Abstract
We consider the aggregation problem in radio networks: find a spanning tree in a given graph and a conflict-free schedule of the edges so as to minimize the latency of the computation. While a large body of literature exists on this and related problems, we give the first approximation results in graphs that are not induced by unit ranges in the plane. We give a polynomial-time \(\tilde{\mathrm {O}}(\sqrt{\overline{d}n})\)-approximation algorithm, where \(\overline{d}\) is the average degree and n the number of vertices in the graph, and show that the problem is \(\varOmega (n^{1-\epsilon })\)-hard (and \(\varOmega ((\overline{d}n)^{1/2-\epsilon })\)-hard) to approximate even on bipartite graphs, for any \(\epsilon > 0\), rendering our algorithm essentially optimal. We target geometrically defined graph classes, and in particular obtain a \(O(\log n)\)-approximation in interval graphs.
Gandhi and Oh are partly supported by NSF grants CCF 1218620 and CCF 1433220. Halldórsson and Konrad are supported by Icelandic Research Fund grant-of-excellence no. 120032011. Kortsarz is partly supported by NSF grant CCF 1218620.
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- 1.
In [15], unit interval graphs as well as grids and tori are considered, which are all subclasses of unit disc graphs.
- 2.
We use the notation \(\tilde{\mathrm {O}}(.)\), which equals the usual \(\mathrm {O}(.)\) notation where all poly-logarithmic factors are ignored.
- 3.
While the result is surely well known, we were not aware of a reference for this particular version, and thus include the algorithm and a proof in the full version of this paper for completeness.
- 4.
A graph is \(4-\)claw-free, if it doesn’t contain the complete bipartite graph \(K_{1,4}\) as an induced subgraph.
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Gandhi, R., Halldórsson, M.M., Konrad, C., Kortsarz, G., Oh, H. (2015). Radio Aggregation Scheduling. In: Bose, P., Gąsieniec, L., Römer, K., Wattenhofer, R. (eds) Algorithms for Sensor Systems. ALGOSENSORS 2015. Lecture Notes in Computer Science(), vol 9536. Springer, Cham. https://doi.org/10.1007/978-3-319-28472-9_13
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