Given a simple (cuttable) polygon Q drawn on a piece of planar material R, we cut Q out of R by a (small) circular saw with a total number of cuts no more than twice the optimal. This improves the previous approximation ratio of 2.5 obtained by Demaine et al. in 2001.

We find the minimal cutwidth and bisection width values for abelian Cayley graphs with up to 4 generators and present an algorithm for finding the corresponding optimal ordering. We also find minimal cuts of each order. © 2007 Elsevier B.V. All rights reserved.

We consider a generalization of the classical max-cut problem where two objective functions are simultaneously considered. We derive some theorems on the existence and the non-existence of feasible cuts that are at the same time near optimal for both criteria. Furthermore, two approximation algorithms with performance guarantee are presented. The first one is deterministic while the second one ...