How Fast Can We Play Tetris Greedily With Rectangular Pieces?

Consider a variant of Tetris played on a board of width $w$ and infinite height, where the pieces are axis-aligned rectangles of arbitrary integer dimensions, the pieces can only be moved before letting them drop, and a row does not disappear once it is full. Suppose we want to follow a greedy strategy: let each rectangle fall where it will end up the lowest given the current state of the board. To do so, we want a data structure which can always suggest a greedy move. In other words, we want a data structure which maintains a set of $O(n)$ rectangles, supports queries which return where to drop the rectangle, and updates which insert a rectangle dropped at a certain position and return the height of the highest point in the updated set of rectangles. We show via a reduction to the Multiphase problem [P\u{a}tra\c{s}cu, 2010] that on a board of width $w=\Theta(n)$, if the OMv conjecture [Henzinger et al., 2015] is true, then both operations cannot be supported in time $O(n^{1/2-\epsilon})$ simultaneously. The reduction also implies polynomial bounds from the 3-SUM conjecture and the APSP conjecture. On the other hand, we show that there is a data structure supporting both operations in $O(n^{1/2}\log^{3/2}n)$ time on boards of width $n^{O(1)}$, matching the lower bound up to a $n^{o(1)}$ factor.Comment: Correction of typos and other minor correction

"That's not how it should end!": the effect of reader/player response on the development of narrative

When the final instalment of the videogame series Mass Effect was released in March 2012, many fans used online forums to express displeasure at the game's ending. A surprising number suggested that Victorian writers such as Charles Dickens and Sir Arthur Conan Doyle were far more attentive and responsive to their audience's preferences than modern authors or videogame writers. This thesis, in part, seeks to explore the veracity of this idea through a creative-critical comparison of key examples of Victorian serial fiction and modern episodic videogames, and through the creation of an interactive novella. The creative-critical element of the thesis is produced in two formats which examine how serial texts may be considered 'interactive' due to the unique opportunity they provide for readers to influence the act of textual production; the extent to which videogames may be considered serial due to their structure, content, and modes of delivery; the controversies surrounding consumption of serials and videogames; and how techniques relating to characterisation, character death and endings operate within serial and interactive forms. Focussing primarily on Great Expectations, selected Sherlock Holmes stories, and the Mass Effect and Life is Strange videogame series, the role of writer and reader as collaborative participants in the creation of narrative content is examined in particular in relation to the tropes of the magic trick, the telepathic exchange and the detective duo. The creative component of the thesis puts some of these findings into practice by offering a story in which the reader-player gradually comes to realise the effect of their interventions in the narrative. Created using the authoring tool ChoiceScript, Writers Are Not Strangers plays with ideas of co-operation and control, and authorship and agency. Using a modular structure and quality-based salience (text dependent on previous user choices) this multi-branching, multiple-ended text attempts to craft a story in response to its reader, while never fully giving over control

Where have all the games gone? An exploratory study of digital game preservation

It is 50 years since the development of the first computer game and digital games now have an unprecedented influence on our culture. An increasingly popular leisure activity, digital games are also permeating other aspects of society. They continue to influence computer technology through graphics, animation and social networking; an influence which is also being felt in other media, in particular film and television. They are a new art form and they are seen to be influential on children s learning and development. However, despite their pervasiveness and apparent importance within our society and culture, they are still largely ignored as part of our cultural heritage. Dismissed as disposable, entertainment products, they have not specifically been addressed in most of the academic literature on digital preservation which represents a serious omission in past research. This was justification for an exploratory study into the preservation of digital games and the aim of this study has been to explore the value of digital games, their significance in our culture, and the current status of their preservation. Investigating the relationship of games to culture; reviewing current preservation activities and drawing conclusions about the value of digital games and the significance of their preservation were the study s objectives. These have been achieved through interviews with key stakeholders the academic community, as potential users of collections; memory institutions, as potential keepers of collections; fan-based game preservation experts; and representatives from the games industry. In addition to this, case studies of key game preservation activities were explored. Through this research, a clearer picture of attitudes towards digital games and opinions on the need for preservation of these cultural products has been established. It has become apparent that there is a need for more coherent and collaborative efforts to ensure the longevity of these important aspects of digital heritage