Local Maps: New Insights into Mobile Agent Algorithms

In this paper, we study the complexity of computing with mobile agents having small local knowledge. In particular, we show that the number of mobile agents and the amount of local information given initially to agents can significantly influence the time complexity of resolving a distributed problem. Our results are based on a generic scheme allowing to transform a message passing algorithm, running on an $n$-node graph $G$, into a mobile agent one. By generic, we mean that the scheme is independent of both the message passing algorithm and the graph $G$. Our scheme, coupled with a well-chosen clustered representation of the graph, induces $\widetilde{O}(1) ratio between the time complexity of the obtained mobile agent algorithm and the time complexity of the original message passing counterpart, while using$\widetilde{O}(n)$mobile agents. If only$k$agents are allowed ($k$is an integer parameter), then we show that the time ratio is$O(n/\sqrt{k})$. As a consequence, we show that any global labeling function of$G$can be computed by exactly$n$mobile agents knowing their$n^{\epsilon}$-neighborhood in$\widetilde{O}(D)$time,$D$is the diameter of the graph and$\epsilon$is an arbitrary small constant. We apply our generic results for the fundamental problem of computing a leader (resp. a BFS tree) under the additional restriction of$\widetilde{O}(1)$(resp.$\widetilde{O}(n)$) memory bits per agent, and obtain$\widetilde{O}(D)$ time algorithms

Fault-Tolerant Simulation of Message-Passing Algorithms by Mobile Agents

The recently established computational equivalence between the traditional message-passing model and the mobile-agents model is based on the existence of a mobile-agents algorithm that simulates the execution of message-passing algorithms. Like most existing protocols for mobile agents, this simulation protocol works correctly only if the agents are fault-free. We consider the problem of performing the simulation of message-passing algorithms when the simulating agents may crash unexpectedly. We show how to simulate any distributed algorithm for the message-passing model in a mobile-agents system with k agents, tolerating up to f ≤ k−1 crashes during the simulation. Two fault-tolerant simulation algorithms are presented, one for non-anonymous settings (i.e., where either the networks nodes or the agents or both have distinct identities), and one for anonymous systems (where both the network nodes and the agents are anonymous). In both cases, the simulation overhead is polynomial. An interesting feature of the algorithm for the anonymous setting is that it allows for a self-balancing fault-tolerant simulation: Even though the agents may crash at any time, the algorithm ensures that the simulation proceeds flawlessly irrespective of the agent crashes and the system always stabilizes to a state where the workload is equally distributed among the remaining agents