Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0708.0909

On the Self-stabilization of Mobile Robots in Graphs

Lélia Blin·Maria Gradinariu Potop-Butucaru·Sébastien Tixeuil
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

cs.DScs.DC

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Lélia Blin, Maria Gradinariu Potop-Butucaru, Sébastien Tixeuil. 2007-08-08. On the Self-stabilization of Mobile Robots in Graphs. https://arxiv.org/abs/0708.0909

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Computational complexity of the recoverable robust shortest path problem in acyclic digraphs under interval budgeted uncertainty

In this paper, we consider the recoverable robust shortest path problem in acyclic digraphs, employing interval budgeted uncertainty to model uncertain second-stage costs. For the continuous budgeted uncertainty model, we prove that the problem is strongly NP-hard even in layered digraphs. Furthermore, we show that in general acyclic digraphs, the problem cannot be approximated within any constant factor unless $\mathrm{P} = \mathrm{NP}$, nor can it be approximated within a factor of $2^{\log^{1-ε} n}$ for any $ε> 0$ unless $\mathrm{NP} \subseteq \mathrm{DTIME}(n^{\mathrm{poly} \log n})$. For the discrete budgeted uncertainty model, we show that the problem is not approximable unless $\mathrm{P} = \mathrm{NP}$, even in layered digraphs. Finally, we establish that under continuous budgeted uncertainty, the integrality gap of a relaxation allowing a fractional first-stage solution is at least $Ω(\sqrt{n})$.

cs.DS↗
arXiv2026

Odd and Even Harder Problems on Cycle-Factors

For a graph (undirected or directed), a cycle-factor is a collection of vertex-disjoint cycles covering the entire vertex set. Cycle-factors subject to parity constraints arise naturally in the study of structural graph theory and algorithmic complexity. In this work, we study four variants of the problem of finding a cycle-factor subject to the following parity constraints: (1) all cycles are odd, (2) all cycles are even, (3) at least one cycle is odd, and (4) at least one cycle is even. We show that all the variants of the problem are NP-complete both in undirected and directed graphs, even if each vertex is incident to at most three edges. We also prove that the first two variants are NP-complete even for planar directed graphs.

cs.DS↗
arXiv2026

An $n^{8/5+o(1)}$-Time $Ω(λ^3)$-Approximation for Longest Common Subsequence

Let $λ$ denote the ratio of the length of a longest common subsequence of two length-$n$ strings to $n$. Rubinstein, Seddighin, Song and Sun [RSSS19] gave an $Ω(λ^3)$-approximation for LCS running in $\widetilde O(n^{39/20})$ time, where $39/20=1.95$. Song [Son19] mentioned that improving the $n^{1.95}$ running time is an interesting open question. We give an algorithm that computes an $Ω(λ^3)$-approximation of the longest common subsequence in $n^{8/5+o(1)}$ time. This improves the exponent $1.95$ to $1.6+o(1)$.

cs.DS↗