A complete solution to the Maximum Density Still Life Problem
نویسندگان
چکیده
منابع مشابه
A complete solution to the Maximum Density Still Life Problem
The Maximum Density Still Life Problem (CSPLib prob032) is to find the maximum number of live cells that can fit in an n × n region of an infinite board, so that the board is stable under the rules of Conway’s Game of Life. It is considered a very difficult problem and has a raw search space of O(2 2 ). Previous state of the art methods could only solve up to n = 20. We give a powerful reformul...
متن کاملUsing Relaxations in Maximum Density Still Life
The Maximum Density Sill-Life Problem is to fill an n × n board of cells with the maximum number of live cells so that the board is stable under the rules of Conway’s Game of Life. We reformulate the problem into one of minimising “wastage” rather than maximising the number of live cells. This reformulation allows us to compute strong upper bounds on the number of live cells. By combining this ...
متن کاملThe still-Life density problem and its generalizations
A still Life is a subset S of the square lattice Z 2 xed under the transition rule of Conway's Game of Life, i.e. a subset satisfying the following three conditions: 1. No element of Z 2 ? S has exactly three neighbors in S; 2. Every element of S has at least two neighbors in S; 3. Every element of S has at most three neighbors in S. Here a \neighbor" of any x 2 Z 2 is one of the eight lattice ...
متن کاملA Pseudo-Boolean Solution to the Maximum Quartet Consistency Problem
Determining the evolutionary history of a given biological data is an important task in biological sciences. Given a set of quartet topologies over a set of taxa, the Maximum Quartet Consistency (MQC) problem consists of computing a global phylogeny that satisfies the maximum number of quartets. A number of solutions have been proposed for the MQC problem, including Dynamic Programming, Constra...
متن کاملA Complete Explicit Solution to the Log-Optimal Portfolio Problem
Kramkov and Schachermayer (1999) proved the existence of log-optimal portfolios under weak assumptions in a very general setting. For many – but not all – cases, Goll and Kallsen (2000) obtained the optimal solution explicitly in terms of the semimartingale characteristics of the price process. By extending this result, this paper provides a complete explicit characterization of log-optimal por...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Artificial Intelligence
سال: 2012
ISSN: 0004-3702
DOI: 10.1016/j.artint.2012.02.001