## From Algorithms to Working Programs On the Use of Program Checking in LEDA (1998)

Venue: | IN PROC. INT. CONF. ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS 98 |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Mehlhorn98fromalgorithms,

author = {Kurt Mehlhorn and Stefan Näher},

title = {From Algorithms to Working Programs On the Use of Program Checking in LEDA},

booktitle = {IN PROC. INT. CONF. ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS 98},

year = {1998},

pages = {84--93},

publisher = {}

}

### OpenURL

### Abstract

We report on the use of program checking in the LEDA library of efficient data types and algorithms.

### Citations

637 | LEDA: A platform for combinatorial and geometric computing
- Mehlhorn, Naher
- 1995
(Show Context)
Citation Context ... design goal. The actual running time of algorithms with the same asymptotic behavior may differ widely. In this paper we concentrate on the first item. For the other two items we refer the reader to =-=[MN98]-=- and the references therein. 2 Program Checking We start with an example and then generalize. 2.1 Planarity Testing A graph is planar if it can be drawn in the plane without edge crossings. A planarit... |

468 | Testing for the consecutive ones property, interval graphs, and graph planarity using pq-tree algorithms - Booth, Lueker - 1976 |

345 | Self-testing/correcting with applications to numerical problems - Blum, Luby, et al. - 1993 |

305 | Designing Programs that Check Their Work - Blum, Kannan - 1995 |

301 | Maximum matching and a polyhedron with 0, 1-vertices - Edmonds - 1965 |

226 | Tarjan, Efficient planarity testing - Hopcroft, E - 1974 |

112 | A linear algorithm for embedding planar graphs using PQ-trees - Chiba, Nishizeki, et al. - 1985 |

104 | Cederbaum I. An algorithm for planarity testing of graphs - Lempel, Even - 1967 |

101 | Software reliability via run-time result-checking - Wasserman, Blum - 1997 |

76 | Planar Graphs: Theory and Algorithms - Nishizeki, Chiba - 1988 |

70 | An efficient implementation of edmonds’ algorithm for maximum matching on graphs - Gabow - 1976 |

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

34 | On the embedding phase of the Hopcroft and Tarjan planarity testing algorithm. Algorithmica - Mehlhorn, Mutzel - 1996 |

32 | Depth-first search and Kuratowski subgraphs - Williamson - 1984 |

27 | Checking linked data structures - Amato, Loui - 1994 |

25 | Using certification trails to achieve software fault tolerance - Sullivan, Masson - 1990 |

22 | Checking the convexity of polytopes and the planarity of subdivisions - Devillers, Liotta, et al. - 1998 |

21 | Certification trails for data structures - Sullivan, Masson - 1991 |

20 | Reflections on the Pentium division bug - Blum, Wasserman - 1996 |

18 | Certification of computational results - Sullivan, Wilson, et al. - 1995 |

17 | Checking mergeable priority queues - Bright, Sullivan - 1994 |

9 | Checking the integrity of trees - Bright, Sullivan, et al. - 1995 |

8 | On-line error monitoring for several data structures - Bright, Sullivan - 1995 |

5 | A formally verified sorting certifier
- Bright, Sullivan, et al.
- 1997
(Show Context)
Citation Context ...eckers allow to develop trust in an implementation with only minimal intellectual investment. It is even conceivable that checkers can be formally verified by means of automatic program verification. =-=[BSM97]-=- is a first example. Program Libraries: Program libraries contain implemented algorithms. The implementor of a library may want to hide his code (after all, the source code of the programs constitutes... |

2 | Ns A Simple Linear Time Algorithm for Identi~Ting Kuratowski Subgraphs of Non-Planar Graphs - Hundack, Mehlhorn, et al. - 1996 |

1 | Classification and detetection of obstructions to planarity - Karabeg - 1990 |

1 |
Sur le probl`eme the courbes guaches en topologie
- Kuratwoski
- 1930
(Show Context)
Citation Context ...than a page long and the underlying mathematics is simple compared to the mathematics underlying the planarity test. Observe that one only needs to understand that maps of genus zero are 2 Kuratowski =-=[Kur30]-=- has shown that every non-planar graph contains a subdivision of either K5 , the complete graph on five nodes, or K3;3 , the complete bipartite graph with three nodes on either side. 3 A map is an und... |