Monitoring of dynamically changed graph

Monitoring of oriented graphs is a key task in many applications. Such monitoring is very specific when the graph models a communication network including Internet and GRID. A node of the network has local information about the network: if "knows" only about the arcs outgoing from this node, but does not "know" where (to which nodes) these arcs go. The nodes of the network exchange messages through the network links represented as arcs of the graph and act as message transfer channels. The graph monitoring is based on its traversal when message passes each arc in the graph. While there is an untraversed arc, we cannot be certain that it goes to still unmonitored part of the graph. Usually, the graph traversal is performed with a single message circulating in the network. Traversal can be done faster if performed in parallel: multiple messages simultaneously circulate in the network. In this paper we consider the parallel monitoring of a graph aimed at not just the graph traversal, but also collection of complete information about the graph in each its node. Another feature of this work is monitoring of a dynamically changing graph: its arcs can disappear, appear or change their destination nodes. An algorithm is proposed, which provides the collection of full information on the graph in each its node.