Robert Bosch

Continuous line drawings via the traveling salesman problem

We describe how to use the traveling salesman problem to create continuous line drawings of target pictures.

Constraint Programming and Hybrid Formulations for Three Life Designs

Conways game of Life provides an interesting testbed for exploring issues in formulation, symmetry, and optimization with constraint programming and hybrid constraint programming/integer programming methods. We consider three Life pattern-creation problems: finding maximum density still-Lifes, finding smallest immediate predecessor patterns, and finding period-2 oscillators. For the first two problems, integrating integer programming and constraint programming approaches provides a much better solution procedure than either individually. For the final problem, the constraint programming formulation provides the better approach.

Integer Programming and Conway's Game of Life

This article presents integer programming formulations for finding interesting patterns in Conways game of Life, with accompanying exercises and solutions.

A NEW INFINITY-NORM PATH FOLLOWING ALGORITHM FOR LINEAR PROGRAMMING*

We devise a new primal-dual path following algorithm for linear programming that is based entirely on an infinity-norm centering measure. The algorithm makes reductions in a path parameter

Long steps in an O( n 3 L ) algorithm for linear programming

\mu

Simple-closed-curve sculptures of knots and links

, each of which is followed by a sequence of centering steps. The algorithm has similarities with both long step path following and predictor-corrector methods. We also consider a “modified” version of the algorithm that uses partial updating of the projection equations. The analysis of the modified algorithm has some interesting differences compared with previously devised partial updating methods. In particular, partial updating obtains a factor-of-

Opt art

\sqrt{n}

On Partial Updating in a Potential Reduction Linear Programming Algorithm of Kojima, Mizuno, and Yoshise

complexity reduction even though the permissible relative error in the approximate scaling factors is extremely small — only

Maximum density stable patterns in variants of Conway's game of Life

O( 1/ \sqrt{n})

Optimal Card-Collecting Strategies for Magic: The Gathering

.