A nonogram is a logic puzzle where one shades certain cells of a 2D grid to reveal a hidden image. One uses the sequences of numbers on the left and the top of the grid to figure out how many and which cells to shade. We propose a new technique to solve a nonogram using compressive sensing. Our method avoids (1) partial fill-ins, (2) heuristics, and (3) over-complication, and only requires that we solve a binary integer programming problem. / text

Made available in DSpace on 2014-12-17T15:48:07Z (GMT). No. of bitstreams: 1 CamilaNOT_DISSERT.pdf: 4321465 bytes, checksum: d103bd2da647997e8dfd0a8784c2060d (MD5) Previous issue date: 2013-02-01 / Nonogram is a logical puzzle whose associated decision problem is NP-complete. It has applications in pattern recognition problems and data compression, among others. The puzzle consists in determining an assignment of colors to pixels distributed in a N  M matrix that satisfies line and column constraints. A Nonogram is encoded by a vector whose elements specify the number of pixels in each row and column of a figure without specifying their coordinates. This work presents exact and heuristic approaches to solve Nonograms. The depth first search was one of the chosen exact approaches because it is a typical example of brute search algorithm that is easy to implement. Another implemented exact approach was based on the Las Vegas algorithm, so that we intend to investigate whether the randomness introduce by the Las Vegas-based algorithm would be an advantage over the depth first search. The Nonogram is also transformed into a Constraint Satisfaction Problem. Three heuristics approaches are proposed: a Tabu Search and two memetic algorithms. A new function to calculate the objective function is proposed. The approaches are applied on 234 instances, the size of the instances ranging from 5 x 5 to 100 x 100 size, and including logical and random Nonograms / O Nonograma ? um jogo l?gico cujo problema de decis?o associado ? NP-completo. Ele possui aplica??o em problemas de identifica??o de padr?es e de compacta??o de dados, dentre outros. O jogo consiste em determinar uma aloca??o de cores em pixels distribu?dos em uma matriz N  M atendendo restri??es em linhas e colunas. Um Nonograma ? codificado atrav?s de vetores cujos elementos especificam o n?mero de pixels existentes em cada coluna e linha de uma figura, sem especificar suas coordenadas. Este trabalho apresenta abordagens exatas e heur?sticas para solucionar o Nonograma. A Busca em Profundidade foi uma das abordagens exatas escolhida, por ser um exemplo t?pico de algoritmo de for?a bruta de f?cil implementa??o. Outra abordagem exata implementada foi baseada no algoritmo Las Vegas, atrav?s do qual se pretende investigar se a aleatoriedade introduzida pelo algoritmo Las Vegas traria algum benef?cio em rela??o ? Busca em Profundidade. O Nonograma tamb?m ? transformado em um Problema de Satisfa??o de Restri??es. Tr?s abordagens heur?sticas s?o propostas: uma Busca Tabu e dois algoritmos Mem?tico. Uma nova abordagem para o c?lculo da fun??o objetivo ? proposta neste trabalho. As abordagens s?o testadas em 234 casos de teste de tamanho entre 5 x 5 e 100 x 100, incluindo Nonogramas l?gicos e aleat?rios