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Talk:Approximation algorithm - Revision history
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<p><a href="/wiki/User:Cewbot/log/20200122/configuration" title="User:Cewbot/log/20200122/configuration">Maintain {{WPBS}} and vital articles</a>: 2 WikiProject templates. Create {{WPBS}}. Keep majority rating "Start" in {{WPBS}}. Remove 2 same ratings as {{WPBS}} in {{Maths rating}}, {{WPCS}}. Remove 1 deprecated parameter: field.</p>
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<p>Replace <a href="/wiki/Help:Magic_links" title="Help:Magic links">magic links</a> with templates per <a href="/wiki/Special:PermanentLink/772743896#Future_of_magic_links" title="Special:PermanentLink/772743896">local RfC</a> - <a href="/wiki/User:PrimeBOT/13" class="mw-redirect" title="User:PrimeBOT/13">BRFA</a></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:15, 21 June 2017</td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> ^ a b c d e Viggo Kann (1992). On the Approximability of NP-complete Optimization Problems.</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> ^ Johan Håstad (1999). "Some Optimal Inapproximability Results". Journal of the ACM.</div></td>
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<td style="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;"><div> Vazirani, Vijay V. (2003). Approximation Algorithms. Berlin: Springer. <ins style="font-weight: bold; text-decoration: none;">{{</ins>ISBN<ins style="font-weight: bold; text-decoration: none;">|</ins>3540653678<ins style="font-weight: bold; text-decoration: none;">}}</ins>.</div></td>
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<td style="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;"><div> Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, Second Edition. MIT Press and McGraw-Hill, 2001. ISBN<del style="font-weight: bold; text-decoration: none;"> </del>0-262-03293-7. Chapter 35: Approximation Algorithms, pp. 1022–1056.</div></td>
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<td style="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;"><div> Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, Second Edition. MIT Press and McGraw-Hill, 2001. <ins style="font-weight: bold; text-decoration: none;">{{</ins>ISBN<ins style="font-weight: bold; text-decoration: none;">|</ins>0-262-03293-7<ins style="font-weight: bold; text-decoration: none;">}}</ins>. Chapter 35: Approximation Algorithms, pp. 1022–1056.</div></td>
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<td style="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;"><div> Dorit H. Hochbaum, ed. Approximation Algorithms for NP-Hard problems, PWS Publishing Company, 1997. ISBN<del style="font-weight: bold; text-decoration: none;"> </del>0-534-94968-1. Chapter 9: Various Notions of Approximations: Good, Better, Best, and More</div></td>
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<td style="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;"><div> Dorit H. Hochbaum, ed. Approximation Algorithms for NP-Hard problems, PWS Publishing Company, 1997. <ins style="font-weight: bold; text-decoration: none;">{{</ins>ISBN<ins style="font-weight: bold; text-decoration: none;">|</ins>0-534-94968-1<ins style="font-weight: bold; text-decoration: none;">}}</ins>. Chapter 9: Various Notions of Approximations: Good, Better, Best, and More</div></td>
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PrimeBOT
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173.164.197.30: Rought draft~~~~
2011-03-25T05:06:03Z
<p>Rought draft~~~~</p>
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<td style="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;"><div>==Rough draft of research to cite and incorporate, thanks==</div></td>
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<td style="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;"><br /></td>
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<td style="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;"><div>In computer science and operations research, we use approximation algorithms to find approximate solutions to optimization problems. Approximation algorithms are often associated with NP-hard problems; since efficient polynomial time exact algorithms solving NP-hard problems, one settles for polynomial time sub-optimal solutions. Unlike heuristics, where usually we only find reasonably good solutions reasonably fast, one wants provable solution quality and provable run time bounds. Ideally, the approximation is optimal up to a small constant factor (for instance within 5% optimal solution). Approximation algorithms are used often for problems where exact polynomial-time algorithms are known but are too expensive due to the input size.</div></td>
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<td style="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;"><div>A typical example for an approximation algorithm is the vertex cover in graphs: find an uncovered edge and add both endpoints to the vertex cover, until zero endpoints remain. It is clear that the resulting cover is at most twice as large as the optimal one. This is a constant factor approximation algorithm of factor two.</div></td>
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<td style="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;"><div>NP-hard problems vary greatly in their approximability; some, such as the bin packing problem, can be approximated within any factor greater than 1 (a family of approximation algorithms often called a polynomial time approximation scheme or PTAS). Others are possible to approximate but without a constant, or even polynomial factor unless P = NP, such as the maximum clique problem.</div></td>
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<td style="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;"><div>NP-hard problems we can express as integer programs (IP) solved exactly in exponential time. Many approximation algorithms emerge from the linear programming relaxation of the integer program.</div></td>
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<td style="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;"><div>Some approximation algorithms are suitable for some practical applications. They often use IP/LP/Semidefinite solvers, complex data structures or sophisticated algorithmic techniques leading to difficult implementation problems. Also, some approximation algorithms have impractical running times though they do run in polynomial time, for example O(n2000). Yet the study of expensive algorithms is a completely practical pursuit as it yields valuable insights. A classic example is the initial PTAS for Euclidean TSP due to Sanjeev Arora had prohibitive running time, yet ithin a year, Arora refined the ideas into a linear time algorithm. These types of algorithms are worthwhile in applications where we can justify the running time and cost e.g. computational biology, financial engineering, transportation planning, and inventory management. In these scenarios almorithms compete with direct IP corresponding formulations.</div></td>
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<td style="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;"><div>A limit to the approach refers to optimization problems "pure" decision problems like satisfiability, though it is possible to conceive optimization versions of these problems including the maximum satisfiability problem or (Max SAT).</div></td>
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<td style="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;"><div>Inapproximability has been a fruitful area of research in computational complexity theory since the 1990 result of Feige, Goldwasser, Lovasz, Safra and Szegedy on the inapproximability of Independent Set. Now the time has come to embrace the potential gains of approxmability provided these new theories we discuss. Looking back, after Arora et al. proved the PCP theorem in 1991, it was later shown Johnson's 1974 approximation algorithms for Max SAT, Set Cover, Independent Set and Coloring all achieve optimal approximation ratio, assuming P != NP.</div></td>
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<td style="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;"><div>Consider these two items: Performance guarantee and Epsiolon term.</div></td>
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<td style="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;"><div>Performance guarantees for some approximation algorithms allow us to prove certain properties about the approximation of the optimum result. For example, in case ρ-approximation algorithm A has proof value/cost, f(x) approximate solution A(x) instance x will be less (more or less, depending on) factor ρ times value OPT optimum solution.</div></td>
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<td style="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;"><div>where f(y) is value/cost solution y for instant x. Performance guarantee is greater than or equal to 1 and equal to 1 optimal solution. If algorithm A guarantees solutions performance guarantee return at most r(n) A is an r(n)-approximation algorithm approximation ratio r(n). Problem r(n)-approximation algorithm is r(n)-approximable approximation ratio r(n).[1][2]</div></td>
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<td style="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;"><div>Absolute performance guarantee ΡA approximation algorithm A x refers to instant problem RA(x) is performance guarantee A on x (i.e. ρ for problem instant x) =:</div></td>
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<td style="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;"><div>max: f(x) \geq r − 1OPT ρOPT (1 − c)OPT (1 − c)OPT (1 − c)OPT -cBEST OPT − c</div></td>
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<td style="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;"><div>min: f(x) \leq rOPT ρOPT (1 + c)OPT (1 − c) − 1OPT (1 − c) − 1OPT - cBEST OPT + c</div></td>
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<td style="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;"><div>Epsilon term IN literature approximation ratio maximization (minimization) problem c - ϵ (min: c + ϵ) means algorithm approximation ratio cϵ for arbitrary ϵ > 0 ratio show ϵ = 1 example of optimal approximability — existence of approximation — ratio 7 / 8 + ϵ for satisfiable MAX-3SAT instant due Johan Håstad.[3] Mention previously c = 1 problem polynomial-time approximation scheme.</div></td>
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<td style="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;"><div>ϵ-term appearance approximation algorithm introduces multiplicative error plus constant error minimum optimum instant size n infinity as n infinity approximation ratio c k / OPT = c o(1) some constant c + k arbitrary ϵ > 0 link N term k / OPT < ϵ every n ≥ N every fixed ϵ, instant size n < N brute force solution shows approximation ratio exists approximation algorithm guarantee — c ϵ to every ϵ > 0.</div></td>
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<td style="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;"><div> ^ a b c d e Viggo Kann (1992). On the Approximability of NP-complete Optimization Problems.</div></td>
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<td style="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;"><div> ^ Johan Håstad (1999). "Some Optimal Inapproximability Results". Journal of the ACM.</div></td>
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<td style="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;"><div> Vazirani, Vijay V. (2003). Approximation Algorithms. Berlin: Springer. ISBN 3540653678.</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br /></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There was an error on this page, specifically that the "dominance number" is made to sound as if it is a "replacement" for some other measure, whereas the reference I found calls it an orthoganal measure. There should probably still be a section about other measurements of approx. algorithms. The paper [http://www.springerlink.com/content/etkt6c2tl8a58tju/] I found that confirmed this error had some interesting contetnt that perhaps someone should write up. --[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 16:50, 22 August 2006 (UTC)</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There was an error on this page, specifically that the "dominance number" is made to sound as if it is a "replacement" for some other measure, whereas the reference I found calls it an orthoganal measure. There should probably still be a section about other measurements of approx. algorithms. The paper [http://www.springerlink.com/content/etkt6c2tl8a58tju/] I found that confirmed this error had some interesting contetnt that perhaps someone should write up. --[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 16:50, 22 August 2006 (UTC)</div></td>
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173.164.197.30
https://en.wikipedia.org/w/index.php?title=Talk:Approximation_algorithm&diff=330183827&oldid=prev
RobinK: added rating
2009-12-07T04:10:12Z
<p>added rating</p>
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<td style="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;"><br /></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There was an error on this page, specifically that the "dominance number" is made to sound as if it is a "replacement" for some other measure, whereas the reference I found calls it an orthoganal measure. There should probably still be a section about other measurements of approx. algorithms. The paper [http://www.springerlink.com/content/etkt6c2tl8a58tju/] I found that confirmed this error had some interesting contetnt that perhaps someone should write up. --[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 16:50, 22 August 2006 (UTC)</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There was an error on this page, specifically that the "dominance number" is made to sound as if it is a "replacement" for some other measure, whereas the reference I found calls it an orthoganal measure. There should probably still be a section about other measurements of approx. algorithms. The paper [http://www.springerlink.com/content/etkt6c2tl8a58tju/] I found that confirmed this error had some interesting contetnt that perhaps someone should write up. --[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 16:50, 22 August 2006 (UTC)</div></td>
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SineBot: Signing comment by C. lorenz - "References for Approximation Guarantees"
2009-04-24T18:24:29Z
<p>Signing comment by <a href="/wiki/User:C._lorenz" title="User:C. lorenz">C. lorenz</a> - "References for Approximation Guarantees"</p>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== References for Approximation Guarantees ==</div></td>
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<td style="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;"><div>Seeing how there are many different and varying definitions used for approximation guarantees, I would preferably like to see inline sources. The article currently uses ρ-approximation algorithms (relative performance guarantee) and I strongly believe that the definition is taken from Handbook of Approximation Algorithms and Metaheuristics but I cannot verify this myself. The definition used also agrees with "factor δ approximation algorithms" from Vazirani's book but it does not agree with the usual performance ratio which in Cormen et.al. uses the symbol ρ.</div></td>
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<td style="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;"><div>Seeing how there are many different and varying definitions used for approximation guarantees, I would preferably like to see inline sources. The article currently uses ρ-approximation algorithms (relative performance guarantee) and I strongly believe that the definition is taken from Handbook of Approximation Algorithms and Metaheuristics but I cannot verify this myself. The definition used also agrees with "factor δ approximation algorithms" from Vazirani's book but it does not agree with the usual performance ratio which in Cormen et.al. uses the symbol ρ.<ins style="font-weight: bold; text-decoration: none;"> <small><span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:C. lorenz|C. lorenz]] ([[User talk:C. lorenz|talk]] • [[Special:Contributions/C. lorenz|contribs]]) 18:23, 24 April 2009 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot--></ins></div></td>
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SineBot
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C. lorenz: References for Approximation Guarantees
2009-04-24T18:23:16Z
<p>References for Approximation Guarantees</p>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>One is a function, the other is a set. You are right though, it'd probably be less confusing to use another variable.--[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 09:26, 20 June 2007 (UTC)</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>One is a function, the other is a set. You are right though, it'd probably be less confusing to use another variable.--[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 09:26, 20 June 2007 (UTC)</div></td>
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<td style="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;"><div>== References for Approximation Guarantees ==</div></td>
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<td style="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;"><div>Seeing how there are many different and varying definitions used for approximation guarantees, I would preferably like to see inline sources. The article currently uses ρ-approximation algorithms (relative performance guarantee) and I strongly believe that the definition is taken from Handbook of Approximation Algorithms and Metaheuristics but I cannot verify this myself. The definition used also agrees with "factor δ approximation algorithms" from Vazirani's book but it does not agree with the usual performance ratio which in Cormen et.al. uses the symbol ρ.</div></td>
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C. lorenz
https://en.wikipedia.org/w/index.php?title=Talk:Approximation_algorithm&diff=169616505&oldid=prev
Zzuuzz: moved Talk:Nathan Byrne to Talk:Approximation algorithm over redirect: rvv
2007-11-06T15:56:43Z
<p>moved <a href="/wiki/Talk:Nathan_Byrne" title="Talk:Nathan Byrne">Talk:Nathan Byrne</a> to <a href="/wiki/Talk:Approximation_algorithm" title="Talk:Approximation algorithm">Talk:Approximation algorithm</a> over redirect: rvv</p>
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Zzuuzz
https://en.wikipedia.org/w/index.php?title=Talk:Approximation_algorithm&diff=169582529&oldid=prev
Whodoesthis: moved Talk:Approximation algorithm to Talk:Nathan Byrne
2007-11-06T11:44:42Z
<p>moved <a href="/wiki/Talk:Approximation_algorithm" title="Talk:Approximation algorithm">Talk:Approximation algorithm</a> to <a href="/wiki/Talk:Nathan_Byrne" title="Talk:Nathan Byrne">Talk:Nathan Byrne</a></p>
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Whodoesthis
https://en.wikipedia.org/w/index.php?title=Talk:Approximation_algorithm&diff=148400775&oldid=prev
David Eppstein: rm inappropriate bot tag per discussion at Wikipedia_talk:WikiProject_Logic
2007-08-01T01:32:36Z
<p>rm inappropriate bot tag per discussion at <a href="/wiki/Wikipedia_talk:WikiProject_Logic" title="Wikipedia talk:WikiProject Logic">Wikipedia_talk:WikiProject_Logic</a></p>
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<td style="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;"><br /></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There was an error on this page, specifically that the "dominance number" is made to sound as if it is a "replacement" for some other measure, whereas the reference I found calls it an orthoganal measure. There should probably still be a section about other measurements of approx. algorithms. The paper [http://www.springerlink.com/content/etkt6c2tl8a58tju/] I found that confirmed this error had some interesting contetnt that perhaps someone should write up. --[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 16:50, 22 August 2006 (UTC)</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There was an error on this page, specifically that the "dominance number" is made to sound as if it is a "replacement" for some other measure, whereas the reference I found calls it an orthoganal measure. There should probably still be a section about other measurements of approx. algorithms. The paper [http://www.springerlink.com/content/etkt6c2tl8a58tju/] I found that confirmed this error had some interesting contetnt that perhaps someone should write up. --[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 16:50, 22 August 2006 (UTC)</div></td>
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David Eppstein
https://en.wikipedia.org/w/index.php?title=Talk:Approximation_algorithm&diff=148215611&oldid=prev
SatyrBot: SatyrBot auto-adding tag to talk page. See User:SatyrBot/Current project
2007-07-31T06:22:06Z
<p>SatyrBot auto-adding tag to talk page. See <a href="/wiki/User:SatyrBot/Current_project" title="User:SatyrBot/Current project">User:SatyrBot/Current project</a></p>
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<td style="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;"><br /></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There was an error on this page, specifically that the "dominance number" is made to sound as if it is a "replacement" for some other measure, whereas the reference I found calls it an orthoganal measure. There should probably still be a section about other measurements of approx. algorithms. The paper [http://www.springerlink.com/content/etkt6c2tl8a58tju/] I found that confirmed this error had some interesting contetnt that perhaps someone should write up. --[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 16:50, 22 August 2006 (UTC)</div></td>
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<td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There was an error on this page, specifically that the "dominance number" is made to sound as if it is a "replacement" for some other measure, whereas the reference I found calls it an orthoganal measure. There should probably still be a section about other measurements of approx. algorithms. The paper [http://www.springerlink.com/content/etkt6c2tl8a58tju/] I found that confirmed this error had some interesting contetnt that perhaps someone should write up. --[[User:NotQuiteEXPComplete|NotQuiteEXPComplete]] 16:50, 22 August 2006 (UTC)</div></td>
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SatyrBot