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  • Topic: Minimum spanning tree, Graph theory, Spanning tree
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Multi-Channel Scheduling and Spanning Trees: Throughput-Delay Trade-off for Fast Data Collection in Sensor Networks ¨ Amitabha Ghosh, Ozlem Durmaz Incel, V. S. Anil Kumar, and Bhaskar Krishnamachari

Two primary factors that affect the data collection rate (throughput) and timeliness (delay) are: (i) efficiency of the link scheduling protocol, and (ii) structure of the routing tree in terms of its node degrees and radius. In this paper, we utilize multiple frequency channels and design an efficient link scheduling protocol that gives a constant factor approximation on the optimal throughput in delivering aggregated data from all the nodes to the sink. To minimize the maximum delay subject to a given throughput bound, we also design an (α, β)bicriteria approximation algorithm to construct a BoundedDegree Minimum-Radius Spanning Tree, with the radius of the tree at most β times the minimum possible radius for a given degree bound ∆∗ , and the degree of any node at most ∆∗ + α, where α and β are positive constants. Lastly, we evaluate the efficiency of our algorithms on different types of spanning trees, and show that multi-channel scheduling, combined with optimal routing topologies, can achieve the best of both worlds in terms of maximizing the aggregated data collection rate and minimizing the maximum packet delay. Index Terms—Convergecast, TDMA scheduling, multiple channels, routing trees, approximation algorithms.

I. I NTRODUCTION ONVERGECAST, namely the many-to-one flow of data from a set of sources to a common sink over a tree-based routing topology, is a fundamental communication primitive in sensor networks. Such data flows can be triggered either by external events, such as user queries to periodically get a snapshot view of the network, or can be automated over long durations. For real-time, mission-critical, and high datarate applications [1]–[3], it is often critical to simultaneously maximize the data collection rate and minimize packet delays. In addition, when summarized information is required or the measurements are correlated, it is beneficial to aggregate data en route to the sink. This helps in reducing redundancy and the number of transmissions. We refer to such a data collection process under aggregation as aggregated convergecast. Two primary factors that affect the data collection rate and packet delays are: (i) efficiency of the link scheduling protocol,

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A. Ghosh and B. Krishnamachari are with the Dept of Electrical Engineering, University of Southern California, LA, {amitabhg, bkrishna}@usc.edu ¨ O. D. Incel is with NETLAB, Dept of Computer Engineering, Bogazici University, Turkey, ozlem.durmaz@tam.boun.edu.tr V. S. Anil Kumar is with the Dept of Computer Science and Virginia BioInformatics Institute, Virginia Tech, Blacksburg, akumar@vbi.vt.edu

and (ii) structure of the routing tree. A typical sensor node is equipped with a single half-duplex transceiver, using which it can either transmit or receive only one packet at any time. Moreover, nodes very close to each other cannot transmit simultaneously due to interference in the wireless medium. It is shown that for periodic traffic, multiple frequencies under spatial-reuse time division multiple access (TDMA) can eliminate interference and enable more concurrent transmissions [8], thus, enhancing the rate and providing bounds on the completion time of convergecast [12]. In addition, since TDMA protocols assign a dedicated time slot for each node to transmit and allow it to enter sleep modes during inactive periods, they perform well even under heavy traffic conditions and achieve low duty cycles. We note that, although multiple frequencies have been used in the domain of ad hoc networks, their use in sensor networks is new and challenging, especially due to resource constraints on the nodes. However, since current sensor network hardware, such as CC2420 radios, already support multiple frequencies, it is imperative that we take their...
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