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...

Motivated by the problem of supporting energy–efficient broadcasting in ad hoc wireless networks, we study the Minimum Energy Consumption Broadcast Subgraph (MECBS) problem. We present the first logarithmic approximation algorithm for the problem which uses an interesting reduction to Node–Weighted Connected Dominating Set. We also show that an important special instance of the problem can be s...

In ad hoc wireless networks, a successful broadcasting requires that the nodes forwarding the broadcast packet form a connected dominating set to ensure the coverage. An efficient broadcast method should generate a small forward node set without excessive overhead. Neighbor-knowledgebased methods, including neighbor-designating methods and self-pruning methods, are localized algorithms that red...

A Connected Dominating Set (CDS) is used as a virtual backbone for Wireless Sensor Networks (WSNs). Most existing works focus on a Minimum CDS (MCDS), a k-connect mdominating CDS, a minimum routing cost CDS or a bounded-diameter CDS, ignoring the loadbalance factor of CDSs. In this paper, we propose a novel problem – the Load-Balanced CDS (LBCDS) problem, in which constructing an LBCDS and load...