Efficient edge domination in regular graphs

An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p ≥ 3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete. © 2008 Elsevier B.V. All rights reserved.

Dominating induced matchings

We study the problem of determining whether or not a graph G has an induced matching that dominates every edge of the graph, which is also known as efficient edge domination. This problem is known to be NP-complete in general as well as in some restricted domains, such as bipartite graphs or regular graphs. In this paper, we identify a graph parameter to which the complexity of the problem is sensible and produce results of both negative (intractable) and positive (solvable in polynomial time) type. © 2009 Springer Berlin Heidelberg.

Efficient domination through eigenvalues

The paper begins with a new characterization of (k,τ)(k,τ)-regular sets. Then, using this result as well as the theory of star complements, we derive a simplex-like algorithm for determining whether or not a graph contains a (0,τ)(0,τ)-regular set. When τ=1τ=1, this algorithm can be applied to solve the efficient dominating set problem which is known to be NP-complete. If −1−1 is not an eigenvalue of the adjacency matrix of the graph, this particular algorithm runs in polynomial time. However, although it does not work in polynomial time in general, we report on its successful application to a vast set of randomly generated graphs.

Advanced energy efficient coordinated multi-point transmission for OFDMA

The ever-growing energy consumption in mobile networks stimulated by the expected growth in data tra ffic has provided the impetus for mobile operators to refocus network design, planning and deployment towards reducing the cost per bit, whilst at the same time providing a signifi cant step towards reducing their operational expenditure. As a step towards incorporating cost-eff ective mobile system, 3GPP LTE-Advanced has adopted the coordinated multi-point (CoMP) transmission technique due to its ability to mitigate and manage inter-cell interference (ICI). Using CoMP the cell average and cell edge throughput are boosted. However, there is room for reducing energy consumption further by exploiting the inherent exibility of dynamic resource allocation protocols. To this end packet scheduler plays the central role in determining the overall performance of the 3GPP longterm evolution (LTE) based on packet-switching operation and provide a potential research playground for optimizing energy consumption in future networks. In this thesis we investigate the baseline performance for down link CoMP using traditional scheduling approaches, and subsequently go beyond and propose novel energy e fficient scheduling (EES) strategies that can achieve power-e fficient transmission to the UEs whilst enabling both system energy effi ciency gain and fairness improvement. However, ICI can still be prominent when multiple nodes use common resources with di fferent power levels inside the cell, as in the so called heterogeneous networks (Het- Net) environment. HetNets are comprised of two or more tiers of cells. The rst, or higher tier, is a traditional deployment of cell sites, often referred to in this context as macrocells. The lower tiers are termed small cells, and can appear as microcell, picocells or femtocells. The HetNet has attracted signiffi cant interest by key manufacturers as one of the enablers for high speed data at low cost. Research until now has revealed several key hurdles that must be overcome before HetNets can achieve their full potential: bottlenecks in the backhaul must be alleviated, as well as their seamless interworking with CoMP. In this thesis we explore exactly the latter hurdle, and present innovative ideas on advancing CoMP to work in synergy with HetNet deployment, complemented by a novel resource allocation policy for HetNet tighter interference management. As system level simulator has been used to analyze the proposed algorithm/protocols, and results have concluded that up to 20% energy gain can be observed.