10,562 research outputs found
Euclidean TSP with few inner points in linear space
Given a set of points in the Euclidean plane, such that just points
are strictly inside the convex hull of the whole set, we want to find the
shortest tour visiting every point. The fastest known algorithm for the version
when is significantly smaller than , i.e., when there are just few inner
points, works in time [Knauer and Spillner,
WG 2006], but also requires space of order . The best
linear space algorithm takes time [Deineko, Hoffmann, Okamoto,
Woeginer, Oper. Res. Lett. 34(1), 106-110]. We construct a linear space
time algorithm. The new insight is extending the
known divide-and-conquer method based on planar separators with a
matching-based argument to shrink the instance in every recursive call. This
argument also shows that the problem admits a quadratic bikernel.Comment: under submissio
Renormalization for Discrete Optimization
The renormalization group has proven to be a very powerful tool in physics
for treating systems with many length scales. Here we show how it can be
adapted to provide a new class of algorithms for discrete optimization. The
heart of our method uses renormalization and recursion, and these processes are
embedded in a genetic algorithm. The system is self-consistently optimized on
all scales, leading to a high probability of finding the ground state
configuration. To demonstrate the generality of such an approach, we perform
tests on traveling salesman and spin glass problems. The results show that our
``genetic renormalization algorithm'' is extremely powerful.Comment: 4 pages, no figur
Fast movement strategies for a step-and-scan wafer stepper
We describe algorithms for the determination of fast movement strategies for a step-and-scan wafer stepper, a device that is used for the photolithographic processing of integrated circuits. The proposed solution strategy consists of two parts. First, we determine the maximum number of congruent rectangular chips that can be packed on a wafer, subject to the restriction that the chips are placed in a rectangular grid. Second, we find fast movement strategies for scanning all chips of a given packing, given the mechanical restrictions of the wafer stepper. The corresponding combinatorial optimization problem is formulated as a generalized asymmetric traveling salesman problem. We show how feasible scan strategies are determined, and how these strategies are improved by local search techniques, such as iterative improvement based on 2- and 3-exchanges, and simulated annealing based on 2-exchanges.\ud
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