The most vital edges in the minimum spanning tree problem
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Cited by (30)
Parametric matroid interdiction
2024, Discrete OptimizationOn designing networks resilient to clique blockers
2023, European Journal of Operational ResearchCitation Excerpt :The considered combinatorial optimization problems are known as the minimum vertex/edge blocker problem (Mahdavi Pajouh, 2019; Mahdavi Pajouh, Walteros, Boginski, & Pasiliao, 2015; Ries et al., 2010; Wei, Walteros, & Pajouh, 2021) and the most vital (critical) vertices/edges problem (Furini, Ljubi, Martin, & San Segundo, 2019; Veremyev, Boginski, & Pasiliao, 2014a; Veremyev, Prokopyev, & Pasiliao, 2014b; 2015; 2019), respectively. A number of important network characterizations are explored in the context of vertex/edge blockers, such as the clique (Mahdavi Pajouh, 2019; Mahdavi Pajouh, Boginski, & Pasiliao, 2014; Tang, Richard, & Smith, 2016), independent set (Bazgan, Toubaline, & Tuza, 2011), dominating set (Mahdavi Pajouh et al., 2015), vertex cover (Bazgan et al., 2011), spanning tree (Bazgan, Toubaline, & Vanderpooten, 2013; Frederickson & Solis-Oba, 1999; Lin & Chern, 1993), pair-wise connectivity (Arulselvan, Commander, Elefteriadou, & Pardalos, 2009; Di Summa, Grosso, & Locatelli, 2011; 2012; Shen, Nguyen, Xuan, & Thai, 2012; Veremyev et al., 2014a; Veremyev et al., 2014b), shortest path (Israeli & Wood, 2002; Khachiyan et al., 2008; Schieber, Bar-Noy, & Khuller, 1995), matching (Zenklusen, 2010a), and maximum flow (Afshari Rad & Kakhki, 2017; Altner, Ergun, & Uhan, 2010; Ghare, Montgomery, & Turner, 1971; Wollmer, 1964; Wong et al., 2017; Wood, 1993; Zenklusen, 2010b) network properties. In this paper, we focus on the concept of a weighted clique.
A Survey on Mixed-Integer Programming Techniques in Bilevel Optimization
2021, EURO Journal on Computational OptimizationCitation Excerpt :These problems model some of the most traditional and oldest applications arising in the areas of military or homeland security. Besides interdiction of shortest paths (Israeli and Wood, 2002) or maximum flows (Akgün et al., 2011; Cormican et al., 1998; Janjarassuk and Linderoth, 2008; Wood, 1993), problems also have been studied in which the follower solves the spanning tree (Bazgan et al., 2013; Lin and Chern, 1993) or the maximum matching problem (Zenklusen, 2010). These are interdiction problems in which the lower level is an MILP.
Robust recoverable 0–1 optimization problems under polyhedral uncertainty
2019, European Journal of Operational ResearchExact algorithms for the minimum cost vertex blocker clique problem
2019, Computers and Operations ResearchCitation Excerpt :The second one is looking for a subset of vertices or edges within a given size or budget whose deletion results in the greatest change to the considered property. Both problems have been studied in the context of different graph-related properties such as shortest path (Bar-Noy et al., 1995; Israeli and Wood, 2002; Khachiyan et al., 2008), pair-wise connectivity (Arulselvan et al., 2009; Di Summa et al., 2011; 2012; Dinh et al., 2014; 2012; Shen et al., 2013; Veremyev et al., 2014a; 2014b), maximum flow (Afshari Rad and Kakhki, 2017; Altner et al., 2010; Ghare et al., 1971; Wollmer, 1964; Wong et al., 2017; Wood, 1993; Zenklusen, 2010b), spanning tree (Bazgan et al., 2013; Frederickson and Solis-Oba, 1999; Lin and Chern, 1993), matching (Zenklusen, 2010a), dominating set (Mahdavi Pajouh et al., 2015), vertex cover (Bazgan et al., 2011), independent set (Bazgan et al., 2011), and clique (Mahdavi Pajouh et al., 2014; Tang et al., 2016) among others. Clique as a subset of vertices in a graph that are pairwise connected was originally introduced in Luce and Perry (1949).
On recoverable and two-stage robust selection problems with budgeted uncertainty
2018, European Journal of Operational Research