Deterministic Communication in Radio Networks with Large Labels

Gąsieniec, Leszek; Pagourtzis, Aris; Potapov, Igor; Radzik, Tomasz

doi:10.1007/s00453-006-1212-3

Cited by 33 publications

(18 citation statements)

References 43 publications

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“…A distributed O(n) time broadcast protocol for undirected networks, in the model allowing for spontaneous transmissions, as given in [8], can be interpreted as a gossiping protocol in the model of combined messages. Our protocols have transmission structure related to that of the protocols used in [20] as subroutines in an O(n polylog n)-time gossiping protocol for undirected networks.…”

Section: Our Resultsmentioning

confidence: 99%

Many-to-Many Communication in Radio Networks

2007

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Radio networks model wireless data communication when the bandwidth is limited to one wave frequency. The key restriction of such networks is mutual interference of packets arriving simultaneously at a node. The many-to-many (m2m) communication primitive involves p participant nodes from among n nodes in the network, where the distance between any pair of participants is at most d. The task is to have all the participants get to know all the input messages. We consider three cases of the m2m communication problem. In the ad-hoc case, each participant knows only its name and the values of n, p and d. In the partially centralized case, each participant knows the topology of the network and the values of p and d, but does not know the names of the other participants. In the centralized case, each participant knows the topology of the network and the names of all the participants. For the centralized m2m problem, we give deterministic protocols, for both undirected and directed networks, working in O(d + p) time, which is provably optimal. For the partially centralized m2m problem, we give a randomized protocol for undirected networks working in O((d + p + log 2 n) log p) time with high probability (whp), andThe results of this paper appeared in a preliminary form in "On many-to-many communication in packet radio networks" in 119 we show that any deterministic protocol requires (d + p log n log p ) time. For the ad-hoc m2m problem, we develop a randomized protocol for undirected networks that works in O((d + log p) log 2 n + p log p) time whp. We show two lower bounds for the adhoc m2m problem. One lower bound states that any randomized protocol for the m2m ad hoc problem requires (p + d log n d ) expected time. Another lower bound states that for any deterministic protocol for the m2m ad hoc problem, there is a network on which the protocol requires (n log n log(n/d) ) time when n − p(n) = (n) and d > 1, and that it requires (n) time when n − p(n) = o(n).

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Section: Our Resultsmentioning

confidence: 99%

Many-to-Many Communication in Radio Networks

2007

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“…These algorithms assume that the node labels are linear in n. [13] present a Õ(D∆ 2 )-time deterministic algorithm, which was improved to Õ(D∆ 3/2 ) in [22], for polynomially large labels. [29] improved the result on deterministic gossiping from Õ(n 5/3 ) in [28] to Õ(n 4/3 ) in [29]. An excellent survey of results on deterministic gossiping problem is presented by Gasieniec in [21].…”

Section: Related Workmentioning

confidence: 90%

Information dissemination in unknown radio networks with large labels

Vaya¹

2014

Theoretical Computer Science

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We consider the problems of deterministic broadcasting and gossiping in completely unknown ad-hoc radio networks. It is assumed that nothing is known to the nodes of the network about the topology of the network, that is even the size of the network is not known, except that n > 1. This lack of knowledge, about the value of n, is what distinguishes this setting from the vanilla model. For this setting, protocols for the vanilla model, may be executed with multiplicatively large estimates, say 2 i in the ith phase, on the upper bound on the size of the network n. When the respective protocol with estimate 2 i n on the size of the network is run, it will accomplish the task successfully. However, the problem that still remains is to determine when this process should terminate. Thus, to apply this design paradigm successful completion or incompletion of the process should be detected and this knowledge circulated in the network after appropriate number of rounds/phases of the protocol. In radio networks literature, this setting is known as the Acknowledged setting and broadcasting and gossiping problems for it are referred to as Acknowledged broadcasting and gossiping. An important feature of dynamic radio networks is that radio nodes can be dynamically introduced in the network from time to time and can be assigned labels in a much larger range, say polynomial in the size of the network, e.g. [1, . . . ,n c ] for some constant c. It is easy to see that protocols can be designed for the acknowledged setting only when the underlying communication network is strongly connected. We present the following results for these networks: (a) A deterministic protocol for Acknowledged broadcasting which takes NRG(n, n c ) rounds, where NRG(n, n c ) is the round complexity of deterministic gossiping for vanilla model. (b) A deterministic protocol for acknowledged gossiping, which takes O (n 2 lg n) rounds when collision detection mechanism is available. The schedule of the transmissions of nodes in the network, to enable them to infer collisions and discover existence of unknown in-neighborhood as a result, is abstracted as a family of sets of natural numbers which we call the Selecting-Colliding family. We prove the existence of Selecting-Colliding families using the probabilistic method and employ them to design protocol for acknowledged gossiping when no collision detection mechanism is available. Finally, we present a deterministic protocol for Acknowledged broadcasting for bidirectional networks, with a round complexity of O (n lg n) rounds.

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“…There is a vast literature concerning distributed algorithms for various tasks in radio networks. These tasks include, e.g., broadcasting [5,15], gossiping [5,14] and leader election [6,21]. In some cases [5,14], the authors use the model without collision detection, in others [16,21], the collision detection capability is assumed.…”

Section: Related Workmentioning

confidence: 99%

Deterministic Size Discovery and Topology Recognition in Radio Networks with Short Labels

Gańczorz¹,

Jurdziński²,

Lewko³

et al. 2021

Preprint

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We consider the fundamental problems of size discovery and topology recognition in radio networks modeled by simple undirected connected graphs. Size discovery calls for all nodes to output the number of nodes in the graph, called its size, and in the task of topology recognition each node has to learn the topology of the graph and its position in it. In radio networks, nodes communicate in synchronous rounds and start in the same round. In each round a node can either transmit the same message to all its neighbors, or stay silent and listen. At the receiving end, a node v hears a message from a neighbor w in a given round, if v listens in this round, and if w is its only neighbor that transmits in this round. If more than one neighbor of a node v transmits in a given round, there is a collision at v. We do not assume collision detection: in case of a collision, node v does not hear anything (except the background noise that it also hears when no neighbor transmits). The time of a deterministic algorithm for each of the above problems is the worst-case number of rounds it takes to solve it. Nodes have labels which are (not necessarily different) binary strings. Each node knows its own label and can use it when executing the algorithm. The length of a labeling scheme is the largest length of a label.Our goal is to construct short labeling schemes for size discovery and topology recognition in arbitrary radio networks, and to design efficient deterministic algorithms for each of these tasks, using these short schemes. It turns out that the optimal length of labeling schemes for both problems depends on the maximum degree ∆ of the graph. For size discovery, we construct a labeling scheme of length O(log log ∆) (which is known to be optimal, even if collision detection is available) and we design an algorithm for this problem using this scheme and working in time O(log 2 n), where n is the size of the graph. We also show that time complexity O(log 2 n) is optimal for the problem of size discovery, whenever the labeling scheme is of optimal length O(log log ∆). For topology recognition, we construct a labeling scheme of length O(log ∆), and we design an algorithm for this problem using this scheme and working in time O D∆ + min(∆ 2 , n) , where D is the diameter of the graph. We also show that the length of our labeling scheme is asymptotically optimal, by proving that topology recognition in the class of arbitrary radio networks requires labeling schemes of length Ω(log ∆).

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Deterministic Communication in Radio Networks with Large Labels

Cited by 33 publications

References 43 publications

Many-to-Many Communication in Radio Networks

Many-to-Many Communication in Radio Networks

Information dissemination in unknown radio networks with large labels

Deterministic Size Discovery and Topology Recognition in Radio Networks with Short Labels

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