40641420
On Some Applications of Computational Geometry in Manufacturing and Virtual Environments
There are many motivating applications for the study of computational geometry problems. In this talk, we briefly touch on two such application domains — manufacturing and virtual environments. We discuss a few of the applications-driven computational geometry problems in these domains and point to some possible future research directions that will assist in transferring algorithmic methods into practice.
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.
57900050
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational geometry is presented.
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.
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.
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.
15882954
The Development of Type Systems for Object-Oriented Languages
This paper, which is partly tutorial in nature, summarizes some basic research goals in the study and development of typed object-oriented programming languages. These include both immediate repairs to problems with existing languages and the long-term development of more flexible and expressive, yet type-safe, approaches to program organization and design. The technical part of the paper is a summary and comparison of three object models from the literature. We conclude by discussing approaches to selected research problems, including changes in the type of a method from super class to sub class and the use of types that give information about the implementations as well as the interfaces of objects. Such implementation types seem essential for adequate typing of binary operations on objects, for example.
1569108
Distributed Credential Chain Discovery in Trust Management
We introduce a simple Role-based Trust-management language RT0 and a set-theoretic semantics for it. We also introduce credential graphs as a searchable representation of credentials in RT0 and prove that reachability in credential graphs is sound and complete with respect to the semantics of RT0. Based on credential graphs, we give goal-directed algorithms to do credential chain discovery in RT0, both when credential storage is centralized and when credential storage is distributed. A goal-directed algorithm begins with an access-control query and searches for credentials relevant to the query, while avoiding considering the potentially very large number of credentials that are unrelated to the access-control decision at hand. This approach provides better expected-case performance than bottom-up algorithms. We show how our algorithms can be applied to SDSI 2.0 (the 'SDSI' part of SPKI/SDSI 2.0).Our goal-directed, distributed chain discovery algorithm finds and retrieves credentials as needed. We prove that the algorithm is correct by proving that the algorithm is sound and complete with respect to the credential graph composed of the credentials it retrieves, and that the algorithm retrieves all credentials that constitute a traversable chain. We further introduce a storage type system for RT0, which guarantees traversability of chains when credentials are well typed. This type system can also help improve search efficiency by guiding search in the right direction, making distributed chain discovery with large number of credentials feasible.
5176809
DATALOG with Constraints: A Foundation for Trust Management Languages
Trust management (TM) is a promising approach for authorization and access control in distributed systems, based on signed distributed policy statements expressed in a policy language. Although several TM languages are semantically equivalent to subsets of Datalog, Datalog is not sufficiently expressive for fine-grained control of structured resources. We define the class of linearly decomposable unary constraint domains, prove that DATALOG extended with constraints in any combination of such constraint domains is tractable, and show that permissions associated with structured resources fall into this class. We also present a concrete declarative TM language, RT1C, based on constraint DATALOG, and use constraint DATALOG to analyze another TM system, KeyNote, which turns out to be less expressive than RT1C in significant respects, yet less tractable in the worst case. Although constraint DATALOG has been studied in the context of constraint databases, TM applications involve different kinds of constraint domains and have different computational complexity requirements.
9031501
Design of a role-based trust-management framework
We introduce the RT framework, a family of role-based trust management languages for representing policies and credentials in distributed authorization. RT combines the strengths of role-based access control and trust-management systems and is especially suitable for attribute-based access control. Using a few simple credential forms, RT provides localized authority over roles, delegation in role definition, linked roles, and parameterized roles. RT also introduces manifold roles, which can be used to express threshold and separation-of-duty policies, and delegation of role activations. We formally define the semantics of credentials in the RT framework by presenting a translation from credentials to Datalog rules. This translation also shows that this semantics is algorithmically tractable.
2518390
A Compositional Logic for Proving Security Properties of Protocols
We present a logic for proving security properties of protocols that use nonces (randomly generated numbers that uniquely identify a protocol session) and public-key cryptography. The logic, designed around a process calculus with actions for each possible protocol step, consists of axioms about protocol actions and inference rules that yield assertions about protocols composed of multiple steps. Although assertions are written using only steps of the protocol, the logic is sound in a stronger sense: each provable assertion about an action or sequence of actions holds in any run of the protocol that contains the given actions and arbitrary additional actions by a malicious attacker. This approach lets us prove security properties of protocols under attack while reasoning only about the sequence of actions taken by honest parties to the protocol. The main security-specific parts of the proof system are rules for reasoning about the set of messages that could reveal secret data and an invariant ride called the "honesty rule".