Abstract
We study a scenario in which n nodes of a mobile ad-hoc network continuously collect data. Their task is to repeatedly update aggregated information about the data, e.g., the maximum, the sum, or the full information about all data received by all nodes at a given time step. This aggregated information has to be disseminated to all nodes.
We propose two performance measures for distributed algorithms for these tasks: The delay is the maximum time needed until the aggregated information about the data measured at some time is output at all nodes. We assume that a node can broadcast information proportional to a constant number of data items per round. A too large communication volume needed for producing an output can lead to the effect that the delay grows unboundedly over time. Thus, we have to cope with the restriction that outputs are computed not for all but only for a fraction of rounds. We refer to this fraction as the output rate of the algorithm.
Our main technical contributions are trade-offs between delay and output rate for aggregation problems under the assumption of T-stable dynamics in the mobile ad-hoc network: The network is always connected and is stable for time intervals of length 
where 
is the time needed to compute a maximal independent set. For the maximum function, we are able to show that we can achieve an output rate of 
with delay 
. For the sum, we show that it is possible to achieve an output rate of 
with delay 
if 
, and if 
, we can achieve an output rate of 
with delay 
.
This work was partially supported by the German Research Foundation (DFG) within the Priority Program “Algorithms for Big Data” (SPP 1736), by the EU within FET project MULTIPLEX under contract no. 317532, and the International Graduate School “Dynamic Intelligent Systems”.
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Abshoff, S., Meyer auf der Heide, F. (2014). Continuous Aggregation in Dynamic Ad-Hoc Networks. In: Halldórsson, M.M. (eds) Structural Information and Communication Complexity. SIROCCO 2014. Lecture Notes in Computer Science, vol 8576. Springer, Cham. https://doi.org/10.1007/978-3-319-09620-9_16
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DOI: https://doi.org/10.1007/978-3-319-09620-9_16
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