We prove the computational intractability of rotating and placing n square tiles into a 1×n array such that adjacent tiles are compatible—either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as in jigsaw puzzles. Beyond basic NP-hardness, we prove that it is NP-hard even to approximately maximize the number of placed tiles (allowing blanks), while satisfying the...

In this article we describe our research on providing techniques and tools for a particular type of sensemaking — finding embedded narratives or plots across large collections of relatively brief text documents. Our approach is decidedly human-centered and we have created the Jigsaw system as an embodiment of these principles. Jigsaw provides multiple visualizations depicting the documents, the...

A fundamental assumption in machine vision is that the spatial arrangement of pixels is given. In challenging this assumption we have utilised a general relationship that exists between space and behaviour. This relationship presents itself as spatial redundancy, which other researchers have considered problematic. We present a mathematical model and empirical investigations into this relations...

We prove the computational intractability of rotating and placing n square tiles into a 1 × n array such that adjacent tiles are compatible—either equal edge colors, as in edge-matching puzzles, or matching tab/pocket shapes, as in jigsaw puzzles. Beyond basic NP-hardness, we prove that it is NPhard even to approximately maximize the number of placed tiles (allowing blanks), while satisfying th...

This study aims to develop and evaluate a language learning system supported by the ‘flipped jigsaw’ technique, called ‘Flip-J’. This system mainly consists of three functions: (1) the creation of a learning material database, (2) allocation of learning materials, and (3) formation of an expert and jigsaw group. Flip-J was developed as the plugin of the learning management system Moodle, and th...

In the last decade the enterprise of formal semantics has been under attack from several philosophical and linguistic perspectives, and it has certainly suffered from its own scattered state, which hosts quite a variety of paradigms which may seem to be incompatible. It will not do to try and answer the arguments of the critics, because the arguments are often welltaken. The negative conclusion...

1 John Burkhardt, United States Naval Academy, Department of Mechanical Engineering, Annapolis, MD 21402 [email protected] 2 Peter R. Turner, United States Naval Academy, Department of Mathematics, Annapolis, MD 21402 [email protected] Abstract  The use of jigsaw techniques in a multidisciplinary, project-oriented, introductory computational science and engineering course is described. The course r...

Jigsaw puzzles [9] and edge-matching puzzles [5] are two ancient types of puzzle, going back to the 1760s and 1890s, respectively. Jigsaw puzzles involve fitting together a given set of pieces (usually via translation and rotation) into a desired shape (usually a rectangle), often revealing a known image or pattern. The pieces are typically squares with a pocket cut out of or a tab attached to ...

This study describes the development of a ubiquitous cooperative learning environment using proposed annotation services, wireless communication devices, and the Jigsaw method of cooperative learning. The purpose of the study is to investigate the potential benefits of studying digital course materials with embedded annotations. The SQ3R study method is introduced during the individual study ph...

Task-based language Teaching (TBLT) has occupied the pertinent literature for some long years. However, the role of specific task type in developing specific skill type seems to be amongst the intact issues in the literature. To shed more light on this issue, the present study was conducted to compare the effect of jigsaw and decision-making tasks on improving listening and speaking abilities o...