## Orders, Algorithms and Applications: International Workshop ORDAL '94, Lyon, France, July 4-8, 1994. ProceedingsThis volume is the proceedings of the first International Workshop on Orders, Algorithms, and Applications, held at Lyon, France in July 1994. Ordered sets and the more specifically algorithmic aspects of order theory are of increasing importance, for example in graph theory. They enjoy a recognized place in computer science as well as in mathematics, due to various new developments in the last few years. The nine technical papers accepted for this volume and the four invited papers presented offer a representative perspective on theoretical and applicational aspects of orders and related algorithms. |

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### Contents

BitVector Encoding for Partially Ordered Sets | 1 |

What Conies After Interval Orders? | 13 |

Dimension and Algorithms | 33 |

Upward Drawings to Fit Surfaces | 53 |

A Cleanup on Transitive Orientation | 59 |

A Characterization of Graphs with Vertex Cover up to Five | 86 |

Testing hereditary properties efficiently on average | 100 |

Orders ksets and Fast Halfplane Search on Paged Memory | 117 |

Triangle Graphs and Their Coloring | 128 |

Representation of an Order as Union of Interval Orders | 143 |

Minimal Representation of Semiorders with Intervals of Same Length | 162 |

The Computation of the Jump Number of Convex Graphs | 176 |

Fast Lattice Browsing on Sparse Representation | 186 |

### Common terms and phrases

adjacent admissible tuples algorithm alternating cycle free antichains arcs bipartite graphs bit-vector encoding called Clus(c cluster code(x cograph comparability graph contains cotree cycle free matching data structure decomposition defined denote dimension dimensional partial orders DM(P edges efficient elements endpoints given Golumbic graph G halfplane implication class implies independent set induced subgraph input integer intersection interval graph interval orders interval restriction interval tolerance orders isomorphic jump number Lemma linear extension loop maximal maximum clique minimal module NP-complete obstruction set optimal ordered set pairs partial lattice partition pathwidth permutation graphs polynomial poset priority queue problem Proceedings Proof Proposition representing result right border right most sequence semiorder simple trapezoid graph Spinrad suborder subset Theorem theory tolerance graph transitive closure transitive orientation transitive reduction tree treewidth triangle graphs unit interval unit interval representation upward drawing VC-k vertex cover vertices Vm(S