## Abstract

The edge intersection graphs of paths on a grid (or EPG graphs) are graphs whose vertices can be represented as simple paths on a rectangular grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. We consider the case of single-bend paths, namely, the class known as B_{1}-EPG graphs. The motivation for studying these graphs comes from the context of circuit layout problems. It is known that recognizing B_{1}-EPG graphs is NP-complete, nevertheless, optimization problems when given a set of paths in the grid are of considerable practical interest. In this paper, we show that the coloring problem and the maximum independent set problem are both NP-complete for B_{1}-EPG graphs, even when the EPG representation is given. We then provide efficient 4-approximation algorithms for both of these problems, assuming the EPG representation is given. We conclude by noting that the maximum clique problem can be optimally solved in polynomial time for B_{1}-EPG graphs, even when the EPG representation is not given.

Original language | English |
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Title of host publication | Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings |

Pages | 328-340 |

Number of pages | 13 |

DOIs | |

State | Published - 2013 |

Event | 13th International Symposium on Algorithms and Data Structures, WADS 2013 - London, ON, Canada Duration: 12 Aug 2013 → 14 Aug 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8037 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 13th International Symposium on Algorithms and Data Structures, WADS 2013 |
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Country/Territory | Canada |

City | London, ON |

Period | 12/08/13 → 14/08/13 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science

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