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We consider self-stabilizing algorithms to compute a Maximal Independent Set (MIS) in the extremely weak beeping communication model. The model consists of an anonymous network with synchronous rounds. In each round, each vertex can optionally transmit a signal to all its neighbors (beep). After the transmission of a signal, each vertex can only differentiate between no signal received, or at least one signal received. We also consider an extension of this model where vertices can transmit signals through two distinguishable beeping channels. We assume that vertices have some knowledge about the topology of the network. We revisit the not self-stabilizing algorithm proposed by Jeavons, Scott, and Xu (2013), which computes an MIS in the beeping model. We enhance this algorithm to be self-stabilizing, and explore three different variants, which differ in the knowledge about the topology available to the vertices and the number of beeping channels. In the first variant, every vertex knows an upper bound on the maximum degree $\Delta$ of the graph. For this case, we prove that the proposed self-stabilizing version maintains the same run-time as the original algorithm, i.e., it stabilizes after $O(\log n)$ rounds w.h.p. on any $n$-vertex graph. In the second variant, each vertex only knows an upper bound on its own degree. For this case, we prove that the algorithm stabilizes after $O(\log n\cdot \log \log n)$ rounds on any $n$-vertex graph, w.h.p. In the third variant, we consider the model with two beeping channels, where every vertex knows an upper bound of the maximum degree of the nodes in the $1$-hop neighborhood. We prove that this variant stabilizes w.h.p. after $O(\log n)$ rounds.

Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring with two colors. In each step, all nodes change their current color synchronously to the least/most frequent color in their neighborhood and in case of a tie, keep their current color. After a finite number of rounds these systems either reach a fixed point or enter a 2-cycle. The problem of counting the number of fixed points for cellular automata is #P-complete. In this paper we consider cellular automata defined by a tree. We propose an algorithm with run-time $O(n\Delta)$ to count the number of fixed points, here $\Delta$ is the maximal degree of the tree. We also prove upper and lower bounds for the number of fixed points. Furthermore, we obtain corresponding results for pure cycles, i.e., instances where each node changes its color in every round. We provide examples demonstrating that the bounds are sharp. The results are proved for the minority and the majority model., Comment: 15 pages, 11 figures. Extended version of paper to appear at LATIN 2024

Indoor Positioning Systems (IPS) gained importance in many industrial applications. State-of-the-art solutions heavily rely on external infrastructures and are subject to potential privacy compromises, external information requirements, and assumptions, that make it unfavorable for environments demanding privacy and prolonged functionality. In certain environments deploying supplementary infrastructures for indoor positioning could be infeasible and expensive. Recent developments in machine learning (ML) offer solutions to address these limitations relying only on the data from onboard sensors of IoT devices. However, it is unclear which model fits best considering the resource constraints of IoT devices. This paper presents a machine learning-based indoor positioning system, using motion and ambient sensors, to localize a moving entity in privacy concerned factory environments. The problem is formulated as a multivariate time series classification (MTSC) and a comparative analysis of different machine learning models is conducted in order to address it. We introduce a novel time series dataset emulating the assembly lines of a factory. This dataset is utilized to assess and compare the selected models in terms of accuracy, memory footprint and inference speed. The results illustrate that all evaluated models can achieve accuracies above 80 %. CNN-1D shows the most balanced performance, followed by MLP. DT was found to have the lowest memory footprint and inference latency, indicating its potential for a deployment in real-world scenarios., Comment: 18 pages, 9 figures

${\cal A}_\mathsf{deg}$ is a self-stabilizing algorithm that computes a maximal independent set in a finite graph with approximation ratio $(\Delta + 2)/3$. In this note we show that under the central scheduler the number of moves of ${\cal A}_\mathsf{deg}$ is not bounded by a polynomial in $n$.

This paper considers synchronous discrete-time dynamical systems on graphs based on the threshold model. It is well known that after a finite number of rounds these systems either reach a fixed point or enter a 2-cycle. The problem of finding the fixed points for this type of dynamical system is in general both NP-hard and #P-complete. In this paper we give a surprisingly simple graph-theoretic characterization of fixed points and 2-cycles for the class of finite trees. Thus, the class of trees is the first nontrivial graph class for which a complete characterization of fixed points exists. This characterization enables us to provide bounds for the total number of fixed points and pure 2-cycles. It also leads to an output-sensitive algorithm to efficiently generate these states., Comment: 15 pages, 7 figures

For data collection scenarios in the Industrial Internet of Things, wireless communication provides a cost-effective and easy-to-deploy alternative to wired networks. The main focus lies on energy efficiency and reliability, as many devices are battery operated. IEEE 802.15.4 DSME enhances reliability by acknowledging each packet individually, imposing an overhead for each transmitted packet, and increasing energy consumption. In networks with little interference, it may be beneficial to aggregate the acknowledgments for multiple nodes and broadcast them in a compressed format to all nodes in the neighborhood. The IEEE 802.15.4 2012 standard describes such a group acknowledgment scheme which, however, disappears in later iterations of the standard. This paper compares different group acknowledgment schemes and proposes a novel group acknowledgment scheme with the goal to examine whether group acknowledgments constitute a viable alternative to regular acknowledgments in reliable data-collection scenarios. Our analysis suggests that apart from a few cases, GACKs do not constitute a valid alternative to the direct acknowledgement of data packets.

Contention-based wireless channel access methods like CSMA and ALOHA paved the way for the rise of the Internet of Things in industrial applications (IIoT). However, to cope with increasing demands for reliability and throughput, several mostly TDMA-based protocols like IEEE 802.15.4 and its extensions were proposed. Nonetheless, many of these IIoT-protocols still require contention-based communication, e.g., for slot allocation and broadcast transmission. In many cases, subtle but hidden patterns characterize this secondary traffic. Present contention-based protocols are unaware of these hidden patterns and can therefore not exploit this information. Especially in dense networks, they often do not provide sufficient reliability for primary traffic, e.g., they are unable to allocate transmission slots in time. In this paper, we propose QMA, a contention-based multiple access scheme based on Q-learning, which dynamically adapts transmission times to avoid collisions by learning patterns in the contention-based traffic. QMA is designed to be resource-efficient and targets small embedded devices. We show that QMA solves the hidden node problem without the additional overhead of RTS / CTS messages and verify the behaviour of QMA in the FIT IoT-LAB testbed. Finally, QMA's scalability is studied by simulation, where it is used for GTS allocation in IEEE 802.15.4 DSME. Results show that QMA considerably increases reliability and throughput in comparison to CSMA/CA, especially in networks with a high load., Comment: 23 pages, 26 figures

In this paper we investigate the usage of machine learning for interpreting measured sensor values in sensor modules. In particular we analyze the potential of artificial neural networks (ANNs) on low-cost micro-controllers with a few kilobytes of memory to semantically enrich data captured by sensors. The focus is on classifying temporal data series with a high level of reliability. Design and implementation of ANNs are analyzed considering Feed Forward Neural Networks (FFNNs) and Recurrent Neural Networks (RNNs). We validate the developed ANNs in a case study of optical hand gesture recognition on an 8-bit micro-controller. The best reliability was found for an FFNN with two layers and 1493 parameters requiring an execution time of 36 ms. We propose a workflow to develop ANNs for embedded devices., Comment: 21 pages, 13 figures

In this work we extend the recently proposed synchronous broadcast algorithm amnesiac flooding to the case of intermittent communication channels. In amnesiac flooding a node forwards a received message in the subsequent round. There are several reasons that render an immediate forward of a message impossible: Higher priority traffic, overloaded channels, etc. We show that postponing the forwarding for one or more rounds prevents termination. Our extension overcomes this shortcoming while retaining the advantages of the algorithm: Nodes don't need to memorize the reception of a message to guarantee termination and messages are sent at most twice per edge. This extension allows to solve more general broadcast tasks such as multi-source broadcasts and concurrent broadcasts for systems with bounded channel capacities., Comment: 13 pages, 7 figures

In 2015, the IEEE 802.15.4 standard was expanded by the Deterministic and Synchronous Multi-Channel Extension (DSME) to increase reliability, scalability and energy-efficiency in industrial applications. The extension offers a TDMA/FDMA-based channel access, where time is divided into two alternating phases, a contention access period (CAP) and a contention free period (CFP). During the CAP, transmission slots can be allocated offering an exclusive access to the shared medium during the CFP. The fraction $\tau$ of CFP's time slots in a dataframe is a critical value, because it directly influences agility and throughput. A high throughput demands that the CFP is much longer than the CAP, i.e., a high value of the fraction $\tau$, because application data is only sent during the CFP. High agility is given if the expected waiting time to send a CAP message is short and that the length of the CAPs are sufficiently long to accommodate necessary (de)allocations of GTSs, i.e., a low value of the fraction $\tau$. Once DSME is configured according to the needs of an application, the fraction $\tau$ can only assume one of two values and cannot be changed at run-time. In this paper, we propose two extensions of DSME that allow to adopt $\tau$ to the current traffic pattern. We show theoretically and through simulations that the proposed extensions provide a high degree of responsiveness to traffic fluctuations while keeping the throughput high., Comment: 21 pages, 14 figures

The broadcast operation in distributed systems is used to spread information located at some nodes to all other nodes. This operation is often realized by flooding, where the source nodes send a message containing the information to all neighbors. Each node receiving the message for the first time forwards it to all other neighbors. A stateless variant of flooding for synchronous systems is called amnesiac flooding. In this case, every time a node receives a message, it forwards it to those neighbors, from which it did not receive the message in the current round. The algorithm is oblivious and therefore scales very well. Stateless protocols are advantageous in high volume applications, increasing performance by removing the load caused by retention of session information and by providing crash tolerance. In this paper we analyze the termination time of amnesiac flooding. We define the (k,c)-flooding problem, which aims at finding a set $S$ of size $k$, such that amnesiac flooding when started concurrently by all nodes of $S$ terminates in a minimal number of rounds. We prove that this problem is NP-complete. We provide sharp upper and lower bounds for the time complexity of amnesiac flooding and reveal a discrepancy between bipartite and non-bipartite graphs. All results are based on the insight, that for every non-bipartite graph there exists a bipartite graph such that the execution of amnesiac flooding on both graphs is strongly correlated. This construction considerably simplifies existing proofs for amnesiac flooding and allows to analyze the (k,c)-flooding problem., Comment: 14 pages, 12 figures

A vertex subset $S$ of a graph $G=(V,E)$ is a $[1,2]$-dominating set if each vertex of $V\backslash S$ is adjacent to either one or two vertices in $S$. The minimum cardinality of a $[1,2]$-dominating set of $G$, denoted by $\gamma_{[1,2]}(G)$, is called the $[1,2]$-domination number of $G$. In this paper the $[1,2]$-domination and the $[1,2]$-total domination numbers of the generalized Petersen graphs $P(n,2)$ are determined.

This paper introduces a new resource allocation problem in distributed computing called distributed serving with mobile servers (DSMS). In DSMS, there are $k$ identical mobile servers residing at the processors of a network. At arbitrary points of time, any subset of processors can invoke one or more requests. To serve a request, one of the servers must move to the processor that invoked the request. Resource allocation is performed in a distributed manner since only the processor that invoked the request initially knows about it. All processors cooperate by passing messages to achieve correct resource allocation. They do this with the goal to minimize the communication cost. Routing servers in large-scale distributed systems requires a scalable location service. We introduce the distributed protocol GNN that solves the DSMS problem on overlay trees. We prove that GNN is starvation-free and correctly integrates locating the servers and synchronizing the concurrent access to servers despite asynchrony, even when the requests are invoked over time. Further, we analyze GNN for "one-shot" executions, i.e., all requests are invoked simultaneously. We prove that when running GNN on top of a special family of tree topologies---known as hierarchically well-separated trees (HSTs)---we obtain a randomized distributed protocol with an expected competitive ratio of $O(\log n)$ on general network topologies with $n$ processors. From a technical point of view, our main result is that GNN optimally solves the DSMS problem on HSTs for one-shot executions, even if communication is asynchronous. Further, we present a lower bound of $\Omega(\max\{k, \log n/\log\log n\})$ on the competitive ratio for DSMS. The lower bound even holds when communication is synchronous and requests are invoked sequentially., Comment: 34 pages, conference version in ISAAC 2019

Wireless communication is a key element in the realization of the Industrial Internet of Things for flexible and cost-efficient monitoring and control of industrial processes. Wireless mesh networks using IEEE 802.15.4 have a high potential for executing monitoring and control tasks with low energy consumption and low costs for deployment and maintenance. However, conventional medium access techniques based on carrier sensing cannot provide the required reliability for industrial applications. Therefore, the standard was extended with techniques for time-slotted medium access on multiple channels. In this paper, we present openDSME, a comprehensive implementation of the Deterministic and Synchronous Multi-channel Extension (DSME) and propose a method for traffic-aware and decentralized slot scheduling to enable scalable wireless industrial networks. The performance of DSME and our implementation is demonstrated in the OMNeT++ simulator and on a physically deployed wireless network in the FIT/IoT-LAB. It is shown that in the given scenarios, twice as much traffic can be delivered reliably by using DSME instead of CSMA/CA and that the energy consumption can be reduced significantly. The paper is completed by presenting important trade-offs for parameter selection and by uncovering open issues of the current specification that call for further effort in research and standardization., Comment: 27 pages, 18 figures

Wireless mesh networks are a promising technology for connecting sensors and actuators with high flexibility and low investment costs. In industrial applications, however, reliability is essential. Therefore, two time-slotted medium access methods, DSME and TSCH, were added to the IEEE 802.15.4 standard. They allow collision-free communication in multi-hop networks and provide channel hopping for mitigating external interferences. The slot schedule used in these networks is of high importance for the network performance. This paper supports the development of efficient schedules by providing an analytical model for the assessment of such schedules, focused on TSCH. A Markov chain model for the finite queue on every node is introduced that takes the slot distribution into account. The models of all nodes are interconnected to calculate network metrics such as packet delivery ratio, end-to-end delay and throughput. An evaluation compares the model with a simulation of the Orchestra schedule. The model is applied to Orchestra as well as to two simple distributed scheduling algorithms to demonstrate the importance of traffic-awareness for achieving high throughput., Comment: 17 pages, 14 figures

It is known for some time that a random graph $G(n,p)$ contains w.h.p. a Hamiltonian cycle if $p$ is larger than the critical value $p_{crit}= (\log n + \log \log n + \omega_n)/n$. The determination of a concrete Hamiltonian cycle is even for values much larger than $p_{crit}$ a nontrivial task. In this paper we consider random graphs $G(n,p)$ with $p$ in $\tilde{\Omega}(1/\sqrt{n})$, where $\tilde{\Omega}$ hides poly-logarithmic factors in $n$. For this range of $p$ we present a distributed algorithm ${\cal A}_{HC}$ that finds w.h.p. a Hamiltonian cycle in $O(\log n)$ rounds. The algorithm works in the synchronous model and uses messages of size $O(\log n)$ and $O(\log n)$ memory per node., Comment: 17 pages; 4 figures

Testbeds are a key element in the evaluation of wireless multi-hop networks. In order to relieve researchers from the hassle of deploying their own testbeds, remotely controllable testbeds, such as the FIT/IoT-LAB, are built. However, while the IoT-LAB has a high number of nodes, they are deployed in constraint areas. This, together with the complex nature of radio propagation, makes an ad-hoc construction of multi-hop topologies with a high number of hops difficult. This work presents a strategic approach to solve this problem and proposes algorithms to generate topologies with desired properties. The implementation is evaluated for the IoT-LAB testbeds and is provided as open-source software. The results show that preset topologies of various types can be built even in dense wireless testbeds., Comment: 12 pages, 11 figures

This paper presents the novel routing algorithm PSVR for pub/sub systems in ad-hoc networks. Its focus is on scenarios where communications links are unstable and nodes frequently change subscriptions. PSVR presents a compromise of size and maintenance effort for routing tables due to sub- and unsubscriptions and the length of routing paths. Designed in a self-stabilizing manner it scales well with network size. The evaluation reveals that PSVR only needs slightly more messages than a close to optimal routing structure for publication delivery, and creates shorter routing paths than an existing self-stabilizing algorithm. A real world deployment shows the usability of the approach

The IEEE 802.15.4 standard allows for the deployment of cost-effective and energy-efficient multi-hop networks. This document features an in-depth presentation of an analytical model for assessing the performance of such networks. It considers a generic, static topology with Poisson distributed data-collection as well as data-dissemination traffic. The unslotted CSMA/CA MAC layer of IEEE 802.15.4 is closely modeled as well as an enhanced model of the neighborhood allows for consideration of collisions of packets including interferences with acknowledgements. The hidden node problem is taken into account as well as a formerly disregarded effect of repeated collisions of retransmissions. The model has been shown to be suitable to estimate the capacity of large-scale multi-hop networks., Comment: 11 pages, 6 figures

The paper presents techniques to derive upper bounds for the mean time to recover from a single fault for self-stabilizing algorithms in the message passing model. For a new Delta+1-coloring algorithm we analytically derive a bound for the mean time to recover and show that the variance is bounded by a small constant independent of the network's size. For the class of bounded-independence graphs (e.g. unit disc graphs) all containment metrics are in O(1)., Comment: 23 pages, 5 figures

Opacity of Transactional Memory is proposed to be established by incremental validation. Quiescence in terms of epoch-based memory reclamation is applied to deal with doomed transactions causing memory access violations. This method unfortunately involves increased memory consumption and does not cover reclamations outside of transactions. This paper introduces a different method which combines incremental validation with elements of sandboxing to solve these issues., Comment: Keywords: transactional memory, opacity, privatization, memory reclamation

Due to the transient nature of peers, any Peer-to-Peer network is in peril to falling apart if peers do not receive routing table updates periodically. To this end, maintenance, which affects every peer, ensures connectedness and sustained data operation performance. However, a high rate of change in peer population usually incurs lots of network maintenance messages and can severely degrade overall performance. We discuss three methods how to tackle and mitigate the effect of peer fluctuation on a tree-based distributed hash table., Comment: 5 pages