We develop constant-factor approximation algorithms for minimizing the maximum movement made by pebbles on a graph to reach a configuration in which the pebbles form a connected subgraph (connectivity), or interconnect a constant number of stationary nodes (Steiner tree). These problems model the minimization of the total time required to reconfigure a robot swarm to achieve a proximity (e.g., ...

Let G = (V,E) be a connected graph. G is said to be super edge connected (or super-k for short) if every minimum edge cut of G isolates one of the vertex of G. A graph G is called m-super-k if for any edge set S # E(G) with jSj 6m, G S is still super-k. The maximum cardinality of m-super-k is called the edge fault tolerance of super edge connectivity of G. In this paper, we discuss the edge fau...

Considering an under supervised 3D space where a group of mobile devices with limited sensing and communicating capabilities are deployed, this paper aims at proposing a decentralized self-deployment algorithm for agents to get maximum connected coverage topology. The problem is modeled as maximization which is solved completely distributed. In fact each agent tries to maximize its sensing volu...

Abstract: In this paper competition between two network firms is analysed under two alternative regulatory regimes: a global connectivity regulation (GCR) and an efficient component pricing regulation (ECPRe). Whereas a GCR imposes a full quality of reciprocal interconnection, firms will choose vertical product differentiation in order to lower price competition, while under a ECPRe they will c...

We introduce the minimum labelling spanning bi-connected subgraph problem (MLSBP) replacing connectivity by bi-connectivity in the well known minimum labelling spanning tree problem (MLSTP). A graph is bi-connected if, for every two vertices, there are, at least, two vertex-disjoint paths joining them. The problem consists in finding the spanning bi-connected subgraph or block with minimum set ...

For a graph G, the P2-path graph, P2(G), has for vertices the set of all paths of length 2 in G. Two vertices are connected when their union is a path or a cycle of length 3. We present lower bounds on the edge-connectivity, (P2(G)) of a connected graph G and give conditions for maximum connectivity. A maximally edge-connected graph is superif each minimum edge cut is trivial, and it is optimum...

In this paper a tight lower bound for algebraic connectivity of graphs (second smallest eigenvalue of the Laplacian matrix of the graph) based on connection-graph-stability method is introduced. The connection-graph-stability score for each edge is defined as the sum of the length of all the shortest paths making use of that edge. We prove that the algebraic connectivity of the graph is lower b...

The study aims to introduce a new method and approach for measuring the diversity of connectivity with the help of the landscape geometrization, in order to create a new variable useful in landscape metrics and to decrease the costs of landscape planning if its main goal is the enhancement of connectivity. Using induction we identify the landscape elements with geometric elements, calculating t...

This paper suggests a novel segmentation algorithm for separating moving objects from the background in video sequences without any prior information of the sequence nature. We formulate the problem as a connectivity analysis of region adjacency graph (RAG) based on temporal information. The nodes of the RAG represent homogeneous regions and the edges represent temporal information, which is ob...

Topology control is the problem of assigning transmission power values to the nodes of an ad hoc network so that the induced graph satisfies some specified property. The most fundamental such property is that the network/graph be connected. For connectivity, prior work on topology control gave a polynomial time algorithm for minimizing the maximum power assigned to any node (such that the induc...