dr inż. Robert Ostrowski | Politechnika Gdańska

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...

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...

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. In such setting a searcher, once a search strategy initially decides on the label of the searcher, can be present on an edge only if the label of the searcher and the label of the edge are the same. We prove...

Graph searching encompasses a variety of different models, many of which share a property that in optimal strategies fugitive can never access once searched regions. Monotonicity, as it is called, is vital in many established results in the field however its absence significantly impedes the analysis of a given problem. This survey attempts to gather non-monotone models, that are less researched in effort of summarizing the results...