## Abstract

Let G=(V,E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function E → ℕ. In addition, each label l ε ℕ a non-negative cost c(l). The minimum label spanning tree problem (MinLST) asks to find a spanning tree in G that minimizes the overall cost of the labels used by its edges. Equivalently, we aim at finding a minimum cost subset of labels I ⊆ ℕ such that the edge set {e ∈ E: L (e) ∈ I} forms a connected subgraph spanning all vertices. Similarly, in the minimum label s - t path problem (MinLP) the goal is to identify an s-t path minimizing the combined cost of its labels. The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP.

Original language | English |
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Pages (from-to) | 437-453 |

Number of pages | 17 |

Journal | Journal of Combinatorial Optimization |

Volume | 14 |

Issue number | 4 |

DOIs | |

State | Published - Nov 2007 |

Externally published | Yes |

## Keywords

- Approximation algorithms
- Hardness of approximation
- Labeled connectivity

## ASJC Scopus subject areas

- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics