Digraphs Exploration with Little Memory - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2004

Digraphs Exploration with Little Memory

Pierre Fraigniaud
  • Fonction : Auteur
  • PersonId : 835294
David Ilcinkas

Résumé

A mobile entity (e.g., a software agent or a robot) has to explore a graph whose nodes are unlabeled and edge ports are locally labeled at each node. The entity has no {\sl a priori} knowledge of the topology of the graph or of its size. Its task is to traverse all the edges of the graph, and to stop once this is achieved. In order to perform this task, the mobile entity must be given the ability to put markers at nodes. We thus consider two models: the {\em robot model} specifies that the mobile entity (called robot) is given a pebble that can be dropped and removed at nodes; the {\em agent model} specifies that the mobile entity (called agent) has the ability to let messages on whiteboards available at each node. Under the robot model, we show that the robot needs $\Omega(n\log{d})$ bits of memory to perform exploration of digraphs with $n$ nodes and maximum out-degree $d$. We then describe an algorithm that allows exploration of any $n$-node digraph with maximum out-degree $d$ to be accomplished by a robot with a memory of size $O(nd\log{n})$ bits. Under the agent model, we show that digraph exploration cannot be achieved by an agent with no memory. We then describe an exploration algorithm for an agent with a constant-size memory, using a whiteboard of size $O(\log{d})$ bits at every node of out-degree $d$. This latter algorithm shows that the data-structure used by a robot for exploration can be optimally distributed among all nodes.
Fichier principal
Vignette du fichier
STACS2004.pdf (188.49 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00339719 , version 1 (18-11-2008)

Identifiants

Citer

Pierre Fraigniaud, David Ilcinkas. Digraphs Exploration with Little Memory. STACS 2004, Mar 2004, Montpellier, France. pp.246-257, ⟨10.1007/978-3-540-24749-4_22⟩. ⟨hal-00339719⟩
243 Consultations
176 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More