traits) Steel&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Specifics on this knife, in distinct the Sebenza 21, involve the CPM S35VN stainless steel blade, a hardness of 58-59 RC, and a blade thickness of125 inches&lt;/ins&gt;. The &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;blade comes in two distinctive lengths. The smaller sized blade measures 2.94 inches while the longer a single &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;around 3.6 inches. The deal with is made of 6A14V titanium. The thumblug and pocket clip are each produced of titanium as properly. Spyderco Tenacious Leatherman is the Budweiser of multi-tools. There is a whole array &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;other firms &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;make larger high-quality goods but, alas, we never sell adequate books for me to peruse the finer offerings at our local Ross Cutlery shop. Once again, my standard Leatherman appears to &lt;/ins&gt;have &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;enough tools for most conditions&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Sharing my love of smaller or micro knives&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PPP is defined as follows. A function computation problem belongs &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PPP if &lt;/del&gt;it &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;admits a [[polynomial-time reduction]] &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the problem PIGEONHOLE CIRCUIT&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;in &lt;/del&gt;which &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;an input consists of a [[boolean circuit]] having &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;same number of input bits as output bits, and &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;solution consists of either an input vector that is mapped &lt;/del&gt;to the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;output 0, or alternatively two distinct input vectors that are mapped &lt;/del&gt;to the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;same output&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Note that &lt;/del&gt;it is the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pigeonhole principle that guarantees &lt;/del&gt;that a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;solution must exist. A problem is [[Complete_(complexity)|complete]] for &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;class PPP if in addition&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PIGEONHOLE CIRCUIT is reducible &lt;/del&gt;to that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;problem&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PPP contains &lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[PPAD&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;] as a subclass&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;because &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;corresponding problem that defines PPAD&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;known &lt;/del&gt;as &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;END OF THE LINE&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;can be reduced (in &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;straightforward way) &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PIGEONHOLE CIRCUIT&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;At present&lt;/del&gt;, the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;only problems known to &lt;/del&gt;be &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;complete &lt;/del&gt;for &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PPP are variants &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PIGEONHOLE CIRCUIT; this &lt;/del&gt;is a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;deficiency of PPP, since this means &lt;/del&gt;that it &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;has so far failed to capture &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;complexity &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;additional problems&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;However, &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;definition &lt;/del&gt;of the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;class PPP highlights &lt;/del&gt;the way that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the pigeonhole principle &lt;/del&gt;is a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;generalization &lt;/del&gt;of the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&quot;parity argument on a directed graph&quot; principle &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;assures that search problems belonging &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;PPAD are indeed total&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;It is &lt;/del&gt;an open &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;question whether EQUAL SUBSETS &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;complete for PPP&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;where EQUAL SUBSETS &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;defined as follows: &lt;/del&gt;The &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;input consists of &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;set of &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;n&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;positive integers &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;add up &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;less than &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;2^n&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;. The &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;problem &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;to find two distinct subsets &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;these numbers &lt;/del&gt;that have &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the same total&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==References==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{reflist}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Complexity classes]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Rjwilmsi</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Data_stream_clustering&amp;diff=25014&amp;oldid=prev</id>
		<title>en&gt;Frietjes: cleanup (wikitables, html markup, layout, etc.)</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Data_stream_clustering&amp;diff=25014&amp;oldid=prev"/>
		<updated>2013-11-15T21:09:01Z</updated>

		<summary type="html">&lt;p&gt;cleanup (wikitables, html markup, layout, etc.)&lt;/p&gt;
&lt;a href=&quot;https://en.formulasearchengine.com/index.php?title=Data_stream_clustering&amp;amp;diff=25014&amp;amp;oldid=265662&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>en&gt;Frietjes</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Data_stream_clustering&amp;diff=265662&amp;oldid=prev</id>
		<title>en&gt;Melcombe: more conventional approach to start of lead</title>
		<link rel="alternate" type="text/html" href="https://en.formulasearchengine.com/index.php?title=Data_stream_clustering&amp;diff=265662&amp;oldid=prev"/>
		<updated>2012-06-27T23:19:16Z</updated>

		<summary type="html">&lt;p&gt;more conventional approach to start of lead&lt;/p&gt;
&lt;a href=&quot;https://en.formulasearchengine.com/index.php?title=Data_stream_clustering&amp;amp;diff=265662&quot;&gt;Show changes&lt;/a&gt;</summary>
		<author><name>en&gt;Melcombe</name></author>
	</entry>
</feed>