Abstract
In an undirected graph G = (V,E) with a weight function \(w: E \times V \rightarrow \mathbb Q_+\), the weighted degree d w (v;E) of a vertex v is defined as ∑ {w(e,v) |e ∈ E incident with v}. In this paper, we consider a network design problem which has upper-bounds on weighted degrees of vertices as its constraints while the objective is to compute a minimum cost graph with a prescribed connectivity. We propose bi-criteria approximation algorithms based on the iterative rounding, which has been successfully applied to the degree-bounded network design problem. A problem minimizing the maximum weighted degree of vertices is also discussed.
This work was partially supported by Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
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Fukunaga, T., Nagamochi, H. (2009). Network Design with Weighted Degree Constraints. In: Das, S., Uehara, R. (eds) WALCOM: Algorithms and Computation. WALCOM 2009. Lecture Notes in Computer Science, vol 5431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00202-1_19
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