The Transitive Reduction of a Directed Graph

Aho, Alfred V.; Garey, M. R.; Ullman, Jeffrey D.

doi:10.1137/0201008

Cited by 562 publications

(498 citation statements)

References 6 publications

(1 reference statement)

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“…If we add thermodynamic constraints, reaction (3) becomes fully coupled to (1) and thus, we get a stronger result than without these constraints.…”

Section: Introductionmentioning

confidence: 95%

“…In practice, this can lead to a quadratic blow-up of redundant couplings and hence the number of coupled pairs does not really reflect the gained information. In order to get a more adequate description, we computed a minimum set of couplings from which all other couplings can be deduced (also called a transitive reduction [1]). are not only necessary for biomass production (as computed by standard FCA) but cannot work without this function.…”

Section: Practical Comparisonmentioning

confidence: 99%

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Generic flux coupling analysis

Reimers

Goldstein

Bockmayr

2015

Mathematical Biosciences

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a b s t r a c tFlux coupling analysis (FCA) has become a useful tool for aiding metabolic reconstructions and guiding genetic manipulations. Originally, it was introduced for constraint-based models of metabolic networks that are based on the steady-state assumption. Recently, we have shown that the steady-state assumption can be replaced by a weaker lattice-theoretic property related to the supports of metabolic fluxes. In this paper, we further extend our approach and develop an efficient algorithm for generic flux coupling analysis that works with any kind of qualitative pathway model. We illustrate our method by thermodynamic flux coupling analysis (tFCA), which allows studying steady-state metabolic models with loop-law thermodynamic constraints. These models do not satisfy the lattice-theoretic properties required in our previous work. For a selection of genome-scale metabolic network reconstructions, we discuss both theoretically and practically, how thermodynamic constraints strengthen the coupling results that can be obtained with classical FCA.A prototype implementation of tFCA is available at http://hoverboard.io/L4FC.

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“…If we add thermodynamic constraints, reaction (3) becomes fully coupled to (1) and thus, we get a stronger result than without these constraints.…”

Section: Introductionmentioning

confidence: 95%

Section: Practical Comparisonmentioning

confidence: 99%

Generic flux coupling analysis

Reimers

Goldstein

Bockmayr

2015

Mathematical Biosciences

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“…Transitive Reduction (TRD) A directed acyclic graph G ′ is a transitive reduction [6] of the directed graph G provided that (i) G ′ has a directed path from node u to node v if and only if G has a directed path from node u to node v, and (ii) there is no graph with fewer edges than G ′ satisfying the condition (i). For a CNF formula F , a binary clause…”

Section: Equivalent Literal Substitution (Els)mentioning

confidence: 99%

“…TRD is confluent for the class of CNF formulas F for which BIG(F ) is acyclic. This is due to the fact that the transitive reduction of any directed acyclic graph is unique [6]. For directed graphs with cycles, TRD is unique modulo node (literal) equivalence classes.…”

Section: Equivalent Literal Substitution (Els)mentioning

confidence: 99%

Revisiting Hyper Binary Resolution

Heule

Järvisalo

Biere

2013

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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Abstract. This paper focuses on developing efficient inference techniques for improving conjunctive normal form (CNF) Boolean satisfiability (SAT) solvers. We analyze a variant of hyper binary resolution from various perspectives: We show that it can simulate the circuit-level technique of structural hashing and how it can be realized efficiently using so called tree-based lookahead. Experiments show that our implementation improves the performance of state-of-the-art CNFlevel SAT techniques on combinational equivalent checking instances.

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“…which has length at most the diameter of the graph G (1) obtained by solving the 1-dimensional problem on V (1) .…”

Section: Reducing the Diameter In The Shortcutting And Point-insertinmentioning

confidence: 99%

Efficient Provably-Secure Hierarchical Key Assignment Schemes

Santis

Ferrara

Masucci

2007

Mathematical Foundations of Computer Science 2007

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A hierarchical key assignment scheme is a method to assign some private information and encryption keys to a set of classes in a partially ordered hierarchy, in such a way that the private information of a higher class can be used to derive the keys of all classes lower down in the hierarchy.In this paper we design and analyze hierarchical key assignment schemes which are provablysecure and support dynamic updates to the hierarchy with local changes to the public information and without requiring any private information to be re-distributed.• We first consider the problem of constructing a hierarchical key assignment scheme by using as a building block a symmetric encryption scheme. We propose a new construction which is provably secure with respect to key indistinguishability, requires a single computational assumption, and improves on previous proposals.• Then, we show how to reduce key derivation time at the expense of an increment of the amount of public information, by improving a previous result.• Finally, we show how to construct a hierarchical key assignment scheme by using as a building block a public-key broadcast encryption scheme. In particular, one of our constructions provides constant private information and public information linear in the number of classes in the hierarchy.

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The Transitive Reduction of a Directed Graph

Cited by 562 publications

References 6 publications

Generic flux coupling analysis

Generic flux coupling analysis

Revisiting Hyper Binary Resolution

Efficient Provably-Secure Hierarchical Key Assignment Schemes

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