Minimum weight

About: Minimum weight is a research topic. Over the lifetime, 2002 publications have been published within this topic receiving 28244 citations.

Panel flutter optimization by gradient projection

Abstract: A gradient projection optimal control algorithm incorporating conjugate gradient directions of search is described and applied to several minimum weight panel design problems subject to a flutter speed constraint. New numerical solutions are obtained for both simply-supported and clamped homogeneous panels of infinite span for various levels of inplane loading and minimum thickness. The minimum thickness inequality constraint is enforced by a simple transformation of variables.

On Minimum 3-Cuts and Approximating k-Cuts Using Cut Trees

Abstract: This paper describes two results on graph partitioning. Our first result is a non-crossing property of minimum 3-cuts. This property generalizes the results by Gomory-Hu on min-cuts (2-cute) in graphs. We also give an algorithm for finding minimum 3-cuts in O(n3) Max-Flow computations. The second part of the paper describes a Performance Bounding technique based on Cut Trees for solving Partitioning Problems in weighted, undirected graphs. We show how to use this technique to derive approximation algorithms for two problems, the Minimum k-cut problem and the Multi-way cut problem.Our first illustration of the bounding technique is an algorithm for the Minimum k-cut which requires O(kn(m + n log n)) steps and gives an approximation of 2(1-1/k). We then generalise the Bounding Technique to achieve the approximation factor 2 — f(j, k) wheref(j, k) = j/k — (j — 2)/k2 + O(j/k3), j ≥ 3. The algorithm presented for the Minimum k-cut problem is polynomial in n and k for fixed j. We also give an approximation algorithm for the planar Multi-way Cut problem.

Heuristics for planar minimum‐weight perfect metchings

Abstract: Several linear-time approximation algorithms for the minimum-weight perfect matching in a plane are proposed, and their worst- and average-case behaviors are analyzed theoretically as well as experimentally. A linear-time approximation algorithm, named the “spiral-rack algorithm (with preprocess and with tour),” is recommended for practical purposes. This algorithm is successfully applied to the drawing of road maps such as that of the Tokyo city area. I. INTRODUCTION Consider n (an even number) points in a plane. The problem of finding the minimumweight perfect matching, i.e., determining how to match the n points in pairs so as to minimize the sum of the distances between the matched points, as well as Euler’s problem of unicursal traversing on a graph, is of fundamental importance for optimizing the sequence of drawing lines by a mechanical plotter ([2-5, 81; details are discussed in Sec. V). The algorithm which exactly solves this problem in 0(n3) time [6] seems to be too complicated from the practical point of view. Even approximation algorithms of O(n2) or O(n log n) [lo] would not be satisfactory or need some improvement for the application to real-world problems of a size, say, n greater than lo4. In contrast with the matching problem, an Eulerian path can be found in linear time in the’number of edges. In this paper, linear-time* approximation algorithms are proposed for the matching problem in a unit square; their worst-case performances are analyzed theoretically; their average-case performances are investigated both theoretically and experimentally for the case where n points are uniformly distributed on the unit square; and an application to the drawing of a road map is shown. The quality of an approximate solution is measured by the absolute cost of the matching, i.e., the sum of the distances *We adopt the RAM model of computation which executes an arithmetic operation such as addition, multiplication, or integer division (hence, the “floor” operation) in a unit time [ 11.