Julio César Pérez Sansalvador

arXiv2021

Burning graphs through farthest-first traversal

The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify the vulnerability of a graph to contagion. This paper introduces a simple farthest-first traversal-based approximation algorithm for this problem over general graphs. We refer to this proposal as the Burning Farthest-First (BFF) algorithm. BFF runs in $O(n^3)$ steps and has an approximation factor of $3-2/b(G)$, where $b(G)$ is the size of an optimal solution. Despite its simplicity, BFF tends to generate near-optimal solutions when tested over some benchmark datasets; in fact, it returns similar solutions to those returned by much more elaborated heuristics from the literature.

cs.DS↗

arXiv2019

Software System Design based on Patterns for Newton-Type Methods

A wide range of engineering applications uses optimisation techniques as part of their solution process. The researcher uses specialized software that implements well-known optimisation techniques to solve his problem. However, when it comes to develop original optimisation techniques that fit a particular problem the researcher has no option but to implement his own new method from scratch. This leads to large development times and error prone code that, in general, will not be reused for any other application. In this work, we present a novel methodology that simplifies, fasten and improves the development process of scientific software. This methodology guide us on the identification of design patterns. The application of this methodology generates reusable, flexible and high quality scientific software. Furthermore, the produced software becomes a documented tool to transfer the knowledge on the development process of scientific software. We apply this methodology for the design of an optimisation framework implementing Newton's type methods which can be used as a fast prototyping tool of new optimisation techniques based on Newton's type methods. The abstraction, reusability and flexibility of the developed framework is measured by means of Martin's metric. The results indicate that the developed software is highly reusable.

cs.MS↗