Topic
Minimum weight
About: Minimum weight is a research topic. Over the lifetime, 2002 publications have been published within this topic receiving 28244 citations.
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Proceedings Article•
01 Jan 1998
6 citations
Posted Content•
TL;DR: This work provides a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with P min, which is induced by the deletion of the minimum weight edges.
Abstract: We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum partition. This minimum partition Pmin is induced by the deletion of the minimum weight edges. We provide a characterization of the graphs satisfying inheritance of convexity from the underlying game to the restricted game associated with P min.
6 citations
Proceedings Article•
14 Dec 2009TL;DR: In this paper, the authors considered the cases of quasistatic and dynamic loading separately and derived necessary optimality conditions with the aid of variational methods of the theory of optimal control.
Abstract: Rotationally symmetric shells of piece wise constant thickness are studied. The cases of quasistatic and dynamic loading are considered separately whereas the shells may be manufactured from both, elastic and inelastic materials. Minimum weight designs of inelastic shells of piece wise constant thickness are established under the condition that the limit load is fixed. Also the designs of maximum load carrying capacity are determined for given weight (material volume) of the shell. Necessary optimality conditions are derived with the aid of variational methods of the theory of optimal control.
6 citations
14 Feb 2013
TL;DR: The problem of finding a satisfying assignment for a CNF formula that minimizes the weight (the number of variables that are set to 1) is NP-complete even if the formula is a 2-CNF formula.
Abstract: The problem of finding a satisfying assignment for a CNF formula that minimizes the weight (the number of variables that are set to 1) is NP-complete even if the formula is a 2-CNF formula. It generalizes the well-studied problem of finding the smallest hitting set for a family of sets, which can be modeled using a CNF formula with no negative literals. The natural parameterized version of the problem asks for a satisfying assignment of weight at most k.
6 citations
TL;DR: In this article, the authors identify an analytical description for the layout of a minimum volume truss that is uniformly loaded, where two different span conditions are considered: single and multiple spans.
Abstract: The focus of this article is to identify an analytical description for the layout of a minimum volume truss that is uniformly loaded. Two different span conditions are considered: single and multiple spans. The multiple-span condition is supported at equally spaced locations. The methodology utilized for the solution of the problems takes advantage of Maxwell’s Theorem of Load Paths and the properties of reciprocal diagrams in Graphic Statics. This approach provides considerable insight in the properties of the optimal layouts for the given boundary and loading conditions. In Graphic Statics, the solution to a problem is based on tracing two related diagrams: the form and the force diagram. These obtained graphs can also be viewed as the definition of two dual structures. A force diagram created for a truss structure (form diagram) can be understood as the layout of a (dual) structure with its own loading condition. Therefore, the optimization can be conducted in either space (the force or the form). The ...
6 citations