Some experimental results on placement techniques
Maurice Hanan, Peter K. Wolff, et al.
DAC 1976
We present a linear programming-based method for finding `gadgets,' i.e., combinatorial structures reducing constraints of one optimization problem to constraints of another. A key step in this method is a simple observation which limits the search space to a finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by Bellare, Goldreich, and Sudan of how to prove the optimality of gadgets: linear programming duality gives such proofs. The new gadgets, when combined with recent results of Hastad improve the known inapproximability results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 16/17+ε and 12/13+ε respectively, is NP-hard for every ε>0. Prior to this work, the best-known inapproximability thresholds for both problems were 71/72. Without using the gadgets from this paper, the best possible hardness that would follow from Bellare, Goldreich, and Sudan and Hastad is 18/19. We also use the gadgets to obtain an improved approximation algorithm for MAX3 SAT which guarantees an approximation ratio of .801. This improves upon the previous best bound of .7704.
Maurice Hanan, Peter K. Wolff, et al.
DAC 1976
Liqun Chen, Matthias Enzmann, et al.
FC 2005
Ohad Shamir, Sivan Sabato, et al.
Theoretical Computer Science
Elizabeth A. Sholler, Frederick M. Meyer, et al.
SPIE AeroSense 1997