Intruder Capture in Sierpinski Graphs.

In this paper we consider the problem of capturing an intruder in a networked environment. The intruder is defined as a mobile entity that moves arbitrarily fast inside the network and escapes from a team of software agents. The agents have to collaborate and coordinate their moves in order to isolate the intruder. They move asynchronously and they know the network topology they are in is a particular fractal graph, the Sierpiński graph SG n . We first derive lower bounds on the minimum number of agents, number of moves and time steps required to capture the intruder. We then consider two models: one in which agents have a capability, of “seeing” the state of their neighbors; the second one in which the actions of the agents are leaded by a coordinator. One of our goals is to continue a previous study on what is the impact of visibility on complexity: we have found that in this topology the visibility assumption allows us to reach an optimal bound on the number of agents required for the cleaning strategy. On the other hand, the second strategy relies only on local computations but requires an extra agent and a higher (by a constant) complexity in terms of time and number of moves

Minimum Feedback Vertex Set in Pyramid and Mesh of Trees Networks

In this paper we consider the minimum feedback vertex set problem in graphs, i.e., the problem of finding a minimal subset of vertices that have to be removed from a graph, to induce an acyclic subgraph. The problem in NP-hard for general topologies, but many different polynomial time algorithms have been provided for particular networks. In this paper we present close lower and upper bounds to the problem in two different topologies, namely pyramid networks and rectangular mesh of trees networks

Contiguous search problem in Sierpinski graphs

In this paper we consider the problem of capturing an intruder in a particular fractal graph, the Sierpiński graph SG n . The problem consists of having a team of mobile software agents that collaborate in order to capture the intruder. The intruder is a mobile entity that escapes from the team of agents, moving arbitrarily fast inside the network, i.e., traversing any number of contiguous nodes as long as no other agent resides on them. The agents move asynchronously and they know the network topology they are in is a Sierpiński graph SG n . We first derive lower bounds on the minimum number of agents, number of moves and time steps required to capture the intruder. We then consider some variations of the model based on the capabilities of the agents: visibility, where the agents can “see” the state of their neighbors and thus can move autonomously; locality, where the agents can only access local information and thus their moves have to be coordinated by a leader. For each model, we design a capturing strategy and we make some observations. One of our goals is to continue a previous study on what is the impact of visibility on complexity: in this topology we are able to reach an optimal bound on the number of agents required by both cleaning strategies. However, the strategy in the visibility model is fully distributed, whereas the other strategy requires a leader. Moreover, the second strategy requires a higher number of moves and time steps

Distance Routing on Series Parallel Networks

In this paper we consider the problem of routing messages on Series Parallel Graphs (SPGs), and we introduce a new technique called Distance Routing. This technique is based on the idea of encoding in the label of each node x some information about a shortest path from the source of the SPG to x, and from x to the terminal node of the SPG. We first compare shortest path Distance Routing and 1-Interval Routing Schemes on directed SPGs. We then show that Distance Routing can be used to route on bidirectional SPGs, where no general shortest path 1-Interval Routing Scheme can be applied. We also show the relevance of the study of the time complexity in the choice of a Compact Routing method. 1 Introduction In a non anonymous network (i.e., in a network where to each node it is associated a different identity) routing can be easily accomplished if each node has available a routing table. This table has n \Gamma 1 entries (where n is the number of nodes), and shows the edge through which a ..

A State of Art Survey on ZigZag Structures

Zz-structures are particular data structures capable of rep- resenting both hypertextual information and contextual in- terconnections among different information. The focus of this paper is to stimulate new research on this topic, by providing, in a state of the art survey, a short de- scription and comparison of all the material that, to the best of our knowledge, is related to zz-structures: infor- mal and formal descriptions, implementations, languages, demonstrations, projects and applitudes of zz-structures; in fact, despite their large use in different fields, the literature lacks of an exhaustive and up-to-date description of them

Routing in Series Parallel Networks

We consider the problem of routing messages between pairs of nodes of a distributed network, along shortest paths. We introduce a new routing technique, called Distance Routing that, due to its structure, is naturally well applicable on a family of networks called Series Parallel Graphs. We compute the time and space complexities of Distance Routing in Series Parallel Graphs, and we compare them with the relative complexities of Interval Routing, showing the improvement of Distance Routing especially in terms of time complexity