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In Network Processing and Data Aggregation in

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of communication failures because each read<strong>in</strong>g is accounted for <strong>in</strong> many paths towardsthe base station, <strong>and</strong> all would have to fail for the read<strong>in</strong>g to be lost. However, there aretwo drawbacks for the multi-path approach:(1) when many aggregates are to be accumulated, the known energy-efficienttechniques provide only an approximate answer (with accuracy guarantees), <strong>and</strong>(2) when some aggregates are to be accumulated, the message size is longer thanwhen us<strong>in</strong>g the tree approach, thereby consum<strong>in</strong>g more energy.(3) there is the danger to double count the same values because of the multipleparents.<strong>In</strong> the follow<strong>in</strong>g, it is proposed a protocol which recommends a topology called r<strong>in</strong>gs.<strong>In</strong> this topology, nodes are divided <strong>in</strong>to levels accord<strong>in</strong>g to their hop count from the basestation, <strong>and</strong> the multi-path aggregation is performed level-by-level towards the basestation.SYNOPSIS DIFFUSION [8]<strong>In</strong> [8] it is proposed a general framework for achiev<strong>in</strong>g significantly more accurate<strong>and</strong> reliable answers by comb<strong>in</strong><strong>in</strong>g energy-efficient multi-path rout<strong>in</strong>g schemes withtechniques that avoid double-count<strong>in</strong>g. Synopsis Diffusion uses a r<strong>in</strong>gs topology toperform <strong>in</strong>-network aggregation. The partial result at a node is represented as a synopsis,a small digest (e.g., histogram, bit-vectors, sample, etc.) of the data.The synopsis diffusion algorithm consists of two phases:a) a distribution phase <strong>in</strong> which the aggregate query is flooded through the network<strong>and</strong> an aggregation topology is constructed, <strong>and</strong>b) an aggregation phase where the aggregate values are cont<strong>in</strong>ually routed towardsthe query<strong>in</strong>g node.Distribution Phase<strong>In</strong> order to construct a r<strong>in</strong>gs topology, firstly, the base station transmits <strong>and</strong> any nodehear<strong>in</strong>g this transmission is <strong>in</strong> r<strong>in</strong>g 1. At each subsequent step, nodes <strong>in</strong> r<strong>in</strong>g i transmit<strong>and</strong> any node, apart from those that are already <strong>in</strong> a r<strong>in</strong>g, hear<strong>in</strong>g one of thesetransmissions, is <strong>in</strong> r<strong>in</strong>g i + 1. As a result, the r<strong>in</strong>g number def<strong>in</strong>es the level of a node <strong>in</strong>

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