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Two mobile agents, starting from different nodes of an unknown network, haveto meet at the same node. Agents move in synchronous rounds using adeterministic algorithm. Each agent has a different label, which it can use inthe execution of the algorithm, but it does not know the label of the otheragent. Agents do not know any bound on the size of the network. In each roundan agent decides if it remains idle or if it wants to move to one of theadjacent nodes. Agents are subject to delay faults: if an agent incurs a faultin 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. Weconsider three scenarios of fault distribution: random (independently in eachround and for each agent with constant probability 0 < p < 1), unbounded adver-sarial (the adversary can delay an agent for an arbitrary finite number ofconsecutive rounds) and bounded adversarial (the adversary can delay an agentfor at most c consecutive rounds, where c is unknown to the agents). Thequality measure of a rendezvous algorithm is its cost, which is the totalnumber of edge traversals. For random faults, we show an algorithm with costpolynomial in the size n of the network and polylogarithmic in the larger labelL, which achieves rendezvous with very high probability in arbitrary networks.By contrast, for unbounded adversarial faults we show that rendezvous is notfeasible, even in the class of rings. Under this scenario we give a rendezvousalgorithm with cost O(nl), where l is the smaller label, working in arbitrarytrees, and we show that \Omega(l) is the lower bound on rendezvous cost, evenfor the two-node tree. For bounded adversarial faults, we give a rendezvousalgorithm working for arbitrary networks, with cost polynomial in n, andlogarithmic in the bound c and in the larger label L.

Rendezvous in Networks in Spite of Delay Faults