Maria Gradinariu Potop-Butucaru

Exclusive perpetual ring exploration without chirality

In this paper, we study the exclusive perpetual exploration problem with mobile anonymous and oblivious robots in a discrete space. Our results hold for the most generic settings: robots are asynchronous and are not given any sense of direction, so the left and right sense (i.e. chirality) is decided by the adversary that schedules robots for execution, and may change between invocations of a particular robots (as robots are oblivious). We investigate both the minimal and the maximal number of robots that are necessary and sufficient to solve the exclusive perpetual exploration problem. On the minimal side, we prove that three deterministic robots are necessary and sufficient, provided that the size n of the ring is at least 10, and show that no protocol with three robots can exclusively perpetually explore a ring of size less than 10. On the maximal side, we prove that k = n - 5 robots are necessary and sufficient to exclusively perpetually explore a ring of size n when n is coprime with k.

A new self-stabilizing minimum spanning tree construction with loop-free property

The minimum spanning tree (MST) construction is a classical problem in Distributed Computing for creating a globally minimized structure distributedly. Self-stabilization is versatile technique for forward recovery that permits to handle any kind of transient faults in a unified manner. The loopfree property provides interesting safety assurance in dynamic networks where edge-cost changes during operation of the protocol. n nWe present a new self-stabilizing MST protocol that improves on previous known approaches in several ways. First, it makes fewer system hypotheses as the size of the network (or an upper bound on the size) need not be known to the participants. Second, it is loop-free in the sense that it guarantees that a spanning tree structure is always preserved while edge costs change dynamically and the protocol adjusts to a new MST. Finally, time complexity matches the best known results, while space complexity results show that this protocol is the most efficient to date.

Fast Self-stabilizing Minimum Spanning Tree Construction

We present a novel self-stabilizing algorithm for minimum spanning tree (MST) construction. The space complexity of our solution is O(log2 n) bits and it converges in O(n2) rounds. Thus, this algorithm improves the convergence time of all previously known self-stabilizing asynchronous MST algorithms by a multiplicative factor Θ(n), to the price of increasing the best known space complexity by a factor O(log n). The main ingredient used in our algorithm is the design, for the first time in self-stabilizing settings, of a labeling scheme for computing the nearest common ancestor with only O(log2 n) bits.

Brief announcement : discovering and assessing fine-grained metrics in robot networks protocols

In discrete anonymous environments, robot algorithms consist in a list of rules, where each rule takes a configuration of the system as input and outputs the set of robots that are required to move when the system is in this configuration. Based on these rules and on the robots activations by the scheduler, the system globally evolves and, when the algorithm is correct, it solves the targeted problem.

A super-stabilizing log(n)-approximation algorithm for dynamic Steiner trees

This paper proposes a fully dynamic self-stabilizing algorithm for the dynamic Steiner tree problem. The Steiner tree problem aims at constructing a Minimum Spanning Tree (MST) over a subset of nodes called Steiner members, or Steiner group usually denoted S. Steiner trees are good candidates to efficiently implement communication primitives such as publish/subscribe or multicast, essential building blocks in the design of middleware architectures for the new emergent networks (e.g., P2P, sensor or adhoc networks). Our algorithm returns a log(|S|)-approximation of the optimal Steiner tree. It improves over existing solutions in several ways. First, it is fully dynamic, in other words it withstands the dynamism when both the group members and ordinary nodes can join or leave the network. Next, our algorithm is self-stabilizing, that is, it copes with nodes memory corruption. Last but not least, our algorithm is super-stabilizing. That is, while converging to a correct configuration (i.e., a Steiner tree) after a modification of the network, it keeps offering the Steiner tree service during the stabilization time to all members that have not been affected by this modification.

A Superstabilizing log(n)-Approximation Algorithm for Dynamic Steiner Trees

This paper proposes a fully dynamic self-stabilizing algorithm for the Steiner tree problem. The Steiner tree problem aims at constructing a Minimum Spanning Tree (MST) over a subset of nodes called Steiner members, or Steiner group usually denoted S . Steiner trees are good candidates to efficiently implement communication primitives such as publish/subscribe or multicast, essential building blocks in the design of middleware architectures for the new emergent networks (e.g. P2P, sensor or adhoc networks). Our algorithm returns a log|S |-approximation of the optimal Steiner tree. It improves over existing solutions in several ways. First, it is fully dynamic, in other words it withstands the dynamism when both the group members and ordinary nodes can join or leave the network. Next, our algorithm is self-stabilizing, that is, it copes with nodes memory corruption. Last but not least, our algorithm is superstabilizing . That is, while converging to a correct configuration (i.e., a Steiner tree) after a modification of the network, it keeps offering the Steiner tree service during the stabilization time to all members that have not been affected by this modification.

A framework for secure and private P2P publish/subscribe

We propose a novel and totally decentralized strategy for private and secure data exchange in peer-to-peer systems. Our scheme is particularly appealing for point-to-point exchanges and use zero-knowledge mechanisms to preserve privacy. Furthermore, we show how to plug our private and secure data exchange module in existing publish/subscribe architectures. Our proposal enriches the original system with security and privacy making it resilient to a broad class of attacks (e.g. brute-force, eavesdroppers, man-in-the middle or malicious insiders). Additionally, the original properties of the publish/subscribe system are preserved without any degradation. A nice feature of our proposal is the reduce message cost: only one extra message is sent for every message sent in the original system. Note that our contribution is more conceptual than experimental and can be easily exploited by new emergent areas such as P2P Internet Games or Social Networks where a major trend is to achieve a secure and private communication without relying on any fixed infrastructure or centralized authority.

Flocking with Oblivious Robots

We propose a new self-stabilizing flocking algorithm for oblivious robot networks, and prove its correctness. With this algorithm, a flock head emerges from a uniform flock of robots, and the algorithm allows those robots to follow the head, whatever its direction on the plane. Robots are oblivious in that they do not recall the result of their previous computations and do not share a common coordinate system.