Tight Bounds for Black Hole Search with Scattered Agents in Synchronous Rings

We study the problem of locating a particularly dangerous node, the so-called black hole in a synchronous anonymous ring network with mobile agents. A black hole is a harmful stationary process residing in a node of the network and destroying destroys all mobile agents visiting that node without leaving any trace. We consider the more challenging scenario when the agents are identical and initially scattered within the network. Moreover, we solve the problem with agents that have constant-sized memory and carry a constant number of identical tokens, which can be placed at nodes of the network. In contrast, the only known solutions for the case of scattered agents searching for a black hole, use stronger models where the agents have non-constant memory, can write messages in whiteboards located at nodes or are allowed to mark both the edges and nodes of the network with tokens. This paper solves the problem for ring networks containing a single black hole. We are interested in the minimum resources (number of agents and tokens) necessary for locating all links incident to the black hole. We present deterministic algorithms for ring topologies and provide matching lower and upper bounds for the number of agents and the number of tokens required for deterministic solutions to the black hole search problem, in oriented or unoriented rings, using movable or unmovable tokens

Black Hole Search with Finite Automata Scattered in a Synchronous Torus

We consider the problem of locating a black hole in synchronous anonymous networks using finite state agents. A black hole is a harmful node in the network that destroys any agent visiting that node without leaving any trace. The objective is to locate the black hole without destroying too many agents. This is difficult to achieve when the agents are initially scattered in the network and are unaware of the location of each other. Previous studies for black hole search used more powerful models where the agents had non-constant memory, were labelled with distinct identifiers and could either write messages on the nodes of the network or mark the edges of the network. In contrast, we solve the problem using a small team of finite-state agents each carrying a constant number of identical tokens that could be placed on the nodes of the network. Thus, all resources used in our algorithms are independent of the network size. We restrict our attention to oriented torus networks and first show that no finite team of finite state agents can solve the problem in such networks, when the tokens are not movable. In case the agents are equipped with movable tokens, we determine lower bounds on the number of agents and tokens required for solving the problem in torus networks of arbitrary size. Further, we present a deterministic solution to the black hole search problem for oriented torus networks, using the minimum number of agents and tokens

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Faulty node repair and dynamically spawned black hole search

New threats to networks are constantly arising. This justifies protecting network assets and mitigating the risk associated with attacks. In a distributed environment, researchers aim, in particular, at eliminating faulty network entities. More specifically, much research has been conducted on locating a single static black hole, which is defined as a network site whose existence is known a priori and that disposes of any incoming data without leaving any trace of this occurrence. However, the prevalence of faulty nodes requires an algorithm able to (a) identify faulty nodes that can be repaired without human intervention and (b) locate black holes, which are taken to be faulty nodes whose repair does require human intervention. In this paper, we consider a specific attack model that involves multiple faulty nodes that can be repaired by mobile software agents, as well as a virus v that can infect a previously repaired faulty node and turn it into a black hole. We refer to the task of repairing multiple faulty nodes and pointing out the location of the black hole as the Faulty Node Repair and Dynamically Spawned Black Hole Search. Wefirst analyze the attack model we put forth. We then explain (a) how to identify whether a node is either (1) a normal node or (2) a repairable faulty node or (3) the black hole that has been infected by virus v during the search/repair process and, (b) how to perform the correct relevant actions. These two steps constitute a complex task, which, we explain, significantly differs from the traditional Black Hole Search. We continue by proposing an algorithm to solve this problem in an

Searching for black holes in subways.

Abstract Current mobile agent algorithms for mapping faults in computer networks assume that the network is static. However, for large classes of highly dynamic networks (e.g., wireless mobile ad hoc networks, sensor networks, vehicular networks), the topology changes as a function of time. These networks, called delay-tolerant, challenged, opportunistic, etc., have never been investigated with regard to locating faults. We consider a subclass of these networks modelled on an urban subway system. We examine the problem of creating a map of such a subway. More precisely, we study the problem of a team of asynchronous computational entities (the mapping agents) determining the location of black holes in a highly dynamic graph, whose edges are defined by the asynchronous movements of mobile entities (the subway carriers). We determine necessary conditions for the problem to be solvable. We then present and analyze a solution protocol; we show that our algorithm solves the fault mapping problem in subway networks with the minimum number of agents possible, k = γ + 1, where γ is the number of carrier stops at black holes. The number of carrier moves between stations required by the algorithm in the worst case is , where n C is the number of subway trains, and l R is the length of the subway route with the most stops. We establish lower bounds showing that this bound is tight. Thus, our protocol is both agent-optimal and move-optimal

Recherche optimale de trou noir avec cailloux

National audienceUn trou noir est un noeud d'un réseau qui détruit tout agent (ou robot) y entrant sans laisser de trace détectable. L'emplacement du trou noir doit être déterminé par une une équipe d'agents mobiles identiques déployée à partir d'un emplacement sain. Pratiquement tous les résultats existants pour des agents asynchrones supposent la présence à chaque noeud d'une mémoire partagée (tableau blanc), de taille logarithmique, sur laquelle les agents peuvent lire et écrire. Un méchanisme moins puissant et moins exigeant consiste en l'utilisation de cailloux identiques (qui peuvent être déposés sur les noeuds, repris, et transportés par les agents), traditionnellement employés pour l'exploration de graphes sains (i.e. sans trou noir). Deux résultats récents montrent qu'il est possible d'utiliser des cailloux comme moyen de communication pour la recherche de trou noir. Ces résultats autorisent cependant les cailloux à être placés non seulement sur les noeuds mais aussi sur les liens. Ils supposent également que les liens sont FIFO. Dans ce papier, nous considérons le modèle des cailloux idéaux, c'est-à-dire le modèle où un caillou ne peut être placé que sur les noeuds, et pas plus d'un caillou ne peut être placé sur un noeud donné. Nous prouvons que pour les réseaux de topologie connue il est possible d'obtenir exactement les mêmes bornes optimales en utilisant des cailloux idéaux qu'en utilisant des tableaux blancs, et ce même si les liens ne sont pas FIFO. Plus précisément, nous prouvons qu'une équipe de deux agents asynchrones, chacun équipé d'un seul caillou indistinguable (qui ne peut être placé que sur les noeuds, avec au plus un caillou par noeud), peut localiser le trou noir. Ce résultat est obtenu en utilisant le nombre optimal de mouvements $\Theta(n\log{n})$, où n est le nombre de noeuds. Pour résumer, nous fournissons la première preuve que, pour la recherche de trou noir, le modèle des cailloux idéaux est aussi puissant que le modèle des tableaux blancs