How Bad is the Freedom to Flood-It?

Fixed-Flood-It and Free-Flood-It are combinatorial problems on graphs that generalize a very popular puzzle called Flood-It. Both problems consist of recoloring moves whose goal is to produce a monochromatic ("flooded") graph as quickly as possible. Their difference is that in Free-Flood-It the player has the additional freedom of choosing the vertex to play in each move. In this paper, we investigate how this freedom affects the complexity of the problem. It turns out that the freedom is bad in some sense. We show that some cases trivially solvable for Fixed-Flood-It become intractable for Free-Flood-It. We also show that some tractable cases for Fixed-Flood-It are still tractable for Free-Flood-It but need considerably more involved arguments. We finally present some combinatorial properties connecting or separating the two problems. In particular, we show that the length of an optimal solution for Fixed-Flood-It is always at most twice that of Free-Flood-It, and this is tight

How Bad is the Freedom to Flood-It?

International audienceFixed-Flood-It and Free-Flood-It are combinatorial problems on graphs that generalize a very popular puzzle called Flood-It. Both problems consist of recoloring moves whose goal is to produce a monochromatic ("flooded") graph as quickly as possible. Their difference is that in Free-Flood-It the player has the additional freedom of choosing the vertex to play in each move. In this paper, we investigate how this freedom affects the complexity of the problem. It turns out that the freedom is bad in some sense. We show that some cases trivially solvable for Fixed-Flood-It become intractable for Free-Flood-It. We also show that some tractable cases for Fixed-Flood-It are still tractable for Free-Flood-It but need considerably more involved arguments. We finally present some combinatorial properties connecting or separating the two problems. In particular, we show that the length of an optimal solution for Fixed-Flood-It is always at most twice that of Free-Flood-It, and this is tight

Extremal properties of flood-filling games

The problem of determining the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It has been studied extensively from an algorithmic point of view, but basic questions about the maximum number of moves that might be required in the worst case remain unanswered. We begin a systematic investigation of such questions, with the goal of determining, for a given graph, the maximum number of moves that may be required, taken over all possible colourings. We give several upper and lower bounds on this quantity for arbitrary graphs and show that all of the bounds are tight for trees; we also investigate how much the upper bounds can be improved if we restrict our attention to graphs with higher edge-density.Comment: Final version, accepted to DMTC

A system for image-based modeling and photo editing

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2002.Includes bibliographical references (p. 169-178).Traditionally in computer graphics, a scene is represented by geometric primitives composed of various materials and a collection of lights. Recently, techniques for modeling and rendering scenes from a set of pre-acquired images have emerged as an alternative approach, known as image-based modeling and rendering. Much of the research in this field has focused on reconstructing and rerendering from a set of photographs, while little work has been done to address the problem of editing and modifying these scenes. On the other hand, photo-editing systems, such as Adobe Photoshop, provide a powerful, intuitive, and practical means to edit images. However, these systems are limited by their two-dimensional nature. In this thesis, we present a system that extends photo editing to 3D. Starting from a single input image, the system enables the user to reconstruct a 3D representation of the captured scene, and edit it with the ease and versatility of 2D photo editing. The scene is represented as layers of images with depth, where each layer is an image that encodes both color and depth. A suite of user-assisted tools are employed, based on a painting metaphor, to extract layers and assign depths. The system enables editing from different viewpoints, extracting and grouping of image-based objects, and modifying the shape, color, and illumination of these objects. As part of the system, we introduce three powerful new editing tools. These include two new clone brushing tools: the non-distorted clone brush and the structure-preserving clone brush. They permit copying of parts of an image to another via a brush interface, but alleviate distortions due to perspective foreshortening and object geometry.(cont.) The non-distorted clone brush works on arbitrary 3D geometry, while the structure-preserving clone brush, a 2D version, assumes a planar surface, but has the added advantage of working directly in 2D photo-editing systems that lack depth information. The third tool, a texture-illuminance decoupling filter, discounts the effect of illumination on uniformly textured areas by decoupling large- and small-scale features via bilateral filtering. This tool is crucial for relighting and changing the materials of the scene. There are many applications for such a system, for example architectural, lighting and landscape design, entertainment and special effects, games, and virtual TV sets. The system allows the user to superimpose scaled architectural models into real environments, or to quickly paint a desired lighting scheme of an interior, while being able to navigate within the scene for a fully immersive 3D experience. We present examples and results of complex architectural scenes, 360-degree panoramas, and even paintings, where the user can change viewpoints, edit the geometry and materials, and relight the environment.by Byong Mok Oh.Ph.D

Nonholonomic Motion Planning as Efficient as Piano Mover's

We present an algorithm for non-holonomic motion planning (or 'parking a car') that is as computationally efficient as a simple approach to solving the famous Piano-mover's problem, where the non-holonomic constraints are ignored. The core of the approach is a graph-discretization of the problem. The graph-discretization is provably accurate in modeling the non-holonomic constraints, and yet is nearly as small as the straightforward regular grid discretization of the Piano-mover's problem into a 3D volume of 2D position plus angular orientation. Where the Piano mover's graph has one vertex and edges to six neighbors each, we have three vertices with a total of ten edges, increasing the graph size by less than a factor of two, and this factor does not depend on spatial or angular resolution. The local edge connections are organized so that they represent globally consistent turn and straight segments. The graph can be used with Dijkstra's algorithm, A*, value iteration or any other graph algorithm. Furthermore, the graph has a structure that lends itself to processing with deterministic massive parallelism. The turn and straight curves divide the configuration space into many parallel groups. We use this to develop a customized 'kernel-style' graph processing method. It results in an N-turn planner that requires no heuristics or load balancing and is as efficient as a simple solution to the Piano mover's problem even in sequential form. In parallel form it is many times faster than the sequential processing of the graph, and can run many times a second on a consumer grade GPU while exploring a configuration space pose grid with very high spatial and angular resolution. We prove approximation quality and computational complexity and demonstrate that it is a flexible, practical, reliable, and efficient component for a production solution.Comment: 34 pages, 37 figures, 9 tables, 4 graphs, 8 insert

Real-Time Storytelling with Events in Virtual Worlds

We present an accessible interactive narrative tool for creating stories among a virtual populace inhabiting a fully-realized 3D virtual world. Our system supports two modalities: assisted authoring where a human storyteller designs stories using a storyboard-like interface called CANVAS, and exploratory authoring where a human author experiences a story as it happens in real-time and makes on-the-fly narrative trajectory changes using a tool called Storycraft. In both cases, our system analyzes the semantic content of the world and the narrative being composed, and provides automated assistance such as completing partially-specified stories with causally complete sequences of intermediate actions. At its core, our system revolves around events -â?? pre-authored multi-actor task sequences describing interactions between groups of actors and props. These events integrate complex animation and interaction tasks with precision control and expose them as atoms of narrative significance to the story direction systems. Events are an accessible tool and conceptual metaphor for assembling narrative arcs, providing a tightly-coupled solution to the problem of converting author intent to real-time animation synthesis. Our system allows simple and straightforward macro- and microscopic control over large numbers of virtual characters with diverse and sophisticated behavior capabilities, and reduces the complicated action space of an interactive narrative by providing analysis and user assistance in the form of semi-automation and recommendation services