Abstract
We give a polynomial-time \( O\left( {\tfrac{{\log n}} {{\log OPT}}} \right) \)-approximation algorithm for minimum-time broadcast and minimum-time multicast in n-node networks under the single-port vertex-disjoint paths mode. This improves a previous approximation algorithm by Kortsarz and Peleg. In contrast, we give an Ω(log n) lower bound for the approximation ratio of the minimum-time multicast problem in directed networks. This lower bound holds unless NP ⊂ Dtime(n log log n). An important consequence of this latter result is that the Steiner version of the Minimum Degree Spanning Tree (MDST) problem in digraphs cannot be approximated within a constant ratio, as opposed to the undirected version. Finally, we give a polynomial-time O(1)-approximation algorithm for minimum-time gossip (i.e., all-to-all broadcast).
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Fraigniaud, P. (2001). Approximation Algorithms for Minimum-Time Broadcast under the Vertex-Disjoint Paths Mode. In: auf der Heide, F.M. (eds) Algorithms — ESA 2001. ESA 2001. Lecture Notes in Computer Science, vol 2161. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44676-1_37
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