In this paper we consider the classical Connected Dominating Set (CDS) problem. Twenty years ago, Guha and Khuller developed two algorithms for this problem a centralized greedy approach with an approximation guarantee ofH(∆)+2, and a local greedy approach with an approximation guarantee of 2(H(∆) + 1) (where H() is the harmonic function, and ∆ is the maximum degree in the graph). A local greed...

A dominating set D of a graph G is a subset of V (G) such that for every vertex v ∈ V (G), either v ∈ D or there exists a vertex u ∈ D that is adjacent to v in G. Dominating sets of small cardinality are of interest. A connected dominating set C of a graph G is a dominating set of G such that the subgraph induced by the vertices of C in G is connected. A weakly-connected dominating set W of a g...

In this paper, we study a minimum connected dominating set problem (CDS) in wireless networks, which selects a minimum CDS with property that all intermediate nodes inside every pairwise shortest path should be included. Such a minimum CDS (we name this problem as SPCDS) is an important tache of some other algorithms for constructing a minimum CDS. We prove that finding such a minimum SPCDS can...

We give efficient distributed approximation algorithms for weighted versions of the maximum matching problem and the minimum dominating set problem for graphs from minor-closed families. To complement these results we indicate that no efficient distributed algorithm for the minimum weight connected dominating set exists.

Distance-hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. This paper studies distance-hereditary graphs from an algorithmic viewpoint. In particular, we present linear-time algorithms for finding a minimum weighted connected dominating set and a minimum vertex-weighted Steiner tree in a distance-hereditary graph...

In recent years,MANET gain a significant attention for the potential application in battlefield, disaster relief, traffic monitoring and environment monitoring. Construction and maintain of virtual backbone, and energy effective routing in mobile ad hoc wireless network come to be the basic and main problem in MANET. This paper proposed the efficient ENMCDS algorithm for constructing the minimu...

188 Abstract-The lifetime of battery operated wireless sensor networks can be prolonged by energy aware maintenance of the virtual backbone. The energy of a node is depleted quickly during communication and network failure is most likely to occur when the energy of a Minimum Connected Dominating Set (MCDS) node is exhausted. The reconstruction of an alternate backbone without the depleted node ...

For a connected graph G and any non-empty S ⊆ V (G), S is called a weakly connected dominating set of G if the subgraph obtained from G by removing all edges each joining any two vertices in V (G) \ S is connected. The weakly connected domination number γw(G) is defined to be the minimum integer k with |S| = k for some weakly connected dominating set S of G. In this note, we extend a result on ...

A hub set in a graph G is a set U ⊆ V (G) such that any two vertices outside U are connected by a path whose internal vertices lie in U . We prove that h(G) ≤ hc(G) ≤ γc(G) ≤ h(G) + 1, where h(G), hc(G), and γc(G), respectively, are the minimum sizes of a hub set in G, a hub set inducing a connected subgraph, and a connected dominating set. Furthermore, all graphs with γc(G) > hc(G) ≥ 4 are obt...

This paper introduces a novel framework for generating pictorial storylines for given topics from text and image data on the Internet. Unlike traditional text summarization and timeline generation systems, the proposed framework combines text and image analysis and delivers a storyline containing textual, pictorial, and structural information to provide a sketch of the topic evolution. A key id...