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COMBINATORIAL COMPLEXITY
"... BioNetGen: software for rulebased modeling of signal transduction based on the interactions of molecular domains ..."
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BioNetGen: software for rulebased modeling of signal transduction based on the interactions of molecular domains
Conundrum of combinatorial complexity
 IEEE Trans. Pattern Anal. Mach. Intell
, 1998
"... Abstract—This paper examines fundamental problems underlying difficulties encountered by pattern recognition algorithms, neural networks, and rule systems. These problems are manifested as combinatorial complexity of algorithms, of their computational or training requirements. The paper relates part ..."
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Cited by 41 (12 self)
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Abstract—This paper examines fundamental problems underlying difficulties encountered by pattern recognition algorithms, neural networks, and rule systems. These problems are manifested as combinatorial complexity of algorithms, of their computational or training requirements. The paper relates
Combinatorial Complexity of Signed Discs
"... Let C + and C \Gamma be two collections of topological discs of arbitrary radii. The collection of discs is `topological' in the sense that their boundaries are Jordan curves and each pair of Jordan curves intersect at most twice. We prove that the region [C + \Gamma [C \Gamma has combi ..."
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combinatorial complexity at most 10n \Gamma 30 where p = jC + j, q = jC \Gamma j and n = p+q 5. Moreover, this bound is achievable. We also show less precise bounds that are stated as functions of p and q. 1 CKY is supportedby NSF grants #DCR8401898 and #CCR8703458; DLS is supported by NSF grants #CCR
The Combinatorial Complexity of Masterkeying
 Mathematical Methods of Operations Research
, 2001
"... We consider the combinatorial complexity of the algorithmic design of mechanical master key locking systems. Such locking systems use pin tumblers and prole elements (wards) to realize the functional dependencies given by a key/cylinder matrix. We prove that even very restricted versions of the m ..."
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Cited by 2 (0 self)
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We consider the combinatorial complexity of the algorithmic design of mechanical master key locking systems. Such locking systems use pin tumblers and prole elements (wards) to realize the functional dependencies given by a key/cylinder matrix. We prove that even very restricted versions
Combinatorial Complexity: Are We on the Right Way?
"... Abstract: We present a hypothetical approach to support existing methods in dealing with combinatorial complexity and describe the application of said approach to some typical combinatorial problems and techniques. ..."
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Abstract: We present a hypothetical approach to support existing methods in dealing with combinatorial complexity and describe the application of said approach to some typical combinatorial problems and techniques.
THE COMBINATORIAL COMPLEXITY OF POLYGON OVERLAY
"... The number of elementary connected regions arising from polygon overlay of two or more map layers is an important value to have in planning for data stoiage and in making processing time estimates for overlay applications. That number may be computed di rectly from the line graphs of the two (or mor ..."
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more) layers and from the intersection graph(s) of those line graphs. A formula for that computation is derived using tools of algebraic and combinatorial topology which relate the connectivity of a union of sets to the con nectivity of the sets themselves and their intersection. The result
GENERATING COMBINATORIAL COMPLEXES OF POLYHEDRAL TYPE
"... ABSTRACT. The paper describes a method for generating combinatorial complexes of polyhedral type. Building blocks B are implanted into the maximal simplices of a simplicial complex C, on which a group operates as a combinatorial reflection group. Of particular interest is the case where B is a polyh ..."
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ABSTRACT. The paper describes a method for generating combinatorial complexes of polyhedral type. Building blocks B are implanted into the maximal simplices of a simplicial complex C, on which a group operates as a combinatorial reflection group. Of particular interest is the case where B is a
Combinatorial complexity of pathway analysis in metabolic networks
 Mol. Biol. Rep
, 2002
"... Key words: combinatorial complexity in metabolic networks, elementary flux modes, metabolic pathway analysis, structural network analysis Summary Elementary flux mode analysis is a promising approach for a pathwayoriented perspective of metabolic networks. However, in larger networks it is hampered ..."
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Cited by 70 (5 self)
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Key words: combinatorial complexity in metabolic networks, elementary flux modes, metabolic pathway analysis, structural network analysis Summary Elementary flux mode analysis is a promising approach for a pathwayoriented perspective of metabolic networks. However, in larger networks
Optimizing the Topological and Combinatorial Complexity of Isosurfaces
 In ComputerAided Design
, 2005
"... Since the publication of the original Marching Cubes algorithm, numerous variations have been proposed for guaranteeing watertight constructions of triangulated approximations of isosurfaces. Most approaches divide the 3D space into cubes that each occupy the space between eight neighboring samples ..."
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Cited by 5 (0 self)
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of one or more connected components, which we call sheets. The topology and combinatorial complexity of the isosurface is influenced by three types of decisions made during its construction: (1) how to connect the four intersection points on each ambiguous face, (2) how to form interpolating sheets
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 01 integer programs, the maximum clique
Results 1  10
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