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In this paper, we study the problem of constructing quality fault-tolerant Connected Dominating Sets (CDSs) in homogeneous wireless networks, which can be defined as minimum k-Connected m-Dominating Set ((k, m)-CDS) problem in Unit Disk Graphs (UDGs). We found that every existing approximation algorithm for this problem is incomplete for k ≥ 3 in a sense(More)
Given a graph G = (V ,E) with node weight w : V → R+ and a subset S ⊆ V , find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio a lnn for any 0 < a(More)
A Virtual Backbone (VB) of a wireless network is a subset of nodes such that only VB nodes are responsible for routing-related tasks. Since a smaller VB causes less overhead, size is the primary quality factor of VB. Frequently, Unit Disk Graphs (UDGs) are used to model 2D homogeneous wireless networks, and the problem of finding minimum VBs in the networks(More)
Connected Dominating Set is widely used as virtual backbone in wireless networks to improve network performance and optimize routing protocols. Based on special characteristics of ad-hoc and sensor networks, we usually use unit disk graph to represent the corresponding geometrical structures, where each node has a unit transmission range and two nodes are(More)
Given a node-weighted graph, the minimum-weighted dominating set (MWDS) problem is to find a minimum-weighted vertex subset such that, for any vertex, it is contained in this subset or it has a neighbor contained in this set. And the minimum-weighted connected dominating set (MWCDS) problem is to find a MWDS such that the graph induced by this subset is(More)
In this paper, we study the problem of computing quality fault-tolerant virtual backbone in homogeneous wireless network, which is defined as the <i>k</i>-connected <i>m</i>-dominating set problem in a unit disk graph. This problem is NP-hard, and thus many efforts have been made to find a constant factor approximation algorithm for it, but never succeeded(More)
Connected Dominating Set (CDS) has been a well known approach for constructing a virtual backbone to alleviate the broadcasting storm in wireless networks. Previous literature modeled the wireless network in a 2-dimensional plane and looked for the approximated Minimum CDS (MCDS) distributed or centralized to construct the virtual backbone of the wireless(More)
Given a graph G = (V,E) with node weight w : V → R and a subset S ⊆ V , find a minimum total weight tree interconnecting all nodes in S. This is the node-weighted Steiner tree problem which will be studied in this paper. In general, this problem is NP-hard and cannot be approximated by a polynomial time algorithm with performance ratio a lnn for any 0 < a <(More)
Connected Dominating Set is widely used as virtual backbone in wireless Ad-hoc and sensor networks to improve the performance of transmission and routing protocols. Based on special characteristics of Ad-hoc and sensor networks, we usually use unit disk graph to represent the corresponding geometrical structures, where each node has a unit transmission(More)
LetG be a graphwith vertex set V . Amoplex ofG is both a clique and amodulewhose neighborhood is aminimal separator inG or empty. Amoplex ordering ofG is an ordered partition (X1, X2, · · · , Xk) of V for some integer k into moplexes which are defined in the successive transitory elimination graphs, i.e., for 1 6 i 6 k − 1, Xi is a moplex of the graph Gi(More)