The Cost of Global Broadcast in Dynamic Radio Networks

We study the single-message broadcast problem in dynamic radio networks. We show that the time complexity of the problem depends on the amount of stability and connectivity of the dynamic network topology and on the adaptiveness of the adversary providing the dynamic topology. More formally, we model communication using the standard graph-based radio network model. To model the dynamic network, we use a generalization of the synchronous dynamic graph model introduced in [Kuhn et al., STOC 2010]. For integer parameters $T\geq 1$ and $k\geq 1$, we call a dynamic graph $T$-interval $k$-connected if for every interval of $T$ consecutive rounds, there exists a $k$-vertex-connected stable subgraph. Further, for an integer parameter $\tau\geq 0$, we say that the adversary providing the dynamic network is $\tau$-oblivious if for constructing the graph of some round $t$, the adversary has access to all the randomness (and states) of the algorithm up to round $t-\tau$. As our main result, we show that for any $T\geq 1$, any $k\geq 1$, and any $\tau\geq 1$, for a $\tau$-oblivious adversary, there is a distributed algorithm to broadcast a single message in time $O\big(\big(1+\frac{n}{k\cdot\min\left\{\tau,T\right\}}\big)\cdot n\log^3 n\big)$. We further show that even for large interval $k$-connectivity, efficient broadcast is not possible for the usual adaptive adversaries. For a $1$-oblivious adversary, we show that even for any $T\leq (n/k)^{1-\varepsilon}$ (for any constant $\varepsilon>0$) and for any $k\geq 1$, global broadcast in $T$-interval $k$-connected networks requires at least $\Omega(n^2/(k^2\log n))$ time. Further, for a $0$ oblivious adversary, broadcast cannot be solved in $T$-interval $k$-connected networks as long as $T<n-k$.Comment: 17 pages, conference version appeared in OPODIS 201

Beeping a Maximal Independent Set

We consider the problem of computing a maximal independent set (MIS) in an extremely harsh broadcast model that relies only on carrier sensing. The model consists of an anonymous broadcast network in which nodes have no knowledge about the topology of the network or even an upper bound on its size. Furthermore, it is assumed that an adversary chooses at which time slot each node wakes up. At each time slot a node can either beep, that is, emit a signal, or be silent. At a particular time slot, beeping nodes receive no feedback, while silent nodes can only differentiate between none of its neighbors beeping, or at least one of its neighbors beeping. We start by proving a lower bound that shows that in this model, it is not possible to locally converge to an MIS in sub-polynomial time. We then study four different relaxations of the model which allow us to circumvent the lower bound and find an MIS in polylogarithmic time. First, we show that if a polynomial upper bound on the network size is known, it is possible to find an MIS in O(log^3 n) time. Second, if we assume sleeping nodes are awoken by neighboring beeps, then we can also find an MIS in O(log^3 n) time. Third, if in addition to this wakeup assumption we allow sender-side collision detection, that is, beeping nodes can distinguish whether at least one neighboring node is beeping concurrently or not, we can find an MIS in O(log^2 n) time. Finally, if instead we endow nodes with synchronous clocks, it is also possible to find an MIS in O(log^2 n) time.Comment: arXiv admin note: substantial text overlap with arXiv:1108.192

Effect of Communication Delays on the Successful Coordination of a Group of Biomimetic AUVs

In this paper, the influence of delays on the ability of a formation control algorithm to coordinate a group of twelve Biomimetic Autonomous Underwater Vehicles (BAUVs) is investigated. In this study the formation control algorithm is a decentralized methodology based on the behavioural mechanisms of fish within school structures. Incorporated within this algorithm is a representation of the well-known and frequently used communication protocol, Time-Division-Multiple-Access (TDMA). TDMA operates by assigning each vehicle a specific timeslot during which it can broadcast to the remaining members of the group. The size of this timeslot varies depending on a number of operational parameters such as the size of the message being transmitted, the hardware used and the distance between neighbouring vehicles. Therefore, in this work, numerous timeslot sizes are tested that range from theoretical possible values through to values used in practice. The formation control algorithm and the TDMA protocol have been implemented within a validated mathematical of the RoboSalmon BAUV designed and manufactured at the University of Glasgow. The results demonstrate a significant deterioration in the ability of the formation control algorithms as the timeslot size is increased. This deterioration is due to the fact that as the timeslot size is increased, the interim period between successive communication updates increases and as a result, the error between where the formation control algorithm estimates each vehicle to be and where they actually are, increases. As a result, since the algorithm no longer has an accurate representation of the positioning of neighbouring vehicles, it is no longer capable of selecting the correct behavioural equation and subsequently, is unable to coordinate the vehicles to form a stable group structure