175 Years of linear programming: 2. Pivots in column space

The simplex method has been the veritable workhorse of linear programming for five decades now. An elegant geometric interpretation of the simplex method can be visualised by viewing the animation of the algorithm in acolumn space representation. In fact, it is this interpretation that explains why it is called the simplex method. The extreme points of the feasible region (polyhedron) of the linear programme can be shown to correspond to an arrangement of simplices in this geometry and the pivoting operation to a physical pivot from one simplex to an adjacent one in the arrangement. This paper introduces this vivid description of the simplex method as a tutored dance of simplices performing 'pivots in column space'

175 years of linear programming: minimax and cake

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On-line maintenance of optimal machine schedules

Effective and efficient scheduling in a dynamically changing environment is important for real-time control of manufacturing, computer, and telecommunication systems. This paper illustrates the algorithmic and analytical issues associated with developing efficient and effective methods to update schedules on-line. We consider the problem of dynamically scheduling precedence-constrained jobs on a single processor to minimize the maximum completion time penalty. We first develop an efficient technique to reoptimize a rolling schedule when new jobs arrive. The effectiveness of reoptimizing the current schedule as a long-term on-line strategy is measured by bounding its performance relative to oracles that have perfect information about future job arrivals

Godel's explorations in terra incognita

This paper presents an introduction to and an overview of the celebrated incompleteness theorems of Kurt Godel. Starting with Richard's paradox, the logical antimony that motivated Godel to look at encoding metamathematics in the arithmetic of integers, this overview traces the highlights of the encoding and the gist of Godel's final arguments

Hulls and efficient sets for the rectilinear norm

Given a set of points on the plane, we study the structure of their rectilinear hull. We also consider the multiple objective decision of identifying a facility location that minimizes the rectilinear distance to each of these points. We show specific correspondences between the efficient (non-dominated) solutions to the location problem and the rectilinear hulls of point sets in the plane