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...size approximation [2, 11, 12], alerting (all nodes are notified if an event happens at one or more nodes) [14], sorting (n values distributed among n nodes, the i th value is moved to the i th node) =-=[13]-=-, aggregation problems like finding the minimum, maximum, median value and computing the average value [23, 19]. 4. COMMUNICATION MODEL The network consists of a set of n nodes, each node v with a bui...

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...,15], size approximation [3,9], alerting (all nodes are notified if an event happens at one or more nodes) [11], sorting (n values distributed among n nodes, the i th value is moved to the i th node) =-=[10,17]-=-, selection problems like finding the minimum, maximum, median value [16] and computing the average value [13], and do-all (schedule t similar tasks among n nodes with at most f failures) [4]. Note th...

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...nation of di items from qi other stations. By n = ∑p−1 i=0 si we denote total number of items. Let r = ∑p−1 i=0 ri and q = ∑p−1 i=0 qi. We assume that during a single round each station can send or receive no more than single message containing either single key or an integer between 0 and n. 1 We consider two problems. First, sorting n integer keys of range [0, 2m − 1] stored in p stations of a single-hop and single channel radio network. Second, problem of routing of the packets between the stations of the network. 1.1 Previous works Some energy efficient sorting algorithms are described in [7,8,2,3]. Singh and Prasanna [7,8] proposed sorting algorithm based on quick-sort and balanced selection with Θ(log n) energy cost and Θ(n c log n) time cost, where c is the number of communication channels. Sorting based on merging and an algorithm for merging with energetic cost O(log∗ n) has been proposed in [2]. In these algorithms it is assumed that each station stores single key (i.e. p = n). The algorithm described in [3] extends results from [2] for sorting n keys stored in p stations (where each station stores n p keys) with 8n p log2 p + 2(log2 p + 1) log2 p energetic cost and (3n + 2p− 2) l...

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...rk. We assume that the stations are synchronized, each station knows it position in the sequence 1 . . . p, and a single message may contain a single key or a single index in the sequence of keys. In =-=[9]-=- we consider the case when each station stores a single key (and a constant number of auxiliary variables). We show that merging of two sequences of length m can be done with energy cost O(lg ∗ m). No...

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...work. We assume that the stations are synchronized, each station knows it position in the sequence 1 . . . n, and a single message may contain a single key or single index in the sequence of keys. In =-=[8]-=- we consider the case when each station is able to store a single key (and a constant number of auxiliary variables). We show that merging of two sequences of length m can be done with energy cost O(l...

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...[12] proposed sorting algorithm based on quick-sort and energetically balanced implementation of sequential selection algorithm. This algorithm sorts in time O(n lg n) with energetic cost O(lg n). In =-=[9]-=- we propose an algorithm, based on merging, sorting in time O(n lg n) with energetic cost O(lg 2 n) that seems to be attractive for practical applications due to its simplicity and very low constants....