arXiv subjects

Maria Potop-Butucaru

Publications and source records attributed to Maria Potop-Butucaru.

42 records · Page 3Linked to original sources

arXiv2010

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 $O(\log^2n)$ bits and it converges in $O(n^2)$ 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 $O(\log^2n)$ bits.

cs.DC↗

arXiv2010

Universal Loop-Free Super-Stabilization

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). Our 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.

cs.DC↗

arXiv2009

Optimal deterministic ring exploration with oblivious asynchronous robots

We consider the problem of exploring an anonymous unoriented ring of size $n$ by $k$ identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that $k$ must not divide $n$ for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size $n$ is 4. An upper bound of 17 robots holds in the deterministic case while 4 probabilistic robots are sufficient. In this paper, we close the complexity gap in the deterministic setting, by proving that no deterministic exploration is feasible with less than five robots whenever the size of the ring is even, and that five robots are sufficient for any $n$ that is coprime with five. Our protocol completes exploration in O(n) robot moves, which is also optimal.

cs.DS↗

arXiv2009

Byzantine Convergence in Robots Networks: The Price of Asynchrony

We study the convergence problem in fully asynchronous, uni-dimensional robot networks that are prone to Byzantine (i.e. malicious) failures. In these settings, oblivious anonymous robots with arbitrary initial positions are required to eventually converge to an a apriori unknown position despite a subset of them exhibiting Byzantine behavior. Our contribution is twofold. We propose a deterministic algorithm that solves the problem in the most generic settings: fully asynchronous robots that operate in the non-atomic CORDA model. Our algorithm provides convergence in 5f+1-sized networks where f is the upper bound on the number of Byzantine robots. Additionally, we prove that 5f+1 is a lower bound whenever robot scheduling is fully asynchronous. This constrasts with previous results in partially synchronous robots networks, where 3f+1 robots are necessary and sufficient.

cs.DC↗

arXiv2009

Optimal Byzantine Resilient Convergence in Asynchronous Robot Networks

We propose the first deterministic algorithm that tolerates up to $f$ byzantine faults in $3f+1$-sized networks and performs in the asynchronous CORDA model. Our solution matches the previously established lower bound for the semi-synchronous ATOM model on the number of tolerated Byzantine robots. Our algorithm works under bounded scheduling assumptions for oblivious robots moving in a uni-dimensional space.

cs.DC↗

arXiv2009

Optimal byzantine resilient convergence in oblivious robot networks

Given a set of robots with arbitrary initial location and no agreement on a global coordinate system, convergence requires that all robots asymptotically approach the exact same, but unknown beforehand, location. Robots are oblivious-- they do not recall the past computations -- and are allowed to move in a one-dimensional space. Additionally, robots cannot communicate directly, instead they obtain system related information only via visual sensors. We draw a connection between the convergence problem in robot networks, and the distributed \emph{approximate agreement} problem (that requires correct processes to decide, for some constant $ε$, values distance $ε$ apart and within the range of initial proposed values). Surprisingly, even though specifications are similar, the convergence implementation in robot networks requires specific assumptions about synchrony and Byzantine resilience. In more details, we prove necessary and sufficient conditions for the convergence of mobile robots despite a subset of them being Byzantine (i.e. they can exhibit arbitrary behavior). Additionally, we propose a deterministic convergence algorithm for robot networks and analyze its correctness and complexity in various synchrony settings. The proposed algorithm tolerates f Byzantine robots for (2f+1)-sized robot networks in fully synchronous networks, (3f+1)-sized in semi-synchronous networks. These bounds are optimal for the class of cautious algorithms, which guarantee that correct robots always move inside the range of positions of the correct robots.

cs.DC↗