26269074
Reaching folded states of a rectangular piece of paper
207132060
Terrain Decomposition and Layered Manufacturing
We consider a problem that arises in generating three-dimensional models by methods of layered manufacturing: How does one decompose a given model P into a small number of sub-models each of which is a terrain polyhedron? Terrain polyhedra have a base facet such that, for each point of the polyhedron, the line segment joining the point to its orthogonal projection on the base facet lies within the polyhedron. Terrain polyhedra are exactly the class of polyhedral models for which it is possible to construct the model using layered manufacturing (with layers parallel to the base facet), without the need for constructing "supports" (which must later be removed). In order to maximize the integrity of a prototype, one wants to minimize the number of individual sub-models that are manufactured and then glued together. We show that it is NP-hard to decide if a three-dimensional model P of genus 0 can be decomposed into k terrain polyhedra. We also prove a two-dimensional version of this theorem, for the case in which P is a polygonal region with holes. Both results still hold if we are restricted to isothetic objects and/or axis-parallel layering directions.
57900050
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational geometry is presented.
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.
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.
14058328
Autonomous Nodes and Distributed Mechanisms
We extend distributed algorithmic mechanism design by considering a new model that allows autonomous nodes executing a distributed mechanism to strategically deviate from the prescribed protocol. Our goal is to motivate agents to contribute to a global objective and resist disruption by a limited number of malicious irrational agents, augmenting market incentives with cryptographic primitives to make certain forms of behavior computationally infeasible. Several techniques for distributing market computation among autonomous agents are illustrated using a marginal cost mechanism for multicast cost sharing from.
896820
A state-transition model of trust management and access control
Abstract: We use a state-transition approach to analyze and compare the core access control mechanisms that are characteristic of a variety of trust management, access control list, and capability-based systems. The framework, which characterizes the set of rights a subject has over an object after any sequence of actions, is based on abstract system states, state transitions, and logical deduction of access control judgments. We present abstract models representing the access control portion of trust management, access control lists, and two versions of capabilities, proving various correspondence and simulation relations between these models. The main results include an equivalence between access control lists (ACLs) and capabilities viewed as rows of the Lampson access matrix and the (proper) subsumption of a form of ACLs by an "unforgeable reference" form of capabilities. The access control mechanism at the heart of distributed trust management systems is formally shown to provide a tractable compromise between unrestricted capability passing from the capability models and easy revocation provided by access control lists. The underlying simulations show how trust management compares with more established access control mechanisms, independent of features such as local name spaces and certificate authorization hierarchies.
15907814
Toward a typed foundation for method specialization and inheritance
This paper discusses the phenomenon of method specialization in object-oriented programming languages. A typed function calculus of objects and classes is presented, featuring method specialization when methods are added or redefined. The soundness of the typing rules (without subtyping) is suggested by a translation into a more traditional calculus with recursively-defined record types. However, semantic questions regarding the subtype relation on classes remain open.
15188207
RT: a Role-based Trust-management framework
The RT Role-based Trust-management framework provides policy language, semantics, deduction engine, and pragmatic features such as application domain specification documents that help distributed users maintain consistent use of policy terms. This paper provides a general overview of the framework, combining some aspects described in previous publications with recent improvements and explanation of motivating applications.
8879002
Status of clinical gene sequencing data reporting and associated risks for information loss
Clinical gene sequencing is growing in importance and cost-effectiveness. In the past two years, the number of genes associated with disease has grown by roughly 25%. Knowledge of genetic variations will soon guide drug selection and dosages, predict risks from toxin exposures, and inform nutritional needs. Despite the significance of sequencing, methods for reporting results are problematic. Frequent use of paper and infrequent use of naming standards impede data exchange and make incorporation into the electronic medical record difficult. Reports often describe only variations found, rather than all data (all patient bases sequenced). Also, reports frequently do not describe reference data used to define variations. These practices create risks for loss of both data and information. Standardized electronic reporting of all data (all bases sequenced and all reference data) and electronic record systems capable of storing these results would both prevent data loss and simplify the preservation of information those data provide.