57900050
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational geometry is presented.
9802380
Generating Random Polygons with Given Vertices
Abstract The problem of generating “random” geometric objects is motivated by the need to generate test instances for geometric algorithms. We examine the specific problem of generating a random x-monotone polygon on a given set of n vertices. Here, “random” is taken to mean that we select uniformly at random a polygon, from among all those x-monotone polygons having the given n vertices. We give an algorithm that generates a random monotone polygon in O(n) time and space after O(K) preprocessing time, where n
16007270
Point Probe Decision Trees for Geometric Concept Classes
A fundamental problem in model-based computer vision is that of identifying to which of a given set of concept classes of geometric models an observed model belongs. Considering a “probe” to be an oracle that tells whether or not the observed model is present at a given point in an image, we study the problem of computing efficient strategies (“decision trees”) for probing an image, with the goal to minimize the number of probes necessary (in the worst case) to determine in which class the observed model belongs. We prove a hardness result and give strategies that obtain decision trees whose height is within a log factor of optimal.
11557966
An algorithmic study of manufacturing paperclips and other folded structures
We study algorithmic aspects of bending wires and sheet metal into a specified structure. Problems of this type are closely related to the question of deciding whether a simple non-self-intersecting wire structure (a carpenter's ruler) can be straightened, a problem that was open for several years and has only recently been solved in the affirmative. If we impose some of the constraints that are imposed by the manufacturing process, we obtain quite different results. In particular, we study the variant of the carpenter's ruler problem in which there is a restriction that only one joint can be modified at a time. For a linkage that does not self-intersect or self-touch, the recent results of Connelly et al. and Streinu imply that it can always be straightened, modifying one joint at a time. However, we show that for a linkage with even a single vertex degeneracy, it becomes NP-hard to decide if it can be straightened while altering only one joint at a time. If we add the restriction that each joint can be altered at most once, we show that the problem is NP-complete even without vertex degeneracies. In the special case, arising in wire forming manufacturing, that each joint can be altered at most once, and must be done sequentially from one or both ends of the linkage, we give an efficient algorithm to determine if a linkage can be straightened.
7753820
Approximate Geometric Pattern Matching Under Rigid Motions
We present techniques for matching point-sets in two and three dimensions under rigid-body transformations. We prove bounds on the worst-case performance of these algorithms to be within a small constant factor of optimal and conduct experiments to show that the average performance of these matching algorithms is often better than that predicted by the worst-case bounds.
47079265
The Lazy Bureaucrat Scheduling Problem
We introduce a new class of scheduling problems in which the optimization is performed by the worker (single "machine") who performs the tasks. The worker's objective may be to minimize the amount of work he does (he is "lazy"). He is subject to a constraint that he must be busy when there is work that he can do; we make this notion precise, particularly when preemption is allowed. The resulting class of "perverse" scheduling problems, which we term "Lazy Bureaucrat Problems," gives rise to a rich set of new questions that explore the distinction between maximization and minimization in computing optimal schedules.
19578302
A lambda calculus of objects and method specialization
An untyped lambda calculus, extended with object primitives that reflect the capabilities of so-called delegation-based object-oriented languages, is presented. A type inference system allows static detection of errors, such as message not understood, while at the same time allowing the type of an inherited method to be specialized to the type of the inheriting object. Type soundness, in the form of a subject-reduction theorem, is proved, and examples illustrating the expressiveness of the pure calculus are presented.<<ETX>>
118949965
On the Relationships Between Notions of Simulation-Based Security
Several compositional forms of simulation-based security have been proposed in the literature, including universal composability, black-box simulatability, and variants thereof. These relations between a protocol and an ideal functionality are similar enough that they can be ordered from strongest to weakest according to the logical form of their definitions. However, determining whether two relations are in fact identical depends on some subtle features that have not been brought out in previous studies. We identify the position of a “master process” in the distributed system, and some limitations on transparent message forwarding within computational complexity bounds, as two main factors. Using a general computational framework, we clarify the relationships between the simulation-based security conditions.
2495572
Adding type parameterization to the Java language
Although the Java programming language has achieved widespread acceptance, one feature that seems sorely missed is the ability to use type parameters (as in Ada generics, C++ templates, and ML polymorphic functions or data types) to allow a general concept to be instantiated to one or more specific types. In this paper, we propose parameterized classes and interfaces in which the type parameter may be constrained to either implement a given interface or extend a given class. This design allows the body of a parameterized class to refer to methods on objects of the parameter type, without introducing any new type relations into the language. We show that these Java extensions may be implemented by expanding parameterized classes at class load time, without any extension or modification to existing Java bytecode, verifier or bytecode interpreter.
1936302
Communication and re-use of chemical information in bioscience
The current methods of publishing chemical information in bioscience articles are analysed. Using 3 papers as use-cases, it is shown that conventional methods using human procedures, including cut-and-paste are time-consuming and introduce errors. The meaning of chemical terms and the identity of compounds is often ambiguous. valuable experimental data such as spectra and computational results are almost always omitted. We describe an Open XML architecture at proof-of-concept which addresses these concerns. Compounds are identified through explicit connection tables or links to persistent Open resources such as PubChem. It is argued that if publishers adopt these tools and protocols, then the quality and quantity of chemical information available to bioscientists will increase and the authors, publishers and readers will find the process cost-effective.
18008261
Optimization Complexity of Linear Logic Proof Games
A class of linear logic proof games is developed, each with a numeric score that depends on the number of preferred axioms used in a complete or partial proof tree. The complexity of these games is analyzed for the NP-complete multiplicative fragment (MLL) extended with additive constants and the PSPACE-complete multiplicative, additive fragment (MALL) of propositional linear logic. In each case, it is shown that it is as hard to compute an approximation of the best possible score as it is to determine the optimal strategy. Furthermore, it is shown that no efficient heuristics exist unless there is an unexpected collapse in the complexity hierarchy.