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Topic: Approximation algorithm

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	Approximation algorithm - Wikipedia, the free encyclopedia
		A typical example for an approximation algorithm is the one for vertex cover in graphs: Find an uncovered edge and add both endpoints to the vertex cover, until none remain.
		This is in fact a constant factor approximation algorithm with a factor of 2.
		For some approximation algorithms it is possible to prove certain properties about the approximation of the optimum result.
	en.wikipedia.org /wiki/Approximation_algorithm (466 words)

	ApproximationAlgorithms - PineWiki
		An approximation algorithm returns a solution to a combinatorial optimization problem that is provably close to optimal (as opposed to a heuristic that may or may not find a good solution).
		Approximation algorithms are typically used when finding an optimal solution is intractable, but can also be used in some situations where a near-optimal solution can be found quickly and an exact solution is not needed.
		Fully polynomial-time approximation schemes are the holy grail of approximation algorithms; they do not appear to exist for many problems, but when they are available, they are often almost as useful as an optimizing algorithm would be.
	pine.cs.yale.edu /pinewiki/ApproximationAlgorithms (1275 words)

	SPSA Algorithm
		Such algorithms start with an initial "guess" at a solution, and this estimated solution is updated on an iteration-by-iteration basis with the aim of improving the performance measure (objective function).
		The algorithm has desirable properties for both global and local optimization in the sense that the gradient approximation is sufficiently noisy to allow for escape from local minima while being sufficiently informative about the slope of the function to facilitate local convergence.
		This extension is the adaptive SPSA algorithm in Spall (2000), which provides an efficient stochastic analogue to the famous Newton-Raphson algorithm from deterministic optimization (which uses gradients and Hessian [second derivative] matrices of the objective function).
	www.jhuapl.edu /SPSA (1643 words)

	Sphere-Tree Construction Toolkit (Site not responding. Last check: 2007-10-08)
		Prior to the approximation of the sub-sections of the object the adaptive medial axis approximation algorithm is used to improve the medial axis around the region being processed.
		This algorithm is an extension to the Octree algorithm.
		The algorithm also optimises the orientation of the grid of spheres, and their size, so as to minimise the error in the approximation and to minimise the volume of each of the resulting regions.
	isg.cs.tcd.ie /spheretree (1925 words)

	Algorithm - Recipes Encyclopedia
		Algorithms are essential to the way computers process information, because a computer program is essentially an algorithm that tells the computer what specific steps to perform (in what specific order) in order to carry out a specified task, such as calculating employees’ paychecks or printing students’ report cards.
		Probabilistic algorithms are those that make some choices randomly (or pseudo-randomly); for some problems, it can in fact be proved that the fastest solutions must involve some randomness.
		An algorithm designed for such an environment is called a serial algorithm, as opposed to parallel algorithms, which take advantage of computer architectures where several processors can work on a problem at the same time.
	www.recipes.tiptophot.com /recipes/index.php?title=Algorithm (2174 words)

	Polynomial-time approximation scheme - Wikipedia, the free encyclopedia
		In computer science, a polynomial-time approximation scheme (abbreviated PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).
		A PTAS is an algorithm which takes an instance of an optimization problem and a parameter ε>0 and produces a solution of an optimization problem that is within ε factor of being optimal.
		Even more restrictive, and useful in practice, is the fully polynomial-time approximation scheme or FPTAS, which requires the algorithm to be polynomial in both the problem size n and 1/ε.
	en.wikipedia.org /wiki/Polynomial_time_approximation_scheme (324 words)

	Citations: A linear time approximation algorithm for the weighted vertex cover algorithm - Bar-Yehuda, Even ... (Site not responding. Last check: 2007-10-08)
		Ultimately, the performance guarantee of our algorithm beats the performance guarantee of the greedy algorithm in each case of bounded k and coincides with that when k is unbounded.
		Both results can be improved to an approximation factor that is asymptotically better: log log V 2 log V [8, 23] The parameterized complexity [13] of UVC recently has received considerable interest [6, 10, 13, 15, 26, 32] Here, for a given k, the question is to find a vertex cover....
		Both these approximation algorithms have performance ratio 2, and this is in fact the best known for the Min Vertex Cover problem in spite of large e#orts.
	citeseer.ifi.unizh.ch /context/1960249/0 (918 words)

	Approximation algorithms for NP-hard optimization problems (Site not responding. Last check: 2007-10-08)
		One option in such a case is to seek an approximation algorithm -- an algorithm that is guaranteed to run quickly (in time polynomial in the input size) and to produce a solution for which the value of the objective function is quantifiably close to the optimal value.
		Note that this algorithm is not, strictly speaking, an approximation algorithm for any one optimization problem: the output of the algorithm is a solution to one problem while the quality of the output is measured against the optimal value for another.
		The performance of an approximation algorithm would be defined as the probabilistic performance on a probability distribution selected by an adversary from among a large class of distributions.
	www.cs.ucr.edu /~neal/non_arxiv/crc-approx-algs/html (8439 words)

	[No title]
		The common characteristic that we find in algorithms for covering problems is the use of vertex weight reductions (or vertex deletion, which is a special case).
		We are interested in viewing algorithms from the viewpoint of the Local-Ratio theorem \cite{BarEve85}, and its extensions by Bafna, Berman and Fujito \cite{BafBer95}.
		Algorithm BarEven is written in hypergraph terminology, and therefore approximates HVC as well.
	www.cs.technion.ac.il /~reuven/SAVE/PAPERS/LOCAL_RATIO/TR/save (4408 words)

	An Efficient, Error-Bounded Approximation Algorithm for Simulating Quasi-Statics of Complex Linkages
		This algorithm can cull away joints whose contribution to the overall linkage motion is below a given user-defined threshold, thus limiting the computation of the joint accelerations and forces to those that contribute most to the overall motion.
		This paper introduces an algorithm for automatic simplification of the quasi-statics of articulated bodies (in the quasi-statics case, the articulated bodies velocities are zero at all times).
		Based on a user-defined maximum error threshold, the algorithm determines a set of joints which contribute most to the articulated body acceleration, and culls away the other joints (implicitly assuming that their acceleration is zero).
	gamma.cs.unc.edu /AQ (484 words)

	Algorithm for Black Box Global Optimization: RGA
		So, throughout its every step ('try') the algorithm "enriches" the previous set of points and constructs a new approximation f after the OF returns the values on the subset of new (intrinsic) points.
		The approximate function f can be interpreted as prediction of the true value at any point of the domain of search.
		The algorithm is terminated when the minimum of having been calculated values of the OF is reached namely at that point which has been predicted as the point of global minimum provided the value itself is well-predicted.
	www.fi.uib.no /~antonych/RGA0.html (632 words)

	CS684
		The course pre-requisite is CS 681 or equivalent background in algorithms and discrete mathematics.
		We will see that the algorithm we have seen so far, can be viewed as "primal-dual" methods, i.e., methods that make use of this technique to prove the constructed solution is optimal (or close to optimal).
		Approximation Algorithms for Classification Problems with Pairwise Relationships: Metric Partitioning and Markov Random Fields, In the Proceedings of the 40th Annual IEEE Symposium on the Foundations of Computer Science, 1999.
	www.cs.cornell.edu /Courses/cs684/2001fa (1095 words)

	rho-approximation algorithm (Site not responding. Last check: 2007-10-08)
		Definition: An approximation algorithm guaranteed to find a solution at most (or at least, as appropriate) ρ times the optimum.
		The ratio ρ is the performance ratio or relative performance guarantee of the algorithm.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "ρ-approximation algorithm", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/rhoapproxmtn.html (127 words)

	[No title]
		Run an `approximation algorithm' which -always runs in polynomiatl time -produces a solution which is PROBVABLY within a guaranteed factor from the optimal solution.
		E.g We will design an approximation algorithm for the TSP_opt problem when the input graph and costs satisfy the triangle inequality, such that the tour produced by our algorithm will be provably within a factor 2 of the cost of the optimal least costly tour.
		The approximation for TSP had ratio-bound 2 whereas the apprxomation for SET-COVER had a O(ln m) ratio bound.
	theory.lcs.mit.edu /classes/6.046/spring04/lectures/lecture23.txt (1094 words)

	Dictionary of Algorithms and Data Structures
		This is a dictionary of algorithms, algorithmic techniques, data structures, archetypical problems, and related definitions.
		We do not include algorithms particular to business data processing, communications, operating systems or distributed algorithms, programming languages, AI, graphics, or numerical analysis: it is tough enough covering "general" algorithms and data structures.
		Data Structures and Algorithms is a wonderful site with illustrations, explanations, analysis, and code taking the student from arrays and lists through trees, graphs, and intractable problems.
	www.nist.gov /dads (612 words)

	A 1.47-Approximation Algorithm for a Preemptive Single-Machine Scheduling Problem - Goemans, Wein, Williamson, -- ... (Site not responding. Last check: 2007-10-08)
		Abstract: In this note, we give a 1.47-approximation algorithm for the preemptive scheduling of jobs with release dates on a single machine so as to minimize the weighted sum of job completion times; this problem is denoted by 1jr j ; pmtnj P j w j C j in the notation of Lawler et al.
		Our result improves on a 2-approximation algorithm due to Hall, Schulz, Shmoys and Wein [4], and also yields an improved bound on the quality of a well-known linear programming relaxation of the problem.
		55.0%: A 1.47-Approximation Algorithm for a - Preemptive Single-Machine..
	sherry.ifi.unizh.ch /goemans97approximation.html (486 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Greedy 2-approximation algorithm (choose side for each vertex to maximize number of edges across cut).
		Working out the details, the algorithm generated by this method is the following: Consider the vertices sequentially.
		For each vertex, choose the "left" or the "right" side, as follows: if the vertex has more edges to vertices already chosen to be "left" than to vertices chosen to be "right", then choose the vertex to be "right".
	www.cs.ucr.edu /~neal/1998/cosc185-S98/lectures (1458 words)

	David P. Williamson: Selected Publications
		Approximation algorithms for MAX 3-CUT and other problems via complex semidefinite programming, with Michel Goemans.
		Approximate k-MSTs and k-Steiner trees via the primal-dual method and Lagrangean relaxation, with Fabian Chudak and Tim Roughgarden.
		A primal-dual schema based approximation algorithm for the element connectivity problem, with Kamal Jain, Ion Mandoiu, and Vijay Vazirani.
	legacy.orie.cornell.edu /~dpw/publications.html (556 words)

	[No title]
		An algorithm $A$ is called an $r$-approximation algorithm if for all instances $G,\omega$, $A$ returns an $r$-approximate cover.
		While the Maximum Clique problem is known to be hard to approximate, as shown by Hastad \cite{Has96}, Hochboum \cite{Hoc97} has developed a 4-approximation for the Min Clique-Complement problem.
		This implies that the algorithm is a 2-approximation, by Theorem \ref{th:ccp1}.
	www.cs.technion.ac.il /~reuven/SAVE/PAPERS/CLIQUE_COMPLEMENT/IPL980511/save (775 words)

	[No title]
		An approximation scheme for an optimization problem is an approximation algorithm that takes as input an instance of the problem and a value
		The approximation scheme is polynomial-time approximation scheme if it runs in time polynomial in the size n of the input.
		For TSP with triangle inequality, Approx-TSP-Tour is an approximation algorithm with a ratio bound of 2.
	ranger.uta.edu /~cook/aa/transcript/ln28f (560 words)

	Approximation Algorithm for (ResearchIndex) (Site not responding. Last check: 2007-10-08)
		Following a series of preliminary results, Hannenhalli and Pevzner developed the first exact polynomial time algorithm for the problem of...
		0.6: A 2-Approximation Algorithms for Genome Rearrangements by..
		21 Exact and approximation algorithms for the inversion distanc..
	citeseer.ist.psu.edu /632250.html (483 words)

	Blog
		Unfortunately, the paper I had been working on for the past couple of weeks had to be postponed because the algorithm changed the day before the deadline.
		The paper has some good results in it, so it might even get accepted, though I hear that acceptance at a big conference like SODA can be something of a crapshoot.
		The algorithm was pretty complicated, so a few weeks ago I decided to step back and see if I could make it simpler.
	www.win.tue.nl /~cgray/blog.html (548 words)

	Polyline Simplification
		Vertex reduction is the brute-force algorithm for polyline simplification.
		More specifically, in the DP algorithm, the two extreme endpoints of a polyline are connected with a straight line as the initial rough approximation of the polyline.
		Second, since this algorithm depends on a 2D convex hull algorithm, it only applies to planar polylines, whereas the VR and DP algorithms can be used for any dimension.
	geometryalgorithms.com /Archive/algorithm_0205/algorithm_0205.htm (2127 words)

	SAT 2004 - Approximation algorithm for random MAX-KSAT (Site not responding. Last check: 2007-10-08)
		An approximation algorithm for random K-SAT formulas (MAX-R-KSAT) is herein discussed.
		The proposed algorithm is similar to the unit clause with majority rule algorithm studied in [Franco et all 1986] for the random 3-SAT problem.
		The new approximation ratio is achieved by using a better algorithm than the one proposed in [De la Vega et all 2002], along with a new upper bound on the maximum number of clauses that can be satisfied in a random K-SAT formula [Achlioptas et all 2003].
	www.satisfiability.org /SAT04/accepted/49.html (130 words)

	Efficient Approximation Algorithm for Minimizing Makespan on Uniformly Related Machines - Chekuri, Bender ... (Site not responding. Last check: 2007-10-08)
		Abstract: We obtain a new efficient approximation algorithm for scheduling precedence constrained jobs on machines with different speeds.
		Open problem 2 Design a polynomial time approximation algorithm for Q j prec j C max with constant performance guarantee (i.e....
		An efficient approximation algorithm for minimizing makespan on uniformly related machines.
	sherry.ifi.unizh.ch /1883.html (501 words)

	Fast Swept Volume Approximation of Complex Polyhedral Models
		Abstract: We present an efficient algorithm to approximate the swept volume (SV) of a complex polyhedron along a given trajectory.
		We also present a novel and fast algorithm for computing the signed distance of surface primitives as well as a number of techniques based on surface culling, fast marching level-set methods and rasterization hardware to improve the performance of the overall algorithm.
		In practice, it is able to compute a bounded-error approximation in tens of seconds for models composed of thousands of polygons sweeping along a complex trajectory.
	gamma.cs.unc.edu /SV (304 words)

	Citebase - An Efficient Approximation Algorithm for Point Pattern Matching Under Noise
		(3) We use expander graphs to speed-up the T-hashing algorithm for \tolerant-LCP when the size of the matched set is required to be large, at the expense of approximation in the matched set size.
		Our algorithms also work when the transformation μ is allowed to be scaling transformation.
		Approximation Algorithms for 3-D Commom Substructure Identification in Drug and Protein Molecules.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:cs/0506019 (757 words)

	Approximation algorithm for the Subset-sum problem
		In the subset-sum problem we wish to find a subset of A.1,...,A.N whose sum is as large as possible but not larger than T (capacity of the knapsack).
		This algorithms is evolved from Exponential-time exact algorithm.
		I compared the algorithms for solution of the Subset-sum problem and my algorithm DIOPHANT for solution of the diophantine equations.
	www.geocities.com /zabrodskyvlada/aat/a_suba.html (297 words)

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