Self-stabilizing distributed algorithms for acyclic graphs

A self-stabilizing distributed system is a network of processors, which when started from an arbitrary and possibly illegal state, always returns to a legal state in a finite number of steps. Two self-stabilizing protocols for distributed systems are presented in this thesis. The first protocol topologically sorts the processors in a distributed system of directed acyclic graph (DAG) topology and uses this information to build a shortest path routing table in each node in the system to all accessible nodes from that node. The second protocol determines the rank of the individual processors in a distributed tree network based on the values possessed by them. Due to the self-stabilizing nature of these protocols the system can withstand transient errors and recover automatically from them

Mending Partial Solutions with Few Changes

In this paper, we study the notion of mending: given a partial solution to a graph problem, how much effort is needed to take one step towards a proper solution? For example, if we have a partial coloring of a graph, how hard is it to properly color one more node? In prior work (SIROCCO 2022), this question was formalized and studied from the perspective of mending radius: if there is a hole that we need to patch, how far do we need to modify the solution? In this work, we investigate a complementary notion of mending volume: how many nodes need to be modified to patch a hole? We focus on the case of locally checkable labeling problems (LCLs) in trees, and show that already in this setting there are two infinite hierarchies of problems: for infinitely many values 0 < ? ? 1, there is an LCL problem with mending volume ?(n^?), and for infinitely many values k ? 1, there is an LCL problem with mending volume ?(log^k n). Hence the mendability of LCL problems on trees is a much more fine-grained question than what one would expect based on the mending radius alone

Almost optimal asynchronous rendezvous in infinite multidimensional grids

Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ&gt; 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δ-dimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(d δ polylog d). This bound for the case of 2d-grids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(d δ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δ-dimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(d δ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δ-dimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O( ( d)), where r = min(r1, r2) and for r ≥ 1. r)δpolylog ( d r

Deciding and verifying network properties locally with few output bits

International audienceGiven a boolean predicate on labeled networks (e.g., the network is acyclic, or the network is properly colored, etc.), deciding in a distributed manner whether a given labeled network satisfies that predicate typically consists, in the standard setting, of every node inspecting its close neighborhood, and outputting a boolean verdict, such that the network satisfies the predicate if and only if all nodes output true. In this paper, we investigate a more general notion of distributed decision in which every node is allowed to output a constant number $b\geq 1$ of bits, which are gathered by a central authority emitting a global boolean verdict based on these outputs, such that the network satisfies the predicate if and only if this global verdict equals true. We analyze the power and limitations of this extended notion of distributed decision

Improved Cardinality Bounds for Rectangle Packing Representations

Axis-aligned rectangle packings can be characterized by the set of spatial relations that hold for pairs of rectangles (west, south, east, north). A representation of a packing consists of one satisfied spatial relation for each pair. We call a set of representations complete for n ∈ ℕ if it contains a representation of every packing of any n rectangles. Both in theory and practice, fastest known algorithms for a large class of rectangle packing problems enumerate a complete set R of representations. The running time of these algorithms is dominated by the (exponential) size of R. In this thesis, we improve the best known lower and upper bounds on the minimum cardinality of complete sets of representations. The new upper bound implies theoretically faster algorithms for many rectangle packing problems, for example in chip design, while the new lower bound imposes a limit on the running time that can be achieved by any algorithm following this approach. The proofs of both results are based on pattern-avoiding permutations. Finally, we empirically compute the minimum cardinality of complete sets of representations for small n. Our computations directly suggest two conjectures, connecting well-known Baxter permutations with the set of permutations avoiding an apparently new pattern, which in turn seem to generate complete sets of representations of minimum cardinality

Analysis and implementation of distributed algorithms for multi-robot systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 159-166).Distributed algorithms for multi-robot systems rely on network communications to share information. However, the motion of the robots changes the network topology, which affects the information presented to the algorithm. For an algorithm to produce accurate output, robots need to communicate rapidly enough to keep the network topology correlated to their physical configuration. Infrequent communications will cause most multirobot distributed algorithms to produce less accurate results, and cause some algorithms to stop working altogether. The central theme of this work is that algorithm accuracy, communications bandwidth, and physical robot speed are related. This thesis has three main contributions: First, I develop a prototypical multi-robot application and computational model, propose a set of complexity metrics to evaluate distributed algorithm performance on multi-robot systems, and introduce the idea of the robot speed ratio, a dimensionless measure of robot speed relative to message speed in networks that rely on multi-hop communication. The robot speed ratio captures key relationships between communications bandwidth, mobility, and algorithm accuracy, and can be used at design time to trade off between them. I use this speed ratio to evaluate the performance of existing distributed algorithms for multi-hop communication and navigation. Second, I present a definition of boundaries in multi-robot systems, and develop new distributed algorithms to detect and characterize them. Finally, I define the problem of dynamic task assignment, and present four distributed algorithms that solve this problem, each representing a different trade-off between accuracy, running time, and communication resources. All the algorithms presented in this work are provably correct under ideal conditions and produce verifiable real-world performance.(cont.) They are self-stabilizing and robust to communications failures, population changes, and other errors. All the algorithms were tested on a swarm of 112 robots.by James Dwight McLurkin, IV.Ph.D

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

We revisit the symbolic verification of Markov chains with respect to finite horizon reachability properties. The prevalent approach iteratively computes step-bounded state reachability probabilities. By contrast, recent advances in probabilistic inference suggest symbolically representing all horizon-length paths through the Markov chain. We ask whether this perspective advances the state-of-the-art in probabilistic model checking. First, we formally describe both approaches in order to highlight their key differences. Then, using these insights we develop Rubicon, a tool that transpiles Prism models to the probabilistic inference tool Dice. Finally, we demonstrate better scalability compared to probabilistic model checkers on selected benchmarks. All together, our results suggest that probabilistic inference is a valuable addition to the probabilistic model checking portfolio -- with Rubicon as a first step towards integrating both perspectives.Comment: Technical Report. Accepted at CAV 202

Towards a fully mobile publish/subscribe system

93 p.This PhD thesis makes contributions to support mobility and fault tolerance in a publish/subscribe system. Two protocols are proposed in order to support mobility of all devices in the system, including inside the event notification service. The protocols are designed with the idea that any change due to mobility is completely beyond our control and ability to predict. Moreover, the proposed solutions do not need to know neither the amount of nodes in the system nor their identities before starting, the system is able to adapt to new devices or disconnections and is able to keep operating correctly in a partitioned network. To do so we extend a previously proposed framework called Phoenix that already supported client mobility. Both protocols use a leader election mechanism to create a communication tree in a highly dynamic environment, and use a characteristic of that algorithm to detect topology changes and migrate nodes accordingly

Neuro-RAM Unit with Applications to Similarity Testing and Compression in Spiking Neural Networks

We study distributed algorithms implemented in a simplified biologically inspired model for stochastic spiking neural networks. We focus on tradeoffs between computation time and network complexity, along with the role of noise and randomness in efficient neural computation. It is widely accepted that neural spike responses, and neural computation in general, is inherently stochastic. In recent work, we explored how this stochasticity could be leveraged to solve the \u27winner-take-all\u27 leader election task. Here, we focus on using randomness in neural algorithms for similarity testing and compression. In the most basic setting, given two n-length patterns of firing neurons, we wish to distinguish if the patterns are equal or epsilon-far from equal. Randomization allows us to solve this task with a very compact network, using O((sqrt(n) log n)/epsilon) auxiliary neurons, which is sublinear in the input size. At the heart of our solution is the design of a t-round neural random access memory, or indexing network, which we call a neuro-RAM. This module can be implemented with O(n/t) auxiliary neurons and is useful in many applications beyond similarity testing - e.g., we discuss its application to compression via random projection. Using a VC dimension-based argument, we show that the tradeoff between runtime and network size in our neuro-RAM is nearly optimal. To the best of our knowledge, we are the first to apply these techniques to stochastic spiking networks. Our result has several implications - since our neuro-RAM can be implemented with deterministic threshold gates, it demonstrates that, in contrast to similarity testing, randomness does not provide significant computational advantages for this problem. It also establishes a separation between our networks, which spike with a sigmoidal probability function, and well-studied deterministic sigmoidal networks, whose gates output real number values, and which can implement a neuro-RAM much more efficiently

Creation and maintenance of a communication tree in wireless sensor networks

A local reconfiguration algorithm (INP) for reliable routing in wireless sensor networks that consist of many static (fixed) energy-constrained nodes is introduced in the dissertation. For routing around crash fault nodes, a communication tree structure connecting sensor nodes to the base station (sink or root) is dynamically reconfigured during information dissemination. Unlike other location based routing approaches, INP does not take any support from a high costing system that gives position information such as GPS. For reconfigurations, INP uses only local relational information in the tree structure among nearby nodes by collaboration between the nodes that does not need global maintenance, so that INP is energy efficient and it scales to large sensor networks. The performance of the algorithm is compared to the single path with repair routing scheme (SWR) that uses a global metric and the modified GRAdient broadcast scheme (GRAB-F) that uses interleaving multiple paths by computation and by simulations. The comparisons demonstrate that using local relative information is mostly enough for reconfigurations, and it consumes less energy and mostly better delivery rates than other algorithms especially in dense environments. For the control observer to know the network health status, two new diagnosis algorithms (Repre and Local) that deal with crash faults for wireless sensor networks are also introduced in the dissertation. The control observer knows not only the static faults found by periodic testing but also the dynamic faults found by a path reconfiguration algorithm like INP that is invoked from evidence during information dissemination. With based on this information, the control observer properly treats the network without lateness. Local algorithm is introduced for providing scalability to reduce communication energy consumption when the network size grows. The performance of these algorithms is computationally compared with other crash faults identification algorithm (WSNDiag). The comparisons demonstrate that maintaining the communication tree with local reconfigurations in Repre and Local needs less energy than making a tree per each diagnosis procedure in WSNDiag. They also demonstrate that providing scalability in Local needs less energy than other approaches