1,700 research outputs found

    Rendezvous in Networks in Spite of Delay Faults

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    Two mobile agents, starting from different nodes of an unknown network, have to meet at the same node. Agents move in synchronous rounds using a deterministic algorithm. Each agent has a different label, which it can use in the execution of the algorithm, but it does not know the label of the other agent. Agents do not know any bound on the size of the network. In each round an agent decides if it remains idle or if it wants to move to one of the adjacent nodes. Agents are subject to delay faults: if an agent incurs a fault in a given round, it remains in the current node, regardless of its decision. If it planned to move and the fault happened, the agent is aware of it. We consider three scenarios of fault distribution: random (independently in each round and for each agent with constant probability 0 < p < 1), unbounded adver- sarial (the adversary can delay an agent for an arbitrary finite number of consecutive rounds) and bounded adversarial (the adversary can delay an agent for at most c consecutive rounds, where c is unknown to the agents). The quality measure of a rendezvous algorithm is its cost, which is the total number of edge traversals. For random faults, we show an algorithm with cost polynomial in the size n of the network and polylogarithmic in the larger label L, which achieves rendezvous with very high probability in arbitrary networks. By contrast, for unbounded adversarial faults we show that rendezvous is not feasible, even in the class of rings. Under this scenario we give a rendezvous algorithm with cost O(nl), where l is the smaller label, working in arbitrary trees, and we show that \Omega(l) is the lower bound on rendezvous cost, even for the two-node tree. For bounded adversarial faults, we give a rendezvous algorithm working for arbitrary networks, with cost polynomial in n, and logarithmic in the bound c and in the larger label L

    Partial Gathering of Mobile Agents in Dynamic Tori

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    Move-optimal partial gathering of mobile agents in asynchronous trees

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    In this paper, we consider the partial gathering problem of mobile agents in asynchronous tree networks. The partial gathering problem is a generalization of the classical gathering problem, which requires that all the agents meet at the same node. The partial gathering problem requires, for a given positive integer g, that each agent should move to a node and terminate so that at least g agents should meet at each of the nodes they terminate at. The requirement for the partial gathering problem is weaker than that for the (well-investigated) classical gathering problem, and thus, we clarify the difference on the move complexity between them. We consider two multiplicity detection models: weak multiplicity detection and strong multiplicity detection models. In the weak multiplicity detection model, each agent can detect whether another agent exists at the current node or not but cannot count the exact number of the agents. In the strong multiplicity detection model, each agent can count the number of agents at the current node. In addition, we consider two token models: non-token model and removable token model. In the non-token model, agents cannot mark the nodes or the edges in any way. In the removable-token model, each agent initially leaves a token on its initial node, and agents can remove the tokens. Our contribution is as follows. First, we show that for the non-token model agents require Ω(kn) total moves to solve the partial gathering problem, where n is the number of nodes and k is the number of agents. Second, we consider the weak multiplicity detection and non-token model. In this model, for asymmetric trees, by a previous result agents can achieve the partial gathering in O(kn) total moves, which is asymptotically optimal in terms of total moves. In addition, for symmetric trees we show that there exist no algorithms to solve the partial gathering problem. Third, we consider the strong multiplicity detection and non-token model. In this model, for any trees we propose an algorithm to achieve the partial gathering in O(kn) total moves, which is asymptotically optimal in terms of total moves. At last, we consider the weak multiplicity detection and removable-token model. In this model, we propose an algorithm to achieve the partial gathering in O(gn) total moves. Note that in this model, agents require Ω(gn) total moves to solve the partial gathering problem. Hence, the second proposed algorithm is also asymptotically optimal in terms of total moves

    Uniform multi-agent deployment on a ring

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    AbstractWe consider two variants of the task of spreading a swarm of agents uniformly on a ring graph. Ant-like oblivious agents having limited capabilities are considered. The agents are assumed to have little memory, they all execute the same algorithm and no direct communication is allowed between them. Furthermore, the agents do not possess any global information. In particular, the size of the ring (n) and the number of agents in the swarm (k) are unknown to them. The agents are assumed to operate on an unweighted ring graph. Every agent can measure the distance to his two neighbors on the ring, up to a limited range of V edges.The first task considered, is dynamical (i.e. in motion) uniform deployment on the ring. We show that if either the ring is unoriented, or the visibility range is less than ⌊n/k⌋, this is an impossible mission for the agents. Then, for an oriented ring and V≥⌈n/k⌉, we propose an algorithm which achieves the deployment task in optimal time. The second task discussed, called quiescent spread, requires the agents to spread uniformly over the ring and stop moving. We prove that under our model, in which every agent can measure the distance only to his two neighbors, this task is impossible. Subsequently, we propose an algorithm which achieves quiescent but only almost uniform spread.The algorithms we present are scalable and robust. In case the environment (the size of the ring) or the number of agents changes during the run, the swarm adapts and re-deploys without requiring any outside interference

    Asynchronous Gathering in a Torus

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    We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other but are endowed with visibility sensors that allow them to see the positions of the other robots. Most investigations on the gathering problem on the discrete universe are done on ring shaped networks due to the number of symmetric configurations. We extend in this paper the study of the gathering problem on torus shaped networks assuming robots endowed with local weak multiplicity detection. That is, robots cannot make the difference between nodes occupied by only one robot from those occupied by more than one robot unless it is their current node. Consequently, solutions based on creating a single multiplicity node as a landmark for the gathering cannot be used. We present in this paper a deterministic algorithm that solves the gathering problem starting from any rigid configuration on an asymmetric unoriented torus shaped network

    Partial gathering of mobile agents in dynamic rings

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    In this paper, we consider the partial gathering problem of mobile agents in synchronous dynamic bidirectional rings. The partial gathering problem is a generalization of the (well-investigated) total gathering problem, which requires that all k agents distributed in the network terminate at a non-predetermined single node. The partial gathering problem requires, for a given positive integer g(<k), that agents terminate in a configuration such that either at least g agents or no agent exists at each node. The requirement for the partial gathering problem is strictly weaker than that for the total gathering problem, and thus it is interesting to clarify the difference in the move complexity between them. So far, partial gathering has been considered in static graphs. In this paper, we consider this problem in 1-interval connected rings, that is, one of the links in the ring may be missing at each time step. In such networks, we aim to clarify the solvability of the partial gathering problem and the move complexity, focusing on the relationship between values of k and g. First, we consider the case of 3g≤k≤8g−2. In this case, we show that our algorithm can solve the problem with the total number of O(kn) moves, where n is the number of nodes. Since k=O(g) holds when 3g≤k≤8g−2, the move complexity O(kn) in this case can be represented also as O(gn). Next, we consider the case of k≥8g−3. In this case, we show that our algorithm can also solve the problem and its move complexity is O(gn). These results mean that, when k≥3g, the partial gathering problem can be solved also in dynamic rings. In addition, agents require a total number of Ω(gn) (resp., Ω(kn)) moves to solve the partial (resp., total) gathering problem. Thus, the both proposed algorithms can solve the partial gathering problem with the asymptotically optimal total number of O(gn) moves, which is strictly smaller than that for the total gathering problem.23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, November 17-20, 2021, Virtual Conferenc

    Partial Gathering of Mobile Agents in Arbitrary Networks

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    In this paper, we consider the partial gathering problem of mobile agents in arbitrary networks. The partial gathering problem is a generalization of the (well-investigated) total gathering problem, which requires that all the agents meet at the same node. The partial gathering problem requires, for a given positive integer g, that each agent should move to a node and terminate so that at least g agents should meet at each of the nodes they terminate at. The requirement for the partial gathering problem is no stronger than that for the total gathering problem, and thus, we clarify the difference on the move complexity between them. First, we show that agents require Ω(gn+m) total moves to solve the partial gathering problem, where n is the number of nodes and m is the number of communication links. Next, we propose a deterministic algorithm to solve the partial gathering problem in O(gn+m) total moves, which is asymptotically optimal in terms of total moves. Note that, it is known that agents require Ω(kn+m) total moves to solve the total gathering problem in arbitrary networks, where k is the number of agents. Thus, our result shows that the partial gathering problem is solvable with strictly fewer total moves compared to the total gathering problem in arbitrary networks
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