Computing in Additive Networks with Bounded-Information Codes

This paper studies the theory of the additive wireless network model, in which the received signal is abstracted as an addition of the transmitted signals. Our central observation is that the crucial challenge for computing in this model is not high contention, as assumed previously, but rather guaranteeing a bounded amount of \emph{information} in each neighborhood per round, a property that we show is achievable using a new random coding technique. Technically, we provide efficient algorithms for fundamental distributed tasks in additive networks, such as solving various symmetry breaking problems, approximating network parameters, and solving an \emph{asymmetry revealing} problem such as computing a maximal input. The key method used is a novel random coding technique that allows a node to successfully decode the received information, as long as it does not contain too many distinct values. We then design our algorithms to produce a limited amount of information in each neighborhood in order to leverage our enriched toolbox for computing in additive networks

Memory lower bounds for deterministic self-stabilization

In the context of self-stabilization, a \emph{silent} algorithm guarantees that the register of every node does not change once the algorithm has stabilized. At the end of the 90's, Dolev et al. [Acta Inf. '99] showed that, for finding the centers of a graph, for electing a leader, or for constructing a spanning tree, every silent algorithm must use a memory of $\Omega(\log n)$ bits per register in $n$-node networks. Similarly, Korman et al. [Dist. Comp. '07] proved, using the notion of proof-labeling-scheme, that, for constructing a minimum-weight spanning trees (MST), every silent algorithm must use a memory of $\Omega(\log^2n)$ bits per register. It follows that requiring the algorithm to be silent has a cost in terms of memory space, while, in the context of self-stabilization, where every node constantly checks the states of its neighbors, the silence property can be of limited practical interest. In fact, it is known that relaxing this requirement results in algorithms with smaller space-complexity. In this paper, we are aiming at measuring how much gain in terms of memory can be expected by using arbitrary self-stabilizing algorithms, not necessarily silent. To our knowledge, the only known lower bound on the memory requirement for general algorithms, also established at the end of the 90's, is due to Beauquier et al.~[PODC '99] who proved that registers of constant size are not sufficient for leader election algorithms. We improve this result by establishing a tight lower bound of $\Theta(\log \Delta+\log \log n)$ bits per register for self-stabilizing algorithms solving $(\Delta+1)$-coloring or constructing a spanning tree in networks of maximum degree~$\Delta$. The lower bound $\Omega(\log \log n)$ bits per register also holds for leader election

Symmetry Breaking for Answer Set Programming

In the context of answer set programming, this work investigates symmetry detection and symmetry breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We contribute a reduction of symmetry detection to a graph automorphism problem which allows to extract symmetries of a logic program from the symmetries of the constructed coloured graph. We also propose an encoding of symmetry-breaking constraints in terms of permutation cycles and use only generators in this process which implicitly represent symmetries and always with exponential compression. These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be applied to any existing answer set solver. We demonstrate computational impact on benchmarks versus direct application of the solver. Furthermore, we explore symmetry breaking for answer set programming in two domains: first, constraint answer set programming as a novel approach to represent and solve constraint satisfaction problems, and second, distributed nonmonotonic multi-context systems. In particular, we formulate a translation-based approach to constraint answer set solving which allows for the application of our symmetry detection and symmetry breaking methods. To compare their performance with a-priori symmetry breaking techniques, we also contribute a decomposition of the global value precedence constraint that enforces domain consistency on the original constraint via the unit-propagation of an answer set solver. We evaluate both options in an empirical analysis. In the context of distributed nonmonotonic multi-context system, we develop an algorithm for distributed symmetry detection and also carry over symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201

Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls

In this paper we investigate the possibility of reducing the complexity of a system composed of a large number of interacting agents, whose dynamics feature a symmetry breaking. We consider first order stochastic differential equations describing the behavior of the system at the particle (i.e., Lagrangian) level and we get its continuous (i.e., Eulerian) counterpart via a kinetic description. However, the resulting continuous model alone fails to describe adequately the evolution of the system, due to the loss of granularity which prevents it from reproducing the symmetry breaking of the particle system. By suitably coupling the two models we are able to reduce considerably the necessary number of particles while still keeping the symmetry breaking and some of its large-scale statistical properties. We describe such a multiscale technique in the context of opinion dynamics, where the symmetry breaking is induced by the results of some opinion polls reported by the media