## An Efficient Algorithm for Weakly Normal Dominance Constraints (2004)

Venue: | In ACM-SIAM Symposium on Discrete Algorithms |

Citations: | 12 - 1 self |

### BibTeX

@INPROCEEDINGS{Bodirsky04anefficient,

author = {Manuel Bodirsky and Denys Duchier and Joachim Niehren and Sebastian Miele},

title = {An Efficient Algorithm for Weakly Normal Dominance Constraints},

booktitle = {In ACM-SIAM Symposium on Discrete Algorithms},

year = {2004},

publisher = {The ACM Press}

}

### OpenURL

### Abstract

Dominance constraints are logical descriptions of trees. E- cient algorithms for the subclass of normal dominance constraints were proposed recently. We present a new and simpler graph algorithm which solves more expressive weakly normal dominance constraints. We thereby improve on the best previously known algorithm for normal dominance constraints in eciency, coverage, and applicability.

### Citations

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Minimal recursion semantics: an introduction
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(Show Context)
Citation Context ...nance constraints. Weakening normality improves the applicability of dominance constraints: it is convenient for modeling natural language 2 semantics with so called minimal recursion semantics (MRS) =-=[5]-=- which is used in head driven phrase structure grammar (HPSG), one of the mainstream grammar formalisms in computational linguistics (Fig. 5). We propose a novel graph algorithm relying on graph conne... |

137 | Predicate logic unplugged - Bos - 1996 |

122 | Poly-logarithmic deterministic fully-dynamic graph algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity
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Citation Context ...viously known algorithms in eciency (practically and theoretically), coverage, and applicability. It should be possible to further improve the running time using decremental biconnectivity algorithms =-=[8]-=-. 12 constraint graph Mehlhorn time/N Thiel time/N new time/N edges n nodes m solved forms N Chain 2 0.043 0.021 0.021 8 8 2 Chain 3 0.065 0.027 0.020 12 13 5 Chain 4 0.084 0.032 0.019 16 18 14 Chain ... |

104 |
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Citation Context ...thereby improve on the best previously known algorithm for normal dominance constraints in eciency, coverage, and applicability. 1 Introduction Dominance constraints are logical descriptions of trees =-=[2, 10-=-] that can talk about the mother and ancestor relations between the nodes of a tree. They have numerous applications, most of which belong to the area of computational linguistics, e.g. in underspecie... |

80 | The Constraint Language for Lambda Structures HÃ¶che
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Citation Context ...ints We start with an informal exposition of dominance constraints [2,10], then dene normality [1] and relax this notion to weak normality. A formal denition of dominance constraint is available in [6=-=]-=-. f g a a Fig. 1. f(g(a; a)) Let f; g range over the elements of some signature of function symbols withsxed arities and a; b over constants, i.e., function symbols of arity 0. A constructor tree over... |

55 | A platform for combinatorial and geometric computing - LEDA - 1999 |

49 | Obtaining trees from their descriptions: An application to tree-adjoining grammars
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Citation Context ... have numerous applications, most of which belong to the area of computational linguistics, e.g. in underspecied semantics [4-6], underspeci ed discourse [7], and parsing with tree adjoining grammar [=-=1-=-1]. Two problems for dominance constraints are considered in the literature: satisability (i.e., is a given constraint satised by some tree) and enumeration of all solved forms (i.e. of all trees sati... |

37 | An efficient graph algorithm for dominance constraints
- Althaus, Duchier, et al.
(Show Context)
Citation Context ...ting solved forms. Satisability of dominance constraints was proved NP-complete in [9]. This shed doubts on the feasibility of dominance based applications. The doubts were removed by Mehlhorn et al [=-=-=-1], who distinguished the language of normal dominance constraints which suces for many applications and has a polynomial time satisability problem. Subsequently, Thiel [12] showed that satisability o... |

37 | Describing discourse semantics
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Citation Context ...r relations between the nodes of a tree. They have numerous applications, most of which belong to the area of computational linguistics, e.g. in underspecied semantics [4-6], underspeci ed discourse [=-=-=-7], and parsing with tree adjoining grammar [11]. Two problems for dominance constraints are considered in the literature: satisability (i.e., is a given constraint satised by some tree) and enumerati... |

37 | Dominance constraints: Algorithms and complexity
- Koller, Niehren, et al.
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(Show Context)
Citation Context ...constraint). Satisability alone is not needed in the applications; it is subsumed however by the problem of enumerating solved forms. Satisability of dominance constraints was proved NP-complete in [9=-=]-=-. This shed doubts on the feasibility of dominance based applications. The doubts were removed by Mehlhorn et al [1], who distinguished the language of normal dominance constraints which suces for man... |

19 | A polynomial-time fragment of dominance constraints - Koller, Mehlhorn, et al. - 2000 |

11 | Pure dominance constraints - Bodirsky, Kutz - 2002 |

9 |
A axiomatization of the theory of trees
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(Show Context)
Citation Context ... wcc's and the immediate dominance edges X Y j . Using (F1), (F2) and (F3) and the denition of wnd-graphs we verify that (0) the resulting graph G 0 is a wnd-graph, (1) the digraph of G 0 is a tree, (2) contains all disjointness and immediate dominance edges, (3) / RG 0 . Thus G 0 is a solved form that is more specic than G. (3 ) 1) Clearly, if sat(G) fails for all nondeterministic choices then... |

7 |
Pure dominance constraints
- Bodirsky, Kutz
- 2002
(Show Context)
Citation Context ...ational linguistics (Fig. 5). We propose a novel graph algorithm relying on graph connectivity that can enumerate all solved forms of a weakly normal dominance constraint, inspired by an algorithm in =-=[3]-=-. Our algorithm has a simpler correctness proof than the approach in [1]. It uses quadratic time per solved form, thereby improving on the best previously known algorithm for normal dominance constrai... |

1 |
A linear time algorithm for the con problem of dominance graphs
- Thiel
- 2002
(Show Context)
Citation Context ...re removed by Mehlhorn et al [1], who distinguished the language of normal dominance constraints which suces for many applications and has a polynomial time satisability problem. Subsequently, Thiel [=-=12-=-] showed that satisability of normal dominance constraints can be decided in linear time, and thus that the solved forms of a normal dominance constraint can be enumerated in cubic time per solved for... |