Fast Radio Broadcasting with Advice

Abstract

International audienceWe study deterministic broadcasting in radio networks in the recently introduced framework of network algorithms with {\em advice}. We concentrate on the problem of trade-offs between the number of bits of information (size of advice) available to nodes and the time in which broadcasting can be accomplished. In particular, we ask what is the minimum number of bits of information that must be available to nodes of the network, in order to broadcast very fast. For networks in which constant time broadcast is possible under complete knowledge of the network we give a tight answer to the above question: $O(n)$ bits of advice are sufficient but $o(n)$ bits are not, in order to achieve constant broadcasting time in all these networks. This is in sharp contrast with geometric radio networks of constant broadcasting time: we show that in these networks a constant number of bits suffices to broadcast in constant time. For arbitrary radio networks we present a broadcasting algorithm whose time is inverse-proportional to the size of advice

Short Labeling Schemes for Topology Recognition in Wireless Tree Networks

“…In the case of [20] the issue was not efficiency but feasibility: it was shown that Θ(n log n) is the minimum size of advice required to perform monotone connected graph clearing. In [16] the authors studied radio networks for which it is possible to perform centralized broadcasting in constant time. They proved that O(n) bits of advice allow to obtain constant time in such networks, while o(n) bits are not enough.…”

Trade-offs Between the Size of Advice and Broadcasting Time in Trees

“…In the case of [29] the issue was not efficiency but feasibility: it was shown that (n log n) is the minimum size of advice required to perform monotone connected graph clearing. Finally, in [19] the authors studied radio networks for which it is possible to perform centralized broadcasting in constant time. They proved that O(n) bits of advice allow to obtain constant time in such networks, while o(n) bits are not enough.…”

Tradeoffs between cost and information for rendezvous and treasure hunt

“…Following the paradigm of algorithms with advice [1,14,16,21,26,28,29,30,31,32,33,34,36,37,38,44,49], this information is provided to the agents at the start of their navigation by an oracle that knows the network, the starting positions of the agents and, in the case of treasure hunt, the node where the treasure is hidden. The oracle assists the agents by providing them with a binary string called advice, which can be used by the agent during the algorithm execution.…”

“…Providing nodes or agents with information of arbitrary type that can be used to perform network tasks more efficiently has been proposed in [1,14,16,21,26,28,29,30,31,32,33,34,36,37,38,42,44,49]. This approach was referred to as algorithms with advice.…”

“…In the case of [44], the issue was not efficiency but feasibility: it was shown that Θ(n log n) is the minimum size of advice required to perform monotone connected graph clearing. In [36], the authors studied radio networks for which it is possible to perform centralized broadcasting with advice in constant time. They proved that O(n) bits of advice allow to obtain constant time in such networks, while o(n) bits are not enough.…”