Succinct representations of graphs
Information and Control
A note on succinct representations of graphs
Information and Control
Minimal representation of directed hypergraphs
SIAM Journal on Computing
Principles of artificial intelligence
Principles of artificial intelligence
Hyperpaths and shortest hyperpaths
COMO '86 Lectures given at the third session of the Centro Internazionale Matematico Estivo (C.I.M.E.) on Combinatorial optimization
Directed hypergraphs and applications
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
An incremental algorithm for a generalization of the shortest-path problem
Journal of Algorithms
On-line algorithms for satisfiability problems with uncertainty
Selected papers from the international workshop on Uncertainty in databases and deductive systems
Graph Algorithms for Functional Dependency Manipulation
Journal of the ACM (JACM)
Principles of Database Systems
Principles of Database Systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Hypergraph Traversal Revisited: Cost Measures and Dynamic Algorithms
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Directed Hypergraphs: Problems, Algorithmic Results, and a Novel Decremental Approach
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
Linear Time Algorithms for Liveness and Boundedness in Conflict-free Petri Nets
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Directed Hypergraphs as a Modelling Paradigm
Directed Hypergraphs as a Modelling Paradigm
Graphs and Hypergraphs
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We introduce a notion of linear hyperconnection (formally denoted L-hyperpath) between nodes in a directed hypergraph and relate this notion to existing notions of hyperpaths in directed hypergraphs. We observe that many interesting questions in problem domains such as secret transfer protocols, routing in packet filtered networks, and propositional satisfiability are basically questions about existence of L-hyperpaths or about cyclomatic number of directed hypergraphs w.r.t. L-hypercycles (the minimum number of hyperedges that need to be deleted to make a directed hypergraph free of L-hypercycles). We prove that the L-hyperpath existence problem, the cyclomatic number problem, the minimum cyclomatic set problem, and the minimal cyclomatic set problem are each complete for a different level (respectively, NP, ${\it \Sigma}^{p}_{2}$, ${\it \Pi}^{p}_{2}$, and DP) of the polynomial hierarchy.