Abstract
We study the NP-hard problem of approximating a Minimum Routing Cost Spanning Tree in the message passing model with limited bandwidth (CONGEST model). In this problem one tries to find a spanning tree of a graph G over n nodes that minimizes the sum of distances between all pairs of nodes. In the considered model every node can transmit a different (but short) message to each of its neighbors in each synchronous round. We provide a randomized (2 + ε)-approximation with runtime \(\mathcal{O}(D+\frac{\log n}{\varepsilon})\) for unweighted graphs. Here, D is the diameter of G. This improves over both, the (expected) approximation factor \(\mathcal{O}(\log n)\) and the runtime \(\mathcal{O}(D\log^2 n)\) stated in [13].
Due to stating our results in a very general way, we also derive an (optimal) runtime of \(\mathcal{O}(D)\) when considering \(\mathcal{O}(\log n)\)-approximations as in [13]. In addition we derive a deterministic 2-approximation.
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Hochuli, A., Holzer, S., Wattenhofer, R. (2014). Distributed Approximation of Minimum Routing Cost Trees. In: Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2014. Lecture Notes in Computer Science, vol 8576. Springer, Cham. https://doi.org/10.1007/978-3-319-09620-9_11
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DOI: https://doi.org/10.1007/978-3-319-09620-9_11
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