## Abstract

While much of network design focuses mostly on cost (number or weight of edges), node degrees have also played an important role. They have traditionally either appeared as an objective, to minimize the maximum degree (e.g., the Minimum Degree Spanning Tree problem), or as constraints that might be violated to give bicriteria approximations (e.g., the Minimum Cost Degree Bounded Spanning Tree problem). We extend the study of degrees in network design in two ways. First, we introduce and study a new variant of the Survivable Network Design Problem where in addition to the traditional objective of minimizing the cost of the chosen edges, we add a constraint that the ℓp-norm of the node degree vector is bounded by an input parameter. This interpolates between the classical settings of maximum degree (the ℓ∞-norm) and the number of edges (the ℓ1-degree), and has natural applications in distributed systems and VLSI design. We give a constant bicriteria approximation in both measures using convex programming. Second, we provide a polylogarithmic bicriteria approximation for the Degree Bounded Group Steiner problem on bounded treewidth graphs, solving an open problem from [17] and [12].

Original language | English |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2024 |

Editors | Amit Kumar, Noga Ron-Zewi |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959773485 |

DOIs | |

State | Published - Sep 2024 |

Externally published | Yes |

Event | 27th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2024 and the 28th International Conference on Randomization and Computation, RANDOM 2024 - London, United Kingdom Duration: 28 Aug 2024 → 30 Aug 2024 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 317 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 27th International Conference on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2024 and the 28th International Conference on Randomization and Computation, RANDOM 2024 |
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Country/Territory | United Kingdom |

City | London |

Period | 28/08/24 → 30/08/24 |

### Bibliographical note

Publisher Copyright:© Michael Dinitz, Guy Kortsarz, and Shi Li.

## Keywords

- Degrees
- Network Design