Convexity is a notion that has been defined for subsets of R and for subsets of general graphs. A convex cut of a graph G = (V,E) is a 2-partition V1∪̇V2 = V such that both V1 and V2 are convex, i. e., shortest paths between vertices in Vi never leave Vi, i ∈ {1, 2}. Finding convex cuts is NP-hard for general graphs. To characterize convex cuts, we employ the Djoković relation, a reflexive and s...

In this study, the application of gray relational analysis (GRA) and Taguchi method in multi-criteria process parameters selection of turning operation has been investigated. The process responses under study are material removal rate (MRR) and surface roughness (SR); in turn, the input parameters include cutting speed, feed rate, depth of cut and nose radius of the cutting tool. The proposed a...

We present a framework to obtain valid inequalities for reverse convex set: the set of points in polyhedron that lie outside given open set. Reverse sets arise many models, including bilevel optimization and polynomial optimization. An intersection cut is well-known inequality generated from basic solution lies within introduce deriving solutions first propose an extension cuts defines two-term...

We discuss the optimal allocation problem in combinatorial auction, where the items are allocated to bidders so that the sum of the bidders’ utilities is maximized. In this paper, we consider the case where utility functions are given by quadratic functions; the class of quadratic utility functions has a succinct representation but is sufficiently general. The main aim of this paper is to show ...

Cocaine is a common drug of abuse. To detect its use, a screening detection concentration for the cocaine metabolite benzoylecgonine is commonly set at 150 ng/mL and its confirmatory cut-off is set at 100 ng/mL. Studies have suggested that these cut-offs may be set too high, allowing some patients with this substance abuse problem to be missed or improperly monitored. With the advent of liquid ...