Maria Potop-Butucaru

Self-stabilizing minimum degree spanning tree within one from the optimal degree

We propose a self-stabilizing algorithm for constructing a Minimum Degree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most @D^*+1, where @D^* is the minimum possible maximum degree of a spanning tree of the network. To the best of our knowledge, our algorithm is the first self-stabilizing solution for the construction of a minimum degree spanning tree in undirected graphs. The algorithm uses only local communications (nodes interact only with the neighbors at one hop distance). Moreover, the algorithm is designed to work in any asynchronous message passing network with reliable FIFO channels. Additionally, we use a fine grained atomicity model (i.e., the send/receive atomicity). The time complexity of our solution is O(mn^2logn) where m is the number of edges and n is the number of nodes. The memory complexity is O(@dlogn) in the send-receive atomicity model (@d is the maximal degree of the network).

Stabilizing data-link over non-FIFO channels with optimal fault-resilience

Self-stabilizing systems have the ability to converge to a correct behavior when started in any configuration. Most of the work done so far in the self-stabilization area assumed either communication via shared memory or via FIFO channels. This paper is the first to lay the bases for the design of self-stabilizing message passing algorithms over unreliable non-FIFO channels. We propose an optimal stabilizing data-link layer that emulates a reliable FIFO communication channel over unreliable capacity bounded non-FIFO channels (the channel capacity is known to the protocol).

Loop-free super-stabilizing spanning tree construction

We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). n nOur scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of both worlds: super-stabilization, loop-freedom, and optimization of the original metric without any stabilization time penalty. As case study we apply our composition mechanism to two well known metric-dependent spanning trees: the maximum-flow tree and the minimum degree spanning tree.

Stabilizing Distributed R-Trees for Peer-to-Peer Content Routing

Publish/subscribe systems provide useful platforms for delivering data (events) from publishers to subscribers in a decoupled fashion. Developing efficient publish/subscribe schemes in dynamic distributed systems is still an open problem for complex subscriptions (spanning multidimensional intervals). We propose a distributed R-tree (DR-tree) structure that uses R-tree-based spatial filters to construct a peer-to-peer overlay optimized for scalable and efficient selective dissemination of information. We adapt well-known variants of R-trees to organize publishers and subscribers in balanced peer-to-peer networks that support content-based filtering in publish/subscribe systems. DR-tree overlays guarantee subscription and publication times logarithmic in the size of the network while keeping space requirements low (comparable to distributed hash tables). The maintenance of the overlay is local and the structure is balanced with height logarithmic in the number of nodes. DR-tree overlays disseminate messages with no false negatives and very few false positives in the embedded publish/subscribe system. In addition, we propose self-stabilizing algorithms that guarantee consistency despite failures and changes in the peer population.

Self-stabilizing minimum-degree spanning tree within one from the optimal degree

We propose a self-stabilizing algorithm for constructing a Minimum-Degree Spanning Tree (MDST) in undirected networks. Starting from an arbitrary state, our algorithm is guaranteed to converge to a legitimate state describing a spanning tree whose maximum node degree is at most Δ*+ 1, where Δ* is the minimum possible maximum degree of a spanning tree of the network. To the best of our knowledge our algorithm is the first self-stabilizing solution for the construction of a minimum-degree spanning tree in undirected graphs. The algorithm uses only local communications (nodes interact only with the neighbors at one hop distance). Moreover, the algorithm is designed to work in any asynchronous message passing network with reliable FIFO channels. Additionally, we use a fine grained atomicity model (i.e. the send/receive atomicity). The time complexity of our solution is O(mn2 log n) where m is the number of edges and n is the number of nodes. The memory complexity is O(δ log n) in the send-receive atomicity model (δ is the maximal degree of the network).

On the self-stabilization of mobile robots in graphs

Self-stabilization is a versatile technique to withstand any transient fault in a distributed system. Mobile robots (or agents) are one of the emerging trends in distributed computing as they mimic autonomous biologic entities. The contribution of this paper is threefold. First, we present a new model for studying mobile entities in networks subject to transient faults. Our model differs from the classical robot model because robots have constraints about the paths they are allowed to follow, and from the classical agent model because the number of agents remains fixed throughout the execution of the protocol. Second, in this model, we study the possibility of designing self-stabilizing algorithms when those algorithms are run by mobile robots (or agents) evolving on a graph. We concentrate on the core building blocks of robot and agents problems: naming and leader election. Not surprisingly, when no constraints are given on the network graph topology and local execution model, both problems are impossible to solve. Finally, using minimal hypothesis with respect to impossibility results, we provide deterministic and probabilistic solutions to both problems, and show equivalence of these problems by an algorithmic reduction mechanism.

Research note: Self-stabilizing byzantine asynchronous unison

We explore asynchronous unison in the presence of systemic transient and permanent Byzantine faults in shared memory. We observe that the problem is not solvable under a less than strongly fair scheduler or for system topologies with maximum node degree greater than two. We present then a self-stabilizing Byzantine-tolerant solution to asynchronous unison for chain and ring topologies under the central strongly fair daemon. Our algorithm has minimum possible containment radius and optimal stabilization time.

Brief Announcement: Distributed Ledger Technology meets Distributed Shared Register Theory

We prove that the Buchi topology, the automatic topology, the alphabetic topology and the strong alphabetic topology are Polish, and provideconsequences of this. We also show that this cannot be fully extended to the case of a space of infinite labelled binary trees; in particular the Buchi and the Muller topologies in that case are not Polish.Proof-functional logical connectives allow reasoning about the structure of logical proofs, so de facto giving to the latter the status of first-class objects. This is in contrast to classical truth-functional connectives where the meaning of a compound formula is dependent only on the truth value of its subformulas. But also with intuitionistic connectives, where only the existence of certain constructions matters, and not their actual shape. Typed lambda-calculi can serve as formalisms to study proofs as objects and to explore the semantics of logical connectives. At the same time, lambda-calculi with intersection and union types have been studied as tools for analyzing the reduction behavior of terms. The connection between intersection and union types with logics is less clear. Sometimes they are considered the counterpart of proof-functional logical operators, sometimes they are injected (compiled) into well-known logics, such as Combinatory Logic. As such, there is no consensus about which lambda-calculus should be taken as a proof-language for logics corresponding to intersection and union type assignment. In this paper we present a typed lambda calculus, enriched with products, coproducts, explicit coercions, and a related proof-functional logics. This calculus, directly derived by the typed calculus of Dougherty-Liquori, has been proved isomorphic to the Barbanera-Dezani-deLiguoro type assignment system. We also present a logic L∩∪ featuring two proof-functional connectives, namely strong conjunction and strong disjunction. The logics is suitable to be extended with relevant implication , inspired by the B + Relevant Logic of Meyer-Routley. We prove the typed calculus to be isomorphic to the logics L∩∪ and we give a realizability semantics using Mints realizers and a completeness theorem. A prototype implementation is referred.This paper introduces Distributed Ledger Register that mimics the behavior of most popular ledgers such as Bitcoin or Ethereum. Our work is the first to make the connection between the Distributed Ledger Register and the classical theory of shared registers. We furthermore, propose an algorithm that emulates the distributed ledger register.We study a natural extension to the well-known convex hull problem by introducing multiplicity: if we are given a set of convex polygons, and we are allowed to partition the set into multiple components and take the convex hull of each individual component, what is the minimum total sum of the perimeters of the convex hulls? We show why this problem is intriguing, and then introduce a novel algorithm with a run-time cubic in the total number of vertices. In the case that the input polygons are disjoint, we show an optimization that achieves a run-time that, in most cases, is cubic in the total number of polygons, within a logarithmic factor.The knapsack problem is a classic optimisation problem that has been recently extended in the setting of groups. Its study reveals to be interesting since it provides many different behaviours, depending on the considered class of groups. In this paper we deal with groups generated by Mealy automata—a class that is often used to study group-theoretical conjectures—and prove that the knapsack problem is undecidable for this class. In a second time, we construct a graph that, if finite, provides a solution to the knapsack problem. We deduce that the knapsack problem is decidable for the so-called bounded automaton groups, a class where the order and conjugacy problems are already known to be decidable.