Fast–mixed searching and related problems on graphs

Fast-mixed searching and related problems on graphs

Graph Searching and Related Problems

Suppose that there is a robber hiding on vertices or along edges of a graph or digraph. Graph searching is concerned with finding the minimum number of searchers required to capture the robber. We survey the major results of graph searching problems, focusing on algorithmic, structural, and probabilistic aspects of the field.

The p-median and p-center Problems on Bipartite Graphs

Let $G$ be a bipartite graph. In this paper we consider the two kind of location problems namely $p$-center and $p$-median problems on bipartite graphs. The $p$-center and $p$-median problems asks to find a subset of vertices of cardinality $p$, so that respectively the maximum and sum of the distances from this set to all other vertices in $G$ is minimized. For each case we present some proper...

Network Connectivity and Related Optimization Problems on Random Graphs

Network connectivity and propagation problems arise naturally in many social networks. We examine problems where some property, such as an infection or influence, starts from some initially seeded set of nodes and every affected node transmits the property to its neighbors with a probability determined by the connecting edge. Thus the core problem becomes one of connectivity in a random-graph –...

Graph Searching on Chordal Graphs

In the graph searching problem initially a graph with all edges contaminated is pre sented We would like to obtain a state of the graph in which all edges are simultaneously clear by a sequence of moves using searchers The objective is to achieve the desired state by using the least number of searchers Two variations of the graph searching problem are considered in this paper One is the edge se...