@article{05a080b4fb34411f9b6fb5442fd75d97,

title = "An oblivious spanning tree for single-sink buy-at-bulk in low doubling-dimension graphs",

abstract = "We consider the problem of constructing a single spanning tree for the single-sink buy-at-bulk network design problem for doubling-dimension graphs. We compute a spanning tree to route a set of demands along a graph G to or from a designated sink node. The demands could be aggregated at (or symmetrically distributed to) intermediate edges where the fusion cost is specified by a nonnegative concave function f. We describe a novel approach for developing an oblivious spanning tree in the sense that it is independent of the number and location of data sources (or demands) and cost function at the edges. We present a deterministic, polynomial-time algorithm for constructing a spanning tree in low doubling-dimension graphs that guarantees a log 3 D-approximation over the optimal cost, where D is the diameter of the graph G. With a constant fusion-cost function, our spanning tree gives an O(log 3 D)-approximation for every Steiner tree that includes the sink. We also provide a Ω (log n) lower bound for any oblivious tree in low doubling-dimension graphs. To our knowledge, this is the first paper to propose a single spanning tree solution to the single-sink buy-at-bulk network design problem (as opposed to multiple overlay trees).",

keywords = "Spanning tree, approximation algorithm, buy-at-bulk, data fusion, data structure, doubling-dimension graph, network design",

author = "Srivathsan Srinivasagopalan and Costas Busch and Iyengar, {S. S.}",

note = "Funding Information: Supported by US National Science Foundation (NSF) grants 0963793 and 0846081. An earlier version of our work with preliminary results in the context of data aggregation in graphs of low doubling dimension appeared as a brief announcement in [1]. Funding Information: Costas Busch received the BSc degree in 1992 and the MSc degree in 1995 in computer science from the University of Crete, Greece. He received the PhD degree in computer science from Brown University in 2000. He is currently an assistant professor in the Computer Science Department at LSU. His research interests are in the following areas: theory of distributed computing, distributed algorithms and data structures, design and analysis of communication protocols for wireless, sensor, and optical networks, data directories for wireless sensor networks, data streaming algorithms, and algorithmic game theory. He has several publications in theoretical computer science conferences and journals including Symposium on Theory of Computing (STOC), Journal of the ACM, and SIAM journal on Computing. He has also served in the program committees of MOBIHOC, IPDPS, ICDCS, and DCOSS. His research is funded by the US National Science Foundation (NSF). Funding Information: S.S. Iyengar is currently a professor and the chair of the Computer Science Department at Louisiana State University. His publications include six textbooks, five edited books, and more than 400 research papers. His research interests include high-performance algorithms, data structures, data fusion, intelligent systems, and distributed sensor networks. He is serving as an editor of several IEEE Journals and is the founding editor-in-chief of the International Journal of Distributed Sensor Networks. His research has been funded by the US National Science Foundation (NSF), US Defense Advanced Research Projects Agency (DARPA), US Department of Energy (DoE), NASA, ONR, and other agencies. He is a fellow of the ACM, a fellow of the IEEE, a fellow of the AAAS, and a fellow of the SDPS.",

year = "2012",

doi = "10.1109/TC.2011.64",

language = "English (US)",

volume = "61",

pages = "700--712",

journal = "IEEE Transactions on Computers",

issn = "0018-9340",

publisher = "IEEE Computer Society",

number = "5",

}