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The Steiner tree problem in Euclidean space $$E^3$$ E 3 asks for a minimum length network $$T$$ T , called a Euclidean Steiner Minimum Tree (ESMT), spanning a given set of points. This problem is NP-hard and the hardness is inherently due to the number of feasible topologies (underlying graph structure of $$T$$ T ) which increases exponentially as the number of given points...
Location awareness is important in many wireless sensor networks. In sensor networks because of the size, weight, battery life and price some nodes (e.g. GPS-equipped nodes) are self-located but all other nodes have to determine their locations by communication with location-aware neighbors. The classical distance-based technique for location determination is triangulation/lateration (referred to...
In this paper we consider the problem of optimising the construction and haulage costs of underground mining networks. We focus on a model of underground mine networks consisting of ramps in which each ramp has a bounded maximum gradient. The cost depends on the lengths of the ramps, the tonnages hauled through them and their gradients. We model such an underground mine network as an edge-weighted...
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