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Total Outer-Independent Domination Number: Bounds and Algorithms
(MDPI AG, 2025-03-10)
BOSCH PÉREZ, PAUL JESÚS
;
Ernesto Parra Inza
;
Ismael Rios Villamar
;
José Luis Sánchez-Santiesteban
In graph theory, the study of domination sets has garnered significant interest due to its applications in network design and analysis. Consider a graph G(V,E); a subset of its vertices is a total dominating set (TDS) if, for each x∈V(G), there exists an edge in E(G) connecting x to at least one vertex within this subset. If the subgraph induced by the vertices outside the TDS has no edges, the set is called a total outer-independent dominating set (TOIDS). The total outer-independent domination number, denoted as γtoi(G), represents the smallest cardinality of such a set. Deciding if a given graph has a TOIDS with at most r vertices is an NP-complete problem. This study introduces new lower and upper bounds for γtoi(G) and presents an exact solution approach using integer linear programming (ILP). Additionally, we develop a heuristic and a procedure to efficiently obtain minimal TOIDS.
3
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Optimizing the wine transportation process from bottling plants to ports
(2023)
Franco Basso
;
Juan Pablo Contreras
;
Raúl Pezoa
;
Alejandro Troncozo
;
VARAS VALDÉS, MAURICIO ANDRÉS
Scopus© Citations 2 1
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An integrated multi-criteria decision analysis and optimization modeling approach to spatially operational road repair decisions
(2021)
Sättar Ezzati
;
PALMA INFANTE, CRISTIAN DERECK
;
Pete Bettinger
;
Ljusk Ola Eriksson
;
Anjali Awasthi
In this study, we developed a generic cost-effective approach for spatially explicit decision support involving the allocation of road repair treatments. The approach begins with an assessment of the existing road condition to identify the extent of environmental impacts and to determine road repair regimes in a subjective manner using group-decision making efforts. An integer programming model is then formulated by combining expert opinions with operational costs to guide repair schedules required for each road segment at the operational planning level. To demonstrate model performance, we applied it to a 400 km<jats:sup>2</jats:sup> landscape consisting of 289 km of paved roads in the mountainous region of the Hyrcanian forests in Iran. We assessed sensitivity of the inputs, such as weight verification, budgetary limitations, and rehabilitation weights. The results of the subjective analysis show that 76% of the roads analyzed in these forests must be prioritized to receive treatments as intended for logistical purposes. Incorporating the extent of environmental dimensions into operational costs allows us to generate an optimal tradeoff curve by selecting an appropriate treatment for segments of a road network. The approach demonstrated here can be used to design detailed alternative solutions for addressing spatially-informed road decisions under various terrain conditions.
4Scopus© Citations 5
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A multi-objective approach for supporting wine grape harvest operations
(2020)
VARAS VALDÉS, MAURICIO ANDRÉS
;
Franco Basso
;
Sergio Maturana
;
David Osorio
;
Raúl Pezoa
Scopus© Citations 46 3
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Collaborative job scheduling in the wine bottling process
(2020)
Franco Basso
;
Mario Guajardo
;
VARAS VALDÉS, MAURICIO ANDRÉS
7Scopus© Citations 25

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