How to assign votes in a distributed system
Journal of the ACM (JACM)
On generating all maximal independent sets
Information Processing Letters
On the complexity of inferring functional dependencies
Discrete Applied Mathematics - Special issue on combinatorial problems in databases
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
On the frequency of the most frequently occurring variable in dual monotone DNFs
Discrete Mathematics
Data mining, hypergraph transversals, and machine learning (extended abstract)
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
New Results on Monotone Dualization and Generating Hypergraph Transversals
SIAM Journal on Computing
Monotone boolean dualization is in co-NP[log2n]
Information Processing Letters
NP-Completeness: A Retrospective
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Hypergraph Transversal Computation and Related Problems in Logic and AI
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Discovering all most specific sentences
ACM Transactions on Database Systems (TODS)
ICDM '03 Proceedings of the Third IEEE International Conference on Data Mining
Mining border descriptions of emerging patterns from dataset pairs
Knowledge and Information Systems
Parameterized enumeration, transversals, and imperfect phylogeny reconstruction
Theoretical Computer Science - Parameterized and exact computation
Fast Discovery of Interesting Collections of Web Services
WI '06 Proceedings of the 2006 IEEE/WIC/ACM International Conference on Web Intelligence
On the complexity of the multiplication method for monotone CNF/DNF dualization
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
A Worst-Case Analysis of the Sequential Method to List the Minimal Hitting Sets of a Hypergraph
SIAM Journal on Discrete Mathematics
On the complexity of monotone dualization and generating minimal hypergraph transversals
Discrete Applied Mathematics
On Berge Multiplication for Monotone Boolean Dualization
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
The hitting set attack on anonymity protocols
IH'04 Proceedings of the 6th international conference on Information Hiding
Parallel computation of the minimal elements of a poset
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Enumerating all solutions of a boolean CSP by non-decreasing weight
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
| Hi-index | 0.04 |
The computation of all minimal transversals of a given hypergraph in output-polynomial time is a long standing open question known as Transversal Hypergraph Generation. One of the first attempts at this problem-the sequential method [Claude Berge, Hypergraphs, in: North-Holland Mathematical Library, vol. 45, North-Holland, 1989]-is not output-polynomial as was shown by Takata [Ken Takata, A worst-case analysis of the sequential method to list the minimal hitting sets of a hypergraph, SIAM Journal on Discrete Mathematics 21 (4) (2007) 936-946]. Recently, three new algorithms improving the sequential method were published and experimentally shown to perform very well in practice [James Bailey, Thomas Manoukian, Kotagiri Ramamohanarao, A fast algorithm for computing hypergraph transversals and its application in mining emerging patterns, in: Proceedings of the 3rd IEEE International Conference on Data Mining, ICDM 2003, 19-22 December 2003, Melbourne, FL, USA, IEEE Computer Society, 2003, pp. 485-488; Guozhu Dong, Jinyan Li, Mining border descriptions of emerging patterns from dataset pairs, Knowledge and Information Systems 8 (2) (2005) 178-202; Dimitris J. Kavvadias, Elias C. Stavropoulos, An efficient algorithm for the transversal hypergraph generation, Journal of Graph Algorithms and Applications 9 (2) (2005) 239-264]. Nevertheless, a theoretical worst-case analysis has been pending. We close this gap by proving lower bounds for all three algorithms. Thereby, we show that none of them are output-polynomial.