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Topic: Combinatorial explosion

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	Branching factor - Wikipedia, the free encyclopedia
		by following every branch at every node) usually becomes computationally more expensive the higher the branching factor, due to the exponentially increasing number of nodes (combinatorial explosion).
		For example, if the branching factor is 10, then there will be 10 nodes one level from the current position, 100 nodes two levels down, 1000 three levels down, and so on.
		The higher the branching factor, the faster this "explosion" occurs.
	www.wikipedia.org /wiki/Branching_factor (197 words)

	Combinatorial Chemistry - ChemNews.Com 9.3호
		Combinatorial chemistry is quickly changing from the new frontier of chemistry research to a widely practiced methodology.
		While combinatorial chemistry was once the preserve of specialty software, a huge number of ChemDraw users began to ask for combinatorial chemistry functionality within the ChemOffice suite.
		The combinatorial extension to ChemOffice is designed for the increasing number of chemists who seek to utilize combinatorial techniques to build libraries of reasonable size on a weekly basis.
	www.camsoft.co.kr /chemnews/art/56.htm (790 words)

	Jahrbuch-CD der MPG 2003 - Combinatorial complexity of pat
		Elementary flux mode analysis is a promising approach for a pathway-oriented perspective of metabolic networks.
		However, in larger networks it is hampered by the combinatorial explosion of possible routes.
		In this work we give some estimations on the combinatorial complexity including theoretical upper bounds for the number of elementary flux modes in a network of a given size.
	www.mpg.de /forschungsergebnisse/wissVeroeffentlichungen/archivListenJahrbuch/2002/19/publZIM59.html (155 words)

	Combinatorial
		Specialty definitions using "combinatorial": A Language for Intelligent Combinatorial Exploration ♦ Charme, combinator, combinatorial test, computational geometry ♦ DNA computing ♦ full array ♦ geometrical average ♦ k-statistics ♦ Lady Mary Jane ♦ Marie-Johanna, metaheuristic ♦ NP-hard ♦ Programmable Array Logic, programmable logic array, programmable logic device ♦ simulated annealing, Splim ♦ uncomputable function.
		"Combinatorial" is used about 41 times out of a sample of 100 million words spoken or written in English.
		combinatorische toets (combinatorial test), combinatorische explosie (combinatorial explosion), combinatorische classificatie (combinatorial classification), combinatorisch moment (combinatorial power mean), schakelnet (automatic network, combinational circuit, combinational logic system, combinatorial circuit, dialing network, switched network), schakelkring (combinational circuit, combinational logic system, combinatorial circuit).
	www.websters-online-dictionary.org /definition/Combinatorial (600 words)

	Reason
		A combinatorial explosion occurs when a huge number of possible combinations are created by increasing the number of entities that can be combined.
		The combinatorial problem grows mind-bogglingly huge when one considers the various ways just 30,000 human genes and the 100,000 or so proteins they produce can be combined in human cells and tissues.
		So skeptics of genetic engineering argue that such a vast array of complicated interactions may well preclude safe and effective engineering in human beings for such multifactorial genetic illnesses as heart disease and cancer, and for beneficial traits like high intelligence.
	www.reason.com /rb/rb070903.shtml (687 words)

	Hany Farid: Papers (Site not responding. Last check: 2007-10-29)
		The principle difficulty facing side chain prediction algorithms is the combinatorial explosion of simultaneously predicting even a small number (more than ten) of residues.
		One strategy to overcome this combinatorial explosion is to greatly reduce the number of possible configurations of each residue type to only a few rotamer positions; this methodology is adopted in the work presented here.
		Simulated annealing and Monte Carlo statistical sampling techniques are employed to overcome the combinatorial explosion of searching every rotamer configuration of an entire protein.
	www.cs.dartmouth.edu /farid/publications/thesis92.html (363 words)

	An unaverted explosion
		Hence, the combinatorial explosion can be avoided, since only experiences appropriate to a single line of ‘action’ have to be provided and there will be no need to cater to unactualized choices.
		But such a predictor would face a combinatorial explosion just as bad as that confronting the original operator, considered by Dennett, who tries to keep pace with the choices in real time.
		[1] For the sake of (the skeptic's) argument, let us therefore concentrate on the claim that the vat scientist can evade combinatorial explosion by imposing choices on the brain and hence limit the number of ‘input’ sequences to be calculated.
	www.philosophy.su.se /texter/dennett.htm (1481 words)

	[No title]
		Equally amiss is the fact the combinatorial explosion is in tact in your hands.
		>i You are carrying: a combinatorial explosion an unsigned Ronqon peace treaty a simple walking stick (that you're not pretending to use like a bow right now) your clothes (being worn) She catches you looking at the woods and heightens its fear within you by whispering an oboe medley.
		You couldn't possibly still be in love?) (Could you?) >i You are carrying: a combinatorial explosion a signed Ronqon peace treaty a gnarled staff (gripped tightly) your clothes (being worn) >[combinatorial explosion is just silly.] That's neither a verb nor a topic I recognize.
	www-bioc.rice.edu /~lpsmith/IF/transcripts/smoochie/sparrow6.scr (13438 words)

	Plato's Cave: Combinatorial Explosion (Site not responding. Last check: 2007-10-29)
		Furthermore, the proximity relations are not defined by an absolute distance, but rather by relative groupings or clusterings, which may occur at a multitude of spatial scales, as shown below.
		A full encoding of the rules of this algorithm would be even more complex, and would lead to yet more combinatorial problems.
		Furthermore, the Gestalt grouping laws do not act independently but appear to influence each other, so that the final pre-attentive percept is some analog combination of all of the Gestalt grouping laws acting in unison (note the influence of "good continuation", "symmetry (five-fold), and "closure" above).
	cns-alumni.bu.edu /pub/slehar/webstuff/pcave/explosion.html (229 words)

	Combinatorial Game Pedagogy Theory (Site not responding. Last check: 2007-10-29)
		Combinatorial game theory (pedagogy) Blue-Red Hackenbush -- At the finite level, this partizan combinatorial game allows constructions of games whose values are dyadic rational numbers.
		Combinatorial game theory (CGT) is a mathematical theory of games, which...
		Combinatorial game theory (history) Combinatorial game theory (pedagogy)...
	riskmgmt.biz /mysite/economics%20TE2.2/combinatorial-game-pedagogy-theory.html (1029 words)

	Re: rb5: remove combinatorial explosion patch
		Re: rb5: remove combinatorial explosion patch, Richard Boulton,
		Re: rb5: remove combinatorial explosion patch, Raja R Harinath,
		Previous by thread: Re: rb5: remove combinatorial explosion patch
	lists.gnu.org /archive/html/automake-patches/2001-08/msg00029.html (269 words)

	Taming Combinatorial Explosion (Site not responding. Last check: 2007-10-29)
		On the other hand, memorizing that one-liner (and its meaning) would be just as hard as memorizing all of Shakespeare's work.
		This is one example of the combinatorial explosion that would make individual finite strings so improbable that it would not be a good basis for a language.
		"(...) template-induced auto-catalytic processes are excellent means for the taming of the combinatorial explosion.
	www.comdig.org /print_article.php?id_article=778 (274 words)

	World War 1 and 2 - Chart parser
		There may also be a set of probabilities obtained from analysis of a text corpus.
		A systematic search is used to explore the space of possible parses of the input string, and a data structure called a "chart " is used to eliminate backtracking and prevent a combinatorial explosion.
		A common approach is to use a variant of the Viterbi algorithm.
	www.worldwardiary.com /history/Chart_parser (289 words)

	Combs method - Wikipedia, the free encyclopedia
		It is designed to prevent combinatorial explosion in fuzzy logic rules.
		This shows that the Combs method is probably unnecessary for systems that consider only a few sets and a few variables at a time, but some means of taming the combinatorial explosion is needed to allow a complex system.
		This article will focus on the Combs method itself.
	en.wikipedia.org /wiki/Combs_method (249 words)

	Taming combinatorial explosion -- Schuster, 10.1073/pnas.150237097 -- Proceedings of the National Academy of Sciences
		Taming combinatorial explosion -- Schuster, 10.1073/pnas.150237097 -- Proceedings of the National Academy of Sciences
		Assembling objects from building blocks by means of predefined combination rules leads to combinatorial explosions.
		Examples of combinatorial explosion and a catalytic cycle reducing the numbers of possible objects.
	www.pnas.org /cgi/content/full/150237097v1 (1645 words)

	DBMS - June 1998 - Arbor Essbase OLAP Server 5
		Because the typical financial hypercube is comparatively limited in dimensionality and has a logical structure that meshes well with Essbase’s physical architecture, combinatorial explosion has not inhibited Arbor from gaining a major share of the OLAP database server market for financial applications.
		The ROLAP vendors have been able to hold the market for large-scale marketing applications by containing the problem of combinatorial explosion through selective (rather than total) precalculation of dimensional summaries and by dynamically sorting, filtering, and pivoting on "attributes" of primary member categories without making them full-fledged, stored dimensions.
		The first challenge in taming combinatorial explosion was to find a way to reduce the percentage of precalculated cells in a hypercube while minimizing the negative impact on query response time.
	www.dbmsmag.com /9806d08.html (2179 words)

	Gic Chic: The Explosion of Separated Concerns
		In isolation, each of these stakeholders presents a collection of concerns that must be addressed in order to consider the project successful.
		Collectively, they represent a combinatorial explosion of considerations as their needs are taken into account throughout the system's development lifecycle.
		Traditionally, this type of system (that is, the collection of stakeholder concerns throughout the SDLC) would be resolved through some form of multivariate analysis.
	www.aesthesis.com /team/global/tlcowart/blog/tech/2004/10/explosion-of-separated-concerns.html (664 words)

	Combinatorial SNP Motifs (Site not responding. Last check: 2007-10-29)
		Understanding the genetic basis of complex disease will involve a mixture of genetic traits as reflected in combinatorial SNP patterns.
		Biosystemix algorithms can search for predictive, higher order SNP motifs where exhaustive methods fail due to the combinatorial explosion.
		As thousands of SNPs are assayed in studies covering hundreds of individuals, we face the serious data mining challenge of the combinatorial explosion in extracting predictive multi-SNP patterns. Biosystemix uses heuristic association mining methods that can provide valuable results when powerful computational hardware becomes overloaded.
	www.biosystemix.com /index_files/BiosystemixCombinatorialSNPMotifs.htm (164 words)

	Barnard and Downs: Markush Techniques for Combinatorial Libraries
		Though there are several important differences between the Markush structures in patents and those which may be used to describe combinatorial libraries, some of the same techniques can be used to avoid enumerating the individual compounds covered for diversity analysis purposes.
		With a view to possible future requirements, provision is also made for the inclusion of generic (homolgy-variant) partial structures, and the data structure also includes certain other features for position and frequency variation.
		It could also be generated from other formats used for representation of combinatorial libraries, such as Tripos Inc.'s Sybyl Line Notation (SLN) [Ash et al., 1997], and MDL's RGfiles.
	www.daylight.com /meetings/mug97/Barnard/970227JB.html (3327 words)

	combinatorial - Definition of combinatorial - combinatorial in Encyclopedia - DictionaryWords.net (Site not responding. Last check: 2007-10-29)
		--- [from gcide] --- :combinatorial \combinatorial\ combinatory \combinatory\adj.
		produced by a process of combining; as, a combinatorial explosion of possibilities; -- used especially in reference to mathematical or statistical processes of computing possible combinations.
		PJC] --- [from wn] --- :combinatorial adj 1: relating to or involving combinations [syn: combinative, combinatory] 2: relating to the combination and arrangement of elements in sets
	www.dictionarywords.net /find/word/combinatorial (80 words)

	PASCAL -
		We propose an alternative approach in which multiplicative pixel interactions are described by a series of Wiener functionals.
		Since the functionals are estimated implicitly via polynomial kernels, the combinatorial explosion associated with the classical higher-order statistics is avoided.
		First results show that image structures such as lines or corners can be predicted correctly, and that pixel interactions up to the order of five play an important role in natural images.
	eprints.pascal-network.org /archive/00000375 (129 words)

	An Accelerated IMM-JPDA Algorithm for Tracking Multiple Maneuvering Targets in Clutter (Site not responding. Last check: 2007-10-29)
		Theoretically, for example, the MHT method is known to be the most powerful approach to tracking multiple maneuvering targets in clutter.
		This method, however, very often leads to combinatorial explosion and computational overload that restricts its implementation.
		Hypotheses generation is another combinatorial problem that will be discussed in the next section.
	www.isn.ethz.ch /researchpub/publihouse/infosecurity/volume_9/B5/B5_index.htm (3150 words)

	BIOwulf's Mathematical Tools (part 2 of 3)
		People like to use that phrase a lot: "more than the number of particles in the known universe." But that's just peanuts to the combinatorial explosion.
		The number of subsets of 22,000 objects is mind-numbingly bigger than the number of particles the universe could hold.
		So my point, and I do have one, is that because of the combinatorial explosion there is no way we are going to try all possible subsets of what we are calling the columns or the dimensions of data.
	www.well.com /~abs/Biowulf/biowulf_screenplay2.html (2275 words)

	2.1.2 The Problem: Combinatorial Explosion
		The naive way of solving combinatorial problems can be paraphrased as `generate and test': In a first step one enumerates all combinations from which one selects all solutions in the second step.
		In most cases however, `generate and test' is simply not feasible.
		In this case, the generation step runs into a combinatorial explosion (from which it usually returns only several billions of years later).
	ps.uni-sb.de /~niehren/Web/Vorlesungen/Oz-NL-SS01/vorlesung/node5.html (388 words)

	DIMACS Mini-Workshop on Combinatorial Structures in Molecular Biology (Site not responding. Last check: 2007-10-29)
		Biology's connection to combinatorial mathematics has been solid since Mendel and rapidly expanding since Watson and Crick.
		Recent work in mapping the human genome, however, has underscored the problem of combinatorial explosion: even with today's vast computing power, many simple-sounding combinatorial tasks in molecular biology are beyond reach.
		The biological areas we should emphasize include sequence analysis, protein structure prediction, evolutionary tree reconstruction, phylogeny, RNA secondary structure, and certain questions in the fascinating area of popula- tion genetics, applied to prebiotic molecules a la Eigen.
	www.dimacs.rutgers.edu /Workshops/Combinatorial/announcement.html (399 words)

	The Tunneling Algorithm for Partial CSPs and Combinatorial Optimization Problems - Voudouris, Tsang (ResearchIndex) (Site not responding. Last check: 2007-10-29)
		Abstract: Constraint satisfaction is the core of a large number of problems, notably scheduling.
		Because of their potential for containing the combinatorial explosion problem in constraint satisfaction, local search methods have received a lot of attention in the last few years.
		The problem with these methods is that they can be trapped in local minima.
	citeseer.lcs.mit.edu /voudouris94tunneling.html (670 words)

	[darcs-users] Eclipse integration, refactoring, and combinatorial explosion? (Site not responding. Last check: 2007-10-29)
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		Practical: how to avoid the combinatorial explosion of commuting > two patches of two arbitrary types?
	abridgegame.org /pipermail/darcs-users/2003/000924.html (1083 words)

	An Algebraic Approach to IP Traceback, from Silicon Defense - White Papers, Webcasts and Case Studies - ZDNet China
		Overview: We present a new solution to the problem of determining the path a packet traversed over the Internet (called the traceback problem) during a denial of service attack.
		Previous solutions to this problem have suffered from combinatorial explosion, and are unable to scale to realistically sized networks.
		This paper reframes the traceback problem as a polynomial reconstruction problem and uses techniques from algebraic coding theory to provide robust methods of transmission and reconstruction.
	cn.itpapers.com /abstract.aspx?scid=902&sortby=title&docid=28070 (190 words)

	Optimizations of the Combinatorial Neural Model
		In this paper we present significant optimizations of the so-called Combinatorial Neural Model (CNM).
		CNM is a hybrid (neural/symbolic) model that has been used in areas such as expert system development and data mining.
		The most important optimization aims at taming combinatorial explosion, which is the main problem inherent to this model.
	csdl.computer.org /comp/proceedings/sbrn/1998/8629/00/86290049abs.htm (162 words)

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