Low-power wireless networks play an important role in the Internet of Things. Typically, these networks consist of a very large number of lossy and low-capacity devices, challenging the current state of the art in protocol design. In this context the Trickle algorithm plays an important role, serving as the basic mechanism for message dissemination in notable protocols such as RPL and MPL. While Trickle's broadcast suppression mechanism has been proven to be efficient, recent work has shown that it is intrinsically unfair in terms of load distribution and that its performance relies strongly on network topology. This can lead to increased end-to-end delays (MPL), or creation of sub-optimal routes (RPL). Furthermore, as highlighted in this work, there is no clear consensus within the research community about what the proper parameter settings of the suppression mechanism should be. We propose an extension to the Trickle algorithm, called adaptive-k, which allows nodes to individually adapt their suppression mechanism to local node density. Supported by analysis and a case study with RPL, we show that this extension allows for an easier configuration of Trickle, making it more robust to network topology.
In more recent work @cite_30 the authors conclude that flooding using Trickle can perform poorly due to its suppression mechanism. Since @math does not change with node density, the suppression mechanism favors nodes with few neighbors, letting them broadcast more often than nodes with more neighbors. This leads to increased traffic along the edges of a network and potentially increased end-to-end delays. They underline the importance of correctly setting @math to avoid such issues. Additionally, they write: ". Similar problems have been identified in @cite_13 , where, due to the suppression mechanism, bottleneck topologies have been shown to be prone to extremely large end-to-end delays.
@cite_30 @cite_13
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Flooding based querying and broadcasting schemes have low hop-delays of Theta(1 R(n)) to reach any node that is a unit distance away, where R(n) is the transmission range of any sensor node. However, in sensor networks with large radio ranges, flooding based broadcasting schemes cause many redundant transmissions leading to a broadcast storm problem. In this paper, we study the role of geographic information and state information (i.e., memory of previous messages or transmissions) in reducing the redundant transmissions in the network. We consider three broadcasting schemes with varying levels of local information where nodes have: (i) no geographic or state information, (ii) coarse geographic information about the origin of the broadcast, and (Hi) no geographic information, but remember previously received messages. For each of these network models, we demonstrate localized forwarding algorithms for broadcast (based on geography or state information) that achieve significant reductions in the transmission overheads while maintaining hop-delays comparable to flooding based schemes. We also consider the related problem of broadcasting to a set of "spatially uniform" points in the network (lattice points) in the regime where all nodes have only a local sense of direction and demonstrate an efficient "sparse broadcast" scheme based on a branching random walk that has a low number of packet transmissions. Thus, our results show that even with very little local information, it is possible to make broadcast schemes significantly more efficient. This paper presents two efficient flooding algorithms based on 1-hop neighbor information. In the first part of the paper, we consider sender-based flooding algorithms, specifically the algorithm proposed by In their paper, propose a sender-based flooding algorithm that can achieve local optimality by selecting the minimum number of forwarding nodes in the lowest computational time complexity O(n logn), where n is the number of neighbors. We show that this optimality only holds for a subclass of sender-based algorithms. We propose an efficient sender-based flooding algorithm based on 1-hop neighbor information that reduces the time complexity of computing forwarding nodes to O(n). In Liu's algorithm, n nodes are selected to forward the message in the worst case, whereas in our proposed algorithm, the number of forwarding nodes in the worst case is 11. In the second part of the paper we propose a simple and highly efficient receiver-based flooding algorithm. When nodes are uniformly distributed, we prove that the probability of two neighbor nodes broadcasting the same messageneighbor nodes broadcasting the same message exponentially decreases when the distance between them decreases or when the node density increases. The analytical results are confirmed using simulation. An edge-Markovian process with birth-rate p and death-rate q generates sequences of graphs (G0,G1,G2,…) with the same node set [n] such that Gt is obtained from Gt−1 as follows: if e ∉ E(Gt−1) then e ∈ E(Gt) with probability p, and if e ∈ E(Gt−1) then e ∉ E(Gt) with probability q. (PODC 2008) analyzed thoroughly information dissemination in such dynamic graphs, by establishing bounds on their flooding time--flooding is the basic mechanism in which every node becoming aware of an information at step t forwards this information to all its neighbors at all forthcoming steps t∦ > t. In this paper, we establish tight bounds on the complexity of flooding for all possible birth rates and death rates, completing the previous results by Moreover, we note that despite its many advantages in term of simplicity and robustness, flooding suffers from its high bandwidth consumption. Hence we also show that flooding in dynamic graphs can be implemented in a more parsimonious manner, so that to save bandwidth, yet preserving efficiency in term of simplicity and completion time. For a positive integer k, we say that the flooding protocol is k-active if each node forwards an information only during the k time steps immediately following the step at which the node receives that information for the first time. We define the reachability threshold for the flooding protocol as the smallest integer k such that, for any source s ∈ [n], the k-active flooding protocol from s completes (i.e., reaches all nodes), and we establish tight bounds for this parameter. We show that, for a large spectrum of parameters p and q, the reachability threshold is by several orders of magnitude smaller than the flooding time. In particular, we show that it is even constant whenever the ratio p (p + q) exceeds log n n. Moreover, we also show that being active for a number of steps equal to the reachability threshold (up to a multiplicative constant) allows the flooding protocol to complete in optimal time, i.e., in asymptotically the same number of steps as when being perpetually active. These results demonstrate that flooding can be implemented in a practical and efficient manner in dynamic graphs. The main ingredient in the proofs of our results is a reduction lemma enabling to overcome the time dependencies in edge-Markovian dynamic graphs. It is well known that in a network with arbitrary (convex) latency functions that are a function of edge traffic, the worst-case ratio, over all inputs, of the system delay caused due to selfish behavior versus the system delay of the optimal centralized solution may be unbounded even if the system consists of only two parallel links. This ratio is called the price of anarchy (PoA). In this paper, we investigate ways by which one can reduce the performance degradation due to selfish behavior. We investigate two primary methods (a) Stackelberg routing strategies, where a central authority, e.g., network manager, controls a fixed fraction of the flow, and can route this flow in any desired way so as to influence the flow of selfish users; and (b) network tolls, where tolls are imposed on the edges to modify the latencies of the edges, and thereby influence the induced Nash equilibrium. We obtain results demonstrating the effectiveness of both Stackelberg strategies and tolls in controlling the price of anarchy. For Stackelberg strategies, we obtain the first results for nonatomic routing in graphs more general than parallel-link graphs, and strengthen existing results for parallel-link graphs, (i) In series-parallel graphs, we show that Stackelberg routing reduces the PoA to a constant (depending on the fraction of flow controlled). (ii) For general graphs, we obtain latency-class specific bounds on the PoA with Stackelberg routing, which give a continuous trade-off between the fraction of flow controlled and the price of anarchy, (iii) In parallel-link graphs, we show that for any given class L of latency functions, Stackelberg routing reduces the PoA to at most α + (1 - α) · ρ(L), where α is the fraction of flow controlled and ρ(L) is the PoA of class L (when α = 0). For network tolls, motivated by the known strong results for nonatomic games, we consider the more general setting of atomic splittable routing games. We show that tolls inducing an optimal flow always exist, even for general asymmetric games with heterogeneous users, and can be computed efficiently by solving a convex program. Furthermore, we give a complete characterization of flows that can be induced via tolls. These are the first results on the effectiveness of tolls for atomic splittable games.