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30
Searching for a black hole in arbitrary networks
 Distributed Computing
, 2002
"... Consider a networked environment, supporting mobile agents, where there is a black hole: a harmful host that disposes of visiting agents upon their arrival, leaving no observable trace of such a destruction. The black hole search problem is the one of assembling a team of asynchronous mobile agents, ..."
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Cited by 48 (25 self)
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Consider a networked environment, supporting mobile agents, where there is a black hole: a harmful host that disposes of visiting agents upon their arrival, leaving no observable trace of such a destruction. The black hole search problem is the one of assembling a team of asynchronous mobile agents, executing the same protocol and communicating by means of whiteboards, to successfully identify the location of the black hole; we are concerned with solutions that are generic (i.e., topologyindependent). We establish tight bounds on the size of the team (i.e., the number of agents), and the cost (i.e., the number of moves) of a sizeoptimal solution protocol. These bounds depend on the a priori knowledge the agents have about the network, and on the consistency of the local labellings. In particular, we prove that: with topological ignorance ∆ + 1 agents are needed and suffice, and the cost is Θ(n 2), where ∆ is the maximal degree of a node and n is the number of nodes in the network; with topological ignorance but in presence of sense of direction only two agents suffice and the cost is Θ(n 2); and with complete topological knowledge only two agents suffice and the cost is Θ(n log n). All the upperbound proofs are constructive.
Rendezvous and election of mobile agents: impact of sense of direction

, 2005
"... Consider a collection of r identical asynchronous mobile agents dispersed on an arbitrary anonymous network of size n. The agents all execute the same protocol and move from node to neighbouring node. At each node there is a whiteboard where the agents can write and read from. The topology of the ne ..."
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Cited by 14 (2 self)
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Consider a collection of r identical asynchronous mobile agents dispersed on an arbitrary anonymous network of size n. The agents all execute the same protocol and move from node to neighbouring node. At each node there is a whiteboard where the agents can write and read from. The topology of the network is unknown to the agents. We examine the problems of rendezvous (i.e., having the agents gather in the same node) and election (i.e., selecting a leader among those agents). These two problems are computationally equivalent in the context examined here. We study conditions for the existence of deterministic generic solutions, i.e., algorithms that solve the two problems regardless of the network topology and the initial placement of the agents. In particular, we study the impact of edgelabeling on the existence of such solutions. Rendezvous and election are unsolvable (i.e., there are no deterministic generic solutions) if gcd(r, n)> 1, regardless of whether or not the edgelabeling has sense of direction. On the other hand, if gcd(r, n) = 1 then the initial placement of the robots in the network creates topological asymmetries that could be exploited to solve the problems. We prove that these asymmetries can be exploited if the edge labeling has sense of direction, but can not if the edgelabeling is arbitrary. The possibility proof is constructive: we present a solution protocol and prove its correctness. The protocol, among other features, uses a dynamic naming mechanism based on sense of direction to overcome the complete anonymity of the system.
From static distributed systems to dynamic systems
 In Proceedings of the 24th IEEE Symposium on Reliable Distributed Systems
, 2005
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Interval Routing Schemes allow Broadcasting with Linear MessageComplexity
, 2000
"... The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required to store the routing tables as small as possible. In this paper, we an ..."
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Cited by 9 (4 self)
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The purpose of compact routing is to provide a labeling of the nodes of a network, and a way to encode the routing tables so that routing can be performed eciently (e.g., on shortest paths) while keeping the memoryspace required to store the routing tables as small as possible. In this paper, we answer a longstanding conjecture by showing that compact routing can also help to perform distributed computations. In particular, we show that a network supporting a shortest path interval routing scheme allows to broadcast with an O(n) messagecomplexity, where n is the number of nodes of the network. As a consequence, we prove that O(n) messages suce to solve leaderelection for any graph labeled by a shortest path interval routing scheme, improving therefore the O(m + n) previous known bound.
Distributed security algorithms by mobile agents
 In Proc. 8th International Conference on Distributed Computing and Networking (ICDCN’06
, 2006
"... Abstract. Mobile Agents have been extensively studied for several years ..."
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Cited by 9 (5 self)
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Abstract. Mobile Agents have been extensively studied for several years
Backward Consistency and Sense of Direction in Advanced Distributed Systems (Extended Abstract)
 IN PROC. OF THE 18TH A.C.M. SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING
, 1999
"... The studies on the relationship between label consistency, computability and complexity assume the existence of local orientation; this assumption is in fact at the basis of the pointtopoint model and is realistic for systems where a communication link can connect only two entities. However, in ..."
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Cited by 8 (5 self)
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The studies on the relationship between label consistency, computability and complexity assume the existence of local orientation; this assumption is in fact at the basis of the pointtopoint model and is realistic for systems where a communication link can connect only two entities. However, in systems which use more advanced communication and interconnection technology such as buses, optical networks, wireless communication media, etc., and more importantly, heterogeneous systems (such as internet) which include any combination of the above, local orientation can not be assumed. In this paper we consider a new type of consistency which we shall call backward consistency and which, unlike sense of direction, can exist even without local orientation. Thus...
Online graph exploration with advice
 Structural Information and Communication Complexity, volume 7355 of Lecture Notes in Computer Science
, 2012
"... Abstract. We study the problem of exploring an unknown undirected graph with nonnegative edge weights. Starting at a distinguished initial vertex s, an agent must visit every vertex of the graph and return to s. Upon visiting a node, the agent learns all incident edges, their weights and endpoints ..."
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Abstract. We study the problem of exploring an unknown undirected graph with nonnegative edge weights. Starting at a distinguished initial vertex s, an agent must visit every vertex of the graph and return to s. Upon visiting a node, the agent learns all incident edges, their weights and endpoints. The goal is to find a tour with minimal cost of traversed edges. This variant of the exploration problem has been introduced by Kalyanasundaram and Pruhs in [18] and is known as a fixed graph scenario. There have been recent advances by Megow, Mehlhorn, and Schweitzer ([19]), however the main question whether there exists a deterministic algorithm with constant competitive ratio (w.r.t. to offline algorithm knowing the graph) working on all graphs and with arbitrary edge weights remains open. In this paper we study this problem in the context of advice complexity, investigating the tradeoff between the amount of advice available to the deterministic agent, and the quality of the solution. We show that Ω(n logn) bits of advice are necessary to achieve a competitive ratio of 1 (w.r.t. an optimal algorithm knowing the graph topology). Furthermore, we give a deterministic algorithm which uses O(n) bits of advice and achieves a constant competitive ratio on any graph with arbitrary weights. Finally, going back to the original problem, we prove a lower bound of 5/2 − for deterministic algorithms working with no advice, improving the best previous lower bound of 2− of Miyazaki, Morimoto, and Okabe from [20]. In this case, significantly more elaborate technique was needed to achieve the result. 1
Setting Port Numbers for Fast Graph Exploration
"... Abstract. We consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of arbitrary size and arbitrary maximum degree. In anonymous graphs, nodes are not labeled but edges are labeled in ..."
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Cited by 5 (1 self)
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Abstract. We consider the problem of periodic graph exploration by a finite automaton in which an automaton with a constant number of states has to explore all unknown anonymous graphs of arbitrary size and arbitrary maximum degree. In anonymous graphs, nodes are not labeled but edges are labeled in a local manner (called local orientation) sothat the automaton is able to distinguish them. Precisely, the edges incident toanodev are given port numbers from 1 to dv, wheredv is the degree of v. Periodic graph exploration means visiting every node infinitely often. We are interested in the length of the period, i.e., the maximum number of edge traversals between two consecutive visits of any node by the automaton in the same state and entering the node by the same port. This problem is unsolvable if local orientations are set arbitrarily. Given this impossibility result, we address the following problem: what is the mimimum function π(n) such that there exist an algorithm for setting the local orientation, and a finite automaton using it, such that the automaton explores all graphs of size n within the period π(n)? The best result so far is the upper bound π(n) ≤ 10n, byDobrev et al. [SIROCCO 2005], using an automaton with no memory (i.e. only one state). In this paper we prove a better upper bound π(n) ≤ 4n. Our automaton uses three states but performs periodic exploration independently of its starting position and initial state. 1
Distributed objects with sense of direction
 In 1st Workshop on Distributed Data and Structures
, 1998
"... An object system consists of a collection of objects and their relations; each object has a state (e.g., local variables) and a behavior (set of actions it may execute) and the global behavior of a system is described in terms of interactions between its objects. ..."
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Cited by 4 (3 self)
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An object system consists of a collection of objects and their relations; each object has a state (e.g., local variables) and a behavior (set of actions it may execute) and the global behavior of a system is described in terms of interactions between its objects.
Locating a Target with an Agent Guided by Unreliable Local Advice
 In Proceedings of the 29th Annual ACM SIGACTSIGOPS Symposium on Principles of Distributed Computing PODC 2010
, 2010
"... We study the problem of finding a destination node t by a mobile agent in an unreliable network having the structure of an unweighted graph, in a model first proposed by Hanusse et al. [21, 20]. Each node is able to give advice concerning the next node to visit so as to go closer to the target t. Un ..."
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We study the problem of finding a destination node t by a mobile agent in an unreliable network having the structure of an unweighted graph, in a model first proposed by Hanusse et al. [21, 20]. Each node is able to give advice concerning the next node to visit so as to go closer to the target t. Unfortunately, exactly k of the nodes, called liars, give advice which is incorrect. It is known that for an nnode graph G of maximum degree ∆ ≥ 3, reaching a target at a distance of d from the initial location may require an expected time of 2 Ω(min{d,k}) , for any d, k = O(log n), even when G is a tree. This paper focuses on strategies which efficiently solve the search problem in scenarios in which, at each node, the agent may only choose between following the local advice, or randomly selecting an incident edge. The strategy which we put forward, called R/A, makes use of a timer (step counter) to alternate between phases of ignoring advice (R) and following advice (A) for a certain number of steps. No knowledge of parameters n, d, or k is required, and the agent need not know by which edge it entered the node of its current location. The performance of this strategy is studied for two classes of regular graphs with extremal values of expansion, namely, for rings and for random ∆regular graphs (an important class of expanders). For the ring, R/A is shown to achieve an expected searching time of 2d+k Θ(1) for a worstcase distribution of liars, which is polynomial in both d and k. For random ∆regular graphs, the expected searching time of the R/A strategy is O(k 3 log 3 n) a.a.s. The polylogA full version of this paper is available online [19]