A New Algorithm for the Hypergraph Transversal Problem

2005 ◽  
pp. 767-776 ◽  
Author(s):  
Leonid Khachiyan ◽  
Endre Boros ◽  
Khaled Elbassioni ◽  
Vladimir Gurvich
Keyword(s):  
Hypergraph Transversal

scholarly journals Incremental Complexity of a Bi-objective Hypergraph Transversal Problem

2015 ◽  
pp. 202-213
Author(s):  
Ricardo Andrade ◽  
Etienne Birmelé ◽  
Arnaud Mary ◽  
Thomas Picchetti ◽  
Marie-France Sagot
Keyword(s):  
Hypergraph Transversal

A global parallel algorithm for the hypergraph transversal problem

2007 ◽  
Vol 101 (4) ◽  
pp. 148-155 ◽  
Author(s):  
Leonid Khachiyan ◽  
Endre Boros ◽  
Khaled Elbassioni ◽  
Vladimir Gurvich
Keyword(s):  
Parallel Algorithm ◽  
Hypergraph Transversal

scholarly journals Translating between Horn Representations and their Characteristic Models

1995 ◽  
Vol 3 ◽  
pp. 349-372 ◽  
Author(s):  
R. Khardon
Keyword(s):  
Alternative Model ◽  
Decision Problem ◽  
Relational Databases ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
The Other ◽  
Database Theory ◽  
Hypergraph Transversal ◽  
The Cost ◽  
Special Case

Characteristic models are an alternative, model based, representation for Horn expressions. It has been shown that these two representations are incomparable and each has its advantages over the other. It is therefore natural to ask what is the cost of translating, back and forth, between these representations. Interestingly, the same translation questions arise in database theory, where it has applications to the design of relational databases. This paper studies the computational complexity of these problems. Our main result is that the two translation problems are equivalent under polynomial reductions, and that they are equivalent to the corresponding decision problem. Namely, translating is equivalent to deciding whether a given set of models is the set of characteristic models for a given Horn expression. We also relate these problems to the hypergraph transversal problem, a well known problem which is related to other applications in AI and for which no polynomial time algorithm is known. It is shown that in general our translation problems are at least as hard as the hypergraph transversal problem, and in a special case they are equivalent to it.

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