19 citations · 39 across the 14 of their papers we have counts for
15 papers
Computing skeletons for rectilinearly-convex obstacles in the rectilinear plane
Marcus Volz, Marcus Brazil, Charl Ras +1
We introduce the concept of an obstacle skeleton which is a set of line segments inside a polygonal obstacle that can be used in place of when performing intersection tests…
The -connected bottleneck Steiner network problem is NP-hard in any plane
M Brazil, C Ras, D Thomas +1
Bottleneck Steiner networks model energy consumption in wireless ad-hoc networks. The task is to design a network spanning a given set of terminals and at most Steiner points s…
The Fast Heuristic Algorithms and Post-Processing Techniques to Design Large and Low-Cost Communication Networks
Yahui Sun, Marcus Brazil, Doreen Thomas +1
It is challenging to design large and low-cost communication networks. In this paper, we formulate this challenge as the prize-collecting Steiner Tree Problem (PCSTP). The objectiv…
Minimal curvature-constrained networks
David Kirszenblat, Kashyapa Sirinanda, Marcus Brazil +3
This paper introduces an exact algorithm for the construction of a shortest curvature-constrained network interconnecting a given set of directed points in the plane and an iterati…
Demonstrating efficiency gains from installing truck turntables at crushers
Marcus Brazil, Peter A Grossman, J Hyam Rubinstein +1
The installation of truck turntables at above-ground crushers has the potential to yield gains in efficiency and productivity by eliminating the need for the trucks to turn around…
Approximating Minimum Steiner Point Trees in Minkowski Planes
M. Brazil, C. J. Ras, D. A. Thomas
Given a set of points, we define a minimum Steiner point tree to be a tree interconnecting these points and possibly some additional points such that the length of every edge is at…
A geometric characterisation of the quadratic min-power centre
M. Brazil, C. J. Ras, D. A. Thomas
For a given set of nodes in the plane the min-power centre is a point such that the cost of the star centred at this point and spanning all nodes is minimised. The cost of the star…
Relay Augmentation for Lifetime Extension of Wireless Sensor Networks
Marcus Brazil, Charl Ras, Doreen Thomas
We propose a novel relay augmentation strategy for extending the lifetime of a certain class of wireless sensor networks. In this class sensors are located at fixed and pre-determi…
Minimum Opaque Covers for Polygonal Regions
J. Scott Provan, Marcus Brazil, Doreen Thomas +1
The Opaque Cover Problem (OCP), also known as the Beam Detector Problem, is the problem of finding, for a set S in Euclidean space, the minimum-length set F which intersects every…
A Flow-dependent Quadratic Steiner Tree Problem in the Euclidean Plane
Marcus Brazil, Charl Ras, Doreen Thomas
We introduce a flow-dependent version of the quadratic Steiner tree problem in the plane. An instance of the problem on a set of embedded sources and a sink asks for a directed tre…
An exact algorithm for the bottleneck 2-connected -Steiner network problem in planes
Marcus Brazil, Charl Ras, Doreen Thomas
We present the first exact polynomial time algorithm for constructing optimal geometric bottleneck 2-connected Steiner networks containing at most Steiner points, where i…
Generalised k-Steiner Tree Problems in Normed Planes
Marcus N. Brazil, Charl J. Ras, Konrad J. Swanepoel +1
The 1-Steiner tree problem, the problem of constructing a Steiner minimum tree containing at most one Steiner point, has been solved in the Euclidean plane by Georgakopoulos and Pa…
The bottleneck 2-connected -Steiner network problem for
M. Brazil, C. J. Ras, D. A. Thomas
The geometric bottleneck Steiner network problem on a set of vertices embedded in a normed plane requires one to construct a graph spanning and a variable set of $k\geq…
The Gilbert Arborescence Problem
M. G. Volz, M. Brazil, C. J. Ras +2
We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations in a normed space and with associated flo…
Designing Optimal Flow Networks
M. G. Volz, M. Brazil, K. J. Swanepoel +1
We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. The network may contain other…