Marcus Brazil

Network augmentation for disaster-resilience against geographically correlated failure

Nicolau Andres-Thio, Marcus Brazil, Charl Ras, Doreen Thomas

Journal article  |  2022  |  NETWORKS

We introduce a formal framework for the study of augmenting networks in the plane for disaster-resilience, where a disaster is mod..

A model for open-pit pushback design with operational constraints

Juan L Yarmuch, Marcus Brazil, Hyam Rubinstein, Doreen A Thomas

Journal article  |  2021  |  OPTIMIZATION AND ENGINEERING

Open-pit mines are surface excavations created to extract valuable material which, in most cases, is located near the surface. Pus..

An exact algorithm for constructing minimum Euclidean skeletons of polygons

Nicolau Andres-Thio, Marcus Brazil, Charl Ras, Doreen Thomas, Marcus Volz

Journal article  |  2021  |  JOURNAL OF GLOBAL OPTIMIZATION

A Euclidean skeleton is a set of edges in the interior (or on the boundary) of a polygon that intersects any line segment that joi..

Simplifying obstacles for Steiner network problems in the plane

Marcus Volz, Marcus Brazil, Charl Ras, Doreen Thomas

Journal article  |  2021  |  NETWORKS

We present methods for simplifying the geometry of polygonal obstacles as a preprocessing step to solving obstacle-avoiding Steine..

Minimum Steiner trees on a set of concyclic points and their center

David Whittle, Marcus Brazil, Peter Alexander Grossman, Joachim Hyam Rubinstein, Doreen A Thomas

Journal article  |  2021  |  INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH

Consider a configuration of points comprising a point q and a set of concyclic points R that are all a given distance r from q in ..

A mathematical model for mineable pushback designs

Juan L Yarmuch, Marcus Brazil, Hyam Rubinstein, Doreen A Thomas

Journal article  |  2021  |  INTERNATIONAL JOURNAL OF MINING RECLAMATION AND ENVIRONMENT

In the design of open pit mines, the region to be mined is partitioned into pushbacks, subregions that allow the mining to be divi..

Computational complexity of the 2-connected Steiner network problem in the ℓp plane

CJ Ras, M Brazil, DA Thomas

Journal article  |  2021  |  Theoretical Computer Science

The geometric 2-connected Steiner network problem asks for a shortest bridgeless network spanning a given set of terminals in the ..

Solving the prize-collecting Euclidean Steiner tree problem

David Whittle, Marcus Brazil, Peter A Grossman, J Hyam Rubinstein, Doreen A Thomas

Journal article  |  2020  |  INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH

The prize-collecting Euclidean Steiner tree (PCEST) problem is a generalization of the well-known Euclidean Steiner tree (EST) pro..

Computing Skeletons for Rectilinearly Convex Obstacles in the Rectilinear Plane

M Volz, M Brazil, C Ras, D Thomas

Journal article  |  2020  |  Journal of Optimization Theory and Applications

We introduce the concept of an obstacle skeleton, which is a set of line segments inside a polygonal obstacle ω that can be used i..

OPTIMAL LOCATION OF AN UNDERGROUND CONNECTOR USING DISCOUNTED STEINER TREE THEORY

KG Sirinanda, M Brazil, PA Grossman, JH Rubinstein, DA Thomas

Journal article  |  2020  |  ANZIAM JOURNAL

The objective of this paper is to demonstrate that the gradient-constrained discounted Steiner point algorithm (GCDSPA) described ..