Every node of an edge-weighted tree network contains a data packet. At some nodes are placed mobile agents, each one possessing an amount of energy (not necessarily the same for all agents). While walking along the network, the agents spend the energy proportionally to the distance traveled and collect copies of the data packets present at the visited network nodes. An agent visiting a node deposits there copies of all currently...

In this work we introduce and study a pursuit-evasion game in which the search is performed by heterogeneous entities. We incorporate heterogeneity into the classical edge search problem by considering edge-labeled graphs: once a search strategy initially assigns labels to the searchers, each searcher can be only present on an edge of its own label. We prove that this problem is not monotone even for trees and we give instances...

The work contains results regarding two problems posed to a group of mobile entities, called agents, and a survey of fields of research from which these problems originate. First, in the heterogeneous graph searching problem, the agents, also called searchers, are asked to find a fugitive in a graph with edges accessible only to specific types of agents. The rules of the edge searching problem are augmented by introducing labels...