391 research outputs found
Time Versus Cost Tradeoffs for Deterministic Rendezvous in Networks
Two mobile agents, starting from different nodes of a network at possibly
different times, have to meet at the same node. This problem is known as
. Agents move in synchronous rounds. Each agent has a
distinct integer label from the set . Two main efficiency
measures of rendezvous are its (the number of rounds until the
meeting) and its (the total number of edge traversals). We
investigate tradeoffs between these two measures. A natural benchmark for both
time and cost of rendezvous in a network is the number of edge traversals
needed for visiting all nodes of the network, called the exploration time.
Hence we express the time and cost of rendezvous as functions of an upper bound
on the time of exploration (where and a corresponding exploration
procedure are known to both agents) and of the size of the label space. We
present two natural rendezvous algorithms. Algorithm has cost
(and, in fact, a version of this algorithm for the model where the
agents start simultaneously has cost exactly ) and time . Algorithm
has both time and cost . Our main contributions are
lower bounds showing that, perhaps surprisingly, these two algorithms capture
the tradeoffs between time and cost of rendezvous almost tightly. We show that
any deterministic rendezvous algorithm of cost asymptotically (i.e., of
cost ) must have time . On the other hand, we show that any
deterministic rendezvous algorithm with time complexity must have
cost
Leader Election for Anonymous Asynchronous Agents in Arbitrary Networks
We study the problem of leader election among mobile agents operating in an
arbitrary network modeled as an undirected graph. Nodes of the network are
unlabeled and all agents are identical. Hence the only way to elect a leader
among agents is by exploiting asymmetries in their initial positions in the
graph. Agents do not know the graph or their positions in it, hence they must
gain this knowledge by navigating in the graph and share it with other agents
to accomplish leader election. This can be done using meetings of agents, which
is difficult because of their asynchronous nature: an adversary has total
control over the speed of agents. When can a leader be elected in this
adversarial scenario and how to do it? We give a complete answer to this
question by characterizing all initial configurations for which leader election
is possible and by constructing an algorithm that accomplishes leader election
for all configurations for which this can be done
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