## Abstract

Routing is a widespread approach to transfer information from a source node to a destination node in many deployed wireless ad-hoc networks. Today's implemented routing algorithms seek to efficiently find the path/route with the largest Full-Duplex (FD) capacity, which is given by the minimum among the point-To-point link capacities in the path. Such an approach may be suboptimal if then the nodes in the selected path are operated in Half-Duplex (HD) mode. Recently, the capacity (up to a constant gap that only depends on the number of nodes in the path) of an HD line network (i.e., a path) has been shown to be equal to half of the minimum of the harmonic means of the capacities of two consecutive links in the path. This paper asks the question of whether it is possible to design a polynomial-Time algorithm that efficiently finds the path with the largest HD capacity in a relay network. The problem of finding such a path is shown to be NP-hard in general. However, if the number of cycles in the network is polynomial in the number of nodes, then a polynomial-Time algorithm can indeed be designed.

Original language | English (US) |
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Title of host publication | 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 89-96 |

Number of pages | 8 |

ISBN (Electronic) | 9781538632666 |

DOIs | |

State | Published - Jul 1 2017 |

Externally published | Yes |

Event | 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 - Monticello, United States Duration: Oct 3 2017 → Oct 6 2017 |

### Publication series

Name | 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 |
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Volume | 2018-January |

### Other

Other | 55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017 |
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Country | United States |

City | Monticello |

Period | 10/3/17 → 10/6/17 |

### Bibliographical note

Funding Information:The work of Y. H. Ezzeldin, M. Cardone and C. Fragouli was supported in part by NSF under Awards 1514531 and 1314937. The work of D. Tuninetti was supported by NSF under Award 1527059.