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Topic: Covering problem

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	maximal conditional covering problem, The INFOR - Find Articles (Site not responding. Last check: 2007-10-10)
		A well-studied extension of the LSCP is the Maximal Covering Location Problem (MCLP), introduced by Church and ReVelle (1974), which seeks to deploy a limited number of servers in such a way that population coverage is maximized.
		The maximal conditional covering problem bears the same relation to the conditional covering problem as the maximal covering location problem does to the location set covering problem in the sense that conditional coverage is sought but not required.
		Moon and Chaudhry's conditional covering problem required servers to be deployed in such a way that all servers were covered by at least one other server in addition to requiring the coverage of all demand nodes.
	www.findarticles.com /p/articles/mi_qa3661/is_199605/ai_n8757471 (1011 words)

	Problem D - World Finals Warmup (Oriental) Contest
		In this problem you are asked to solve some elementary covering problems.
		The basic idea of covering problem is to find out the smallest size of a particular shape that can entirely cover another particular shape.
		Covering problems have many practical applications such as finding smallest possible square sized covers for a round table.
	acm.uva.es /p/v104/10402.html (327 words)

	Set Covering, Packing and Partitioning Problems
		Commonly cited problems having this structure include the crew-scheduling problem where every flight leg of an airline must be scheduled by exactly one cockpit crew; another is the political districting problem whereby regions must be divided into voting districts such that every citizen is assigned to exactly one district.
		Because, for even small instances of the problem, the problem size cannot be explicitly solved, techniques known as column-generation, which began with the seminal work of Gilmore and Gomory [1961] on the cutting stock problem, are employed.
		It is for these larger instances of the problem that approximation techniques, reformulation and exact procedures have been developed that exploit the underlying structure of the problem.
	iris.gmu.edu /~khoffman/papers/set_covering.html (2092 words)

	The complexity of the covering radius problem on lattices and codes (Site not responding. Last check: 2007-10-10)
		For the covering radius on n-dimensional lattices, we show that the problem can be approximated within any constant factor gamma(n) > 1 in random exponential time 2^{O(n)}, it is in AM for gamma(n) = 2, in coAM for gamma(n) = sqrt{n / log n}, and in NP intersected coNP for gamma(n) = sqrt{n}.
		For the covering radius on n-dimensional linear codes, we show that the problem can be solved in deterministic polynomial time for approximation factor gamma(n) = log n, but cannot be solved in polynomial time for some gamma(n) = Omega(log log n) unless NP can be simulated in deterministic n^{O(log log log n)} time.
		Moreover, we prove that the problem is NP-hard for any constant approximation factor, it is Pi_2-hard for some constant approximation factor, and it is in AM for approximation factor 2.
	www-cse.ucsd.edu /users/daniele/papers/CoveringRadius.html (271 words)

	[No title]
		This is a well known problem in "covering" for which there is a good algorithm.
		An implication table is made, then a cover function is formed and simplified, and the term(s) of the simplified cover function with the minimal set factors is(are) optimal.
		This is a variant of the "set cover" problem, which is NP-complete in the general case.
	www.math.niu.edu /~rusin/known-math/95/weaving (529 words)

	Covering A Chessboard With Domino
		Cover two arbitrary but adjacent squares of a chessboard with a piece of domino.
		It's a very legitimate question to ask because obviously, at one extreme, when we remove all but two nonadjacent squares, the problem of covering whatever remains will be unsolvable for at least some configurations.
		Recollecting our original problem, if it were possible to isolate a region of the chessboard that contained an odd number of squares, we would be able to claim that the solution to Problem 3 is 1, just one pair.
	www.cut-the-knot.org /do_you_know/chessboard.shtml (839 words)

	[No title]
		We consider the dual problem of finding the side s(n) of the largest square that can be covered with n unit squares.
		Coverings not attributed to someone else were discovered by the second author.
		We can assume each square is translated and rotated so as to cover as much of the perimeter of S as possible, and that a square T covers the top two corners.
	www.stetson.edu /~efriedma/papers/covering/covering.html (758 words)

	A Genetic Algorithm for the Set Covering Problem - Beasley, Chu (ResearchIndex)
		We propose several modifications to the basic genetic procedures including a new fitness-based crossover operator (fusion), a variable mutation rate and a heuristic feasibility operator tailored specifically for the set covering problem.
		12: A lagrangian heuristic for set-covering problems (context) - Beasley - 1990
		3 A Lagrangean heuristic for set-covering problems (context) - Beasley - 1990
	citeseer.ist.psu.edu /beasley96genetic.html (782 words)

	Covering an Art Gallery
		The art gallery problem was introduced by Victor Klee in 1973 in a discussion with Vasek Chvatal.
		Given a guard with 360 degrees vision, the problem is to determine the minimum number of guards required to cover the gallery.
		There is a well-known approach to finding a guard cover that guarantees no more than n/3 guards - triangulate the polygon, three-color the vertices, and place guards on the vertices with the least-frequently occurring color.
	www.cs.ucsb.edu /~staylor/research/ArtGallery/Art_Gallery_Problem.html (1179 words)

	Knowledge Reuse
		Diagnostic (classification) problems can be characterized as the selection of solutions from a preenumerated set of alternatives (diagnoses) for a problem described by observations (symptoms).
		While the principal problems of diagnostic modeling are quite well understood, and for most domains routine approaches can be offered, the cost effectiveness of large knowledge bases (with more than 1000 symptoms and diagnoses) is a major issue.
		Distributed problem solving is an important step to reduce the size and thereby the complexity of knowledge bases and to increase reuse, because for example a knowledge base for X-ray interpretation can be consulted by many different medical knowledge bases.
	ksi.cpsc.ucalgary.ca /KAW/KAW98/puppe (7014 words)

	covering problem (Site not responding. Last check: 2007-10-10)
		The paper develops a theoretical understanding of the adaptive covering algorithms by relating their behavior to the evolution of a deterministic ordinary differential equation.
		In terms of the covering problem, candidate coverings tend to improve as more data is gathered whenever the ODE is stable.
		This technique of solving the covering problem first appeared in the IEEE Transactions on Signal Processing in October 1994.
	eceserv0.ece.wisc.edu /~sethares/papers/covstab.html (163 words)

	Packing problem - Wikipedia, the free encyclopedia
		Usually the packing must be without gaps or overlaps, but in some packing problems the overlapping (of goods with each other and/or with the boundary of the container) is allowed but should be minimised.
		A classic problem is the sphere packing problem, where one must determine how many spherical objects of given diameter d can be packed into a box of size a × b × c.
		A problem is the square packing problem, where one must determine how many squares of side 1 you can pack into a square of side a.
	en.wikipedia.org /wiki/Packing_problem (588 words)

	Set Covering Problem
		To illustrate this model, consider the following location problem: A county is reviewing the location of its fire stations.
		The jth column of the constraint matrix represents the set of cities that can be served by a fire station in city j.
		We are asked to find a set of such subsets j that covers the set of all cities in the sense that every city appears in the service subset associated with at least one fire station
	www.isl.itu.edu.tr /ya/set_covering.htm (192 words)

	RND Problem Description
		The part of an area that is covered by a transmitter is called a cell.
		The problem we consider recalls the unicost set covering problem (USCP) that is known to be NP-Hard.
		The fitness function accounts for all problem knowledge details in that it scan the binary string provided by the algorithm, therefore computing the covered area as well as other statistical measures that could be needed to assess the quality of the evaluated individual as a tentative solution to the problem.
	neo.lcc.uma.es /opticomm/rnddescription.html (1077 words)

	Free Problem Solving book Covering Successful Problem Solving, Planning Corrective Action, And Plan Implementation.
		This book is intended to help you find all of the "root" causes of the problem, confirm that these are the root causes, and help prepare and carry out the plans needed to completely solve the problem.
		As with any major project, many unexpected problems arose along the way and had to be dealt with.
		Due to the many possible factor relationships in a complicated problem, this approach forces one to be more complete in the analysis and evaluation of the situation.
	www.sonic.net /lwturn (643 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		Given any binate covering problem, represented by a text-format matrix, you will come up with new ideas for (i) row dominance, (ii) column dominance, and (iii) essentials.
		The goal is to reduce the binate covering matrix, (as has already been done in class for unate covering problems, i.e.
		The result should be (1) a reduced binate covering table, and (2) a list of any essential columns which have been removed.
	www1.cs.columbia.edu /~cs4861/handouts/proj-problem-1.txt (776 words)

	Translational Orthotope Covering Problems -- Ben England, UMass Lowell
		As part of this research, software was developed to attempt to solve orthotope covering problems in any number of dimensions.
		A covering problem instance is a target shape and a set of cover shapes -- the problem is to position the cover shapes so that the target is completely covered by them.
		A set of sample 2-d problem instances and solutions generated by this software is available in the relative_perf subdirectory, along with the polygon representation of the problem instances, so that we can compare this solver's performance with a general-purpose polygon covering problem solver.
	www.cs.uml.edu /~bengland/cg/orthotope_cover (472 words)

	Citations: the quasi-minimal solution of the general covering problem - Michalski (ResearchIndex) (Site not responding. Last check: 2007-10-10)
		the problem of mixed data is a traditional one.
		Learning rules from examples is an instance of the setcovering problem [16] with the added restriction that covers of one set cannot intersect with points of another.
		Since this problem is NP hard, the AQ algorithm (that underlies program AQ15c) solves this problem in a quasi optimal manner, that is, finds a solution that is optimal or near optimal.
	citeseer.ist.psu.edu /context/18260/0 (2676 words)

	k-clique (Site not responding. Last check: 2007-10-10)
		The problem of covering edges and vertices in a graph (or in a hypergraph) was motivated by a problem arising in the context of component assembly problem.
		The problem is, given a graph and a clique size k, find the minimum number of k-cliques such that all edges and vertices of the graph are covered by (included in) the cliques.
		It is shown that the algorithms we design, that exploit the structure of this special Set Covering problem, have better performance than those derived from direct applications of general purpose algorithms for the Set Covering.
	riot.ieor.berkeley.edu /~dorit/pub/k-clique.html (209 words)

	Covering problem - Wikipedia, the free encyclopedia
		In combinatorics and computer science, the covering problem is a type of general question: if a certain structure covers another, or how many structures are required to cover another?
		For Petri nets, for example, the covering problem is defined as the question if for a given marking, there exists a run of the net, such that some larger (or equal) marking can be reached.
		Larger means here that all components are at least as large as the ones of the given marking and at least one is properly larger.
	en.wikipedia.org /wiki/Covering_problem (134 words)

	IBM Final Report: Regional Conservation Planning
		Thus, problems may exist that are inherently hard to solve and may require a significant amount of computer time to solve.
		Map of solution to the maximal covering location problem in which all species are covered at least once.
		To facilitate the integration of covering models into the decision making environment, the modeling systems must be made more compatible with the computing operations and technical skills of resource agency staff.
	www.biogeog.ucsb.edu /projects/ibm/report/sciconpln.html (3365 words)

	Set covering (Site not responding. Last check: 2007-10-10)
		50 of these data files are the test problem sets 4 to 6 and A to E from J.E.Beasley "An algorithm for set covering problems" European Journal of Operational Research 31 (1987) 85-93.
		Problem sets 4, 5 and 6 are originally from the Balas and Ho set covering paper.
		The files scpcyc06,..., scpcyc11 correspond to the CYC set of problems (number of edges required to hit every 4-cycle in a hypercube).
	people.brunel.ac.uk /~mastjjb/jeb/orlib/scpinfo.html (144 words)

	Set Packing and Partitioning (Site not responding. Last check: 2007-10-10)
		Other problems involving relationships between a set and some of its subsets are related to set covering.
		The set partitioning problem arises when each set element must appear in exactly one subset, and the constraints in this problem are equality constraints.
		Between FAA regulations and union contracts, determining a feasible crew schedule is a very difficult problem.
	mat.gsia.cmu.edu /orclass/integer/node9.html (383 words)

	Spherical Coverings (Site not responding. Last check: 2007-10-10)
		A library of putatively optimal coverings of the sphere with n equal caps.
		This maximum distance is called the covering radius.
		We give putatively optimal coverings for n = 4,..., 130.
	www.research.att.com /~njas/coverings (109 words)

	Brian's Digest: Set Covering Problem
		You can directly try to solve the problem with a linear optimization algorithm and hope to find an integer solution (happens frequently in small dimensions) or alternatively use branch&bound techniques (slow, since c_j takes only one value) or heuristics.
		For the solution of the problem of Patrizio you need the minimal number of workers so that for each job permissible solution of the corresponding marriage problem exists.
		What is the best available technology (I'm looking for either commercial or public domain software or references to published algoritms) for solving the set covering problem (given a cover of a finite set by sets of given weights, find the subcover of minimal weight).
	www.worms.ms.unimelb.edu.au /digest/set_covering.html (1420 words)

	[No title]
		Previous 2D covering work focuses on specialized forms of P and Q, often addresses the optimization problem of minimizing the number of covering polygons, and identifies many NP-complete Rajasekhar Inkulu covering problems.
		Unlike previous 2D covering work, our algorithm is designed to handle point-set or polygonal P and does not require the covering polygons in Q to be identical.
		In cases where the heuristics find a cover using either a linear or a star intersection graph, the algorithm explores fewer assignments with the heuristics than without the heuristics.
	www.cs.uml.edu /~kdaniels/papers/cccg01_final2.doc (1430 words)

	Set Covering (Site not responding. Last check: 2007-10-10)
		The city is made up of a number of neighborhoods, as illustrated in Figure 1.
		We are asked to find a set of such subsets j that covers the set of all neighborhoods in the sense that every neighborhood appears in the service subset associated with at least one fire station.
		This is an example of the set covering problem.
	mat.gsia.cmu.edu /orclass/integer/node8.html (283 words)

	Problem Surfaces and Instructions for Covering Paneling, Concrete, Mold and Mildew, Tile, Textured Walls, and Cracked ...
		We welcome all inquiries you may have regarding other types of problem surfaces you may have.
		The following instructions for covering problem surfaces have been made available for you to download, read, and/or print.
		All of the following documents are available only in Adobe Portable Document Format (PDF); to read these requires that you have the free Acrobat Reader installed.
	www.roosinternational.com /glass_textile_wallcovering/problem_surfaces.htm (185 words)

	SEMINAR NOTES
		"From covering problems to a conjecture of Turan," South East Regional Meeting On Numbers, Columbia, SC, slides: [ps]
		"On coverings of the integers associated with an irreducibility theorem of A. Schinzel," Millennial Conference on Number Theory, Urbana, IL, paper [pdf]
		Recent advances in covering problems, The Pacific North West Number Theory Conference 9 pdf (1.15 megabytes); see info for similar talk below
	www.math.sc.edu /~filaseta/seminars/seminars.html (915 words)

	Covering Problem Paneling - DoItYourself.com Community Forums
		Two of the walls have both brick (top) and ridged (bottom) paneling, and are covered with vinyl wallpaper over a heavy paper covering.
		Two other walls are half wallpaper/half ridged paneling (exposed), with a chair rail 3' high.
		Technical problems and issues concerning the use of the DoItYourself.com Community Forums contact the Forum Administrator.
	forum.doityourself.com /showthread.php?t=49380 (365 words)

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