14458363
Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric k-MST problem
A method of mixing poly(neopentylglycol)azelate (NPGA) is disclosed which enhances its solubility in polyurethane binders for composite solid propellants. The method comprises withholding the addition of NPGA from the propellant submix and from the total propellant formulation mixing procedure until after the addition of the curing agent has taken place and reaction has taken place for a predetermined period of time with the bonding agent until a "break" in viscosity occurs. The "break" in viscosity has taken place when the other binder ingredients have reacted with the curing agent HDI (hexamethylenediisocyanate) so that immiscibility between the binder ingredients is reduced. The late NPGA addition method resulted not only in apparently complete solubilization of the NPGA but also yielded a propellant with dramatically lower end of mix viscosity (reduced by a factor of 10), superior flow characteristics, and better physical properties. Propellants made by the disclosed method of mixing have desirable lower modulus and higher tensile strength. Thus, the propellant mixed in accordance with the late NPGA addition method yields a propellant with a high tensile strength to modulus ratio. The high tensile strength to modulus ratio at low temperature is an indicator of a good propellant.
57900050
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational geometry is presented.
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.
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.
2523975
Multiset rewriting and the complexity of bounded security protocols
We formalize the Dolev-Yao model of security protocols, using a notation based on multiset rewriting with existentials. The goals are to provide a simple formal notation for describing security protocols, to formalize the assumptions of the Dolev-Yao model using this notation, and to analyze the complexity of the secrecy problem under various restrictions. We prove that, even for the case where we restrict the size of messages and the depth of message encryption, the secrecy problem is undecidable for the case of an unrestricted number of protocol roles and an unbounded number of new nonces. We also identify several decidable classes, including a DEXP-complete class when the number of nonces is restricted, and an NP-complete class when both the number of nonces and the number of roles is restricted. We point out a remaining open complexity problem, and discuss the implications these results have on the general topic of protocol analysis.
2138308
Contract Signing, Optimism, and Advantage
A contract signing protocol lets two parties exchange digital signatures on a pre-agreed text. Optimistic contract signing protocols enable the signers to do so without invoking a trusted third party. However, an adjudicating third party remains available should one or both signers seek timely resolution. We analyze optimistic contract signing protocols using a game-theoretic approach and prove a fundamental impossibility result: in any fair, optimistic, timely protocol, an optimistic player yields an advantage to the opponent. The proof relies on a careful characterization of optimistic play that postpones communication to the third party. Since advantage cannot be completely eliminated from optimistic protocols, we argue that the strongest property attainable is the absence of provable advantage, i.e., abuse-freeness in the sense of Garay-Jakobsson-MacKenzie.
10533033
On the Sequential Nature of Unification
Abstract The problem of unification of terms is log-space complete for P. In deriving this lower bound no use is made of the potentially concise representation of terms by directed acyclic graphs. In addition, the problem remains complete even if infinite substitutions are allowed. A consequence of this result is that parallelism cannot significantly improve on the best sequential solutions for unification. However, we show that for the problem of term matching, an important subcase of unification, there is a good parallel algorithm using O ( log 2 n ) time and n O(1) processors on a PRAM. For the O ( log 2 n ) parallel time upper bound we assume that the terms are represented by directed acyclic graphs; if the longer string representation is used we obtain an O ( log n ) parallel time bound.
7541818
A type system for object initialization in the Java bytecode language
In the standard Java implementation, a Java language program is compiled to Java bytecode. This bytecode may be sent across the network to another site, where it is then interpreted by the Java Virtual Machine. Since bytecode may be written by hand, or corrupted during network transmission, the Java Virtual Machine contains a bytecode verifier that performs a number of consistency checks before code is interpreted. As illustrated by previous attacks on the Java Virtual Machine, these tests, which include type correctness, are critical for system security. In order to analyze existing bytecode verifiers and to understand the properties that should be verified, we develop a precise specification of statically-correct Java bytecode, in the form of a type system. Our focus in this paper is a subset of the bytecode language dealing with object creation and initialization. For this subset, we prove that for every Java bytecode program that satisfies our typing constraints, every object is initialized before it is used. The type system is easily combined with a previous system developed by Stata and Abadi for bytecode subroutines. Our analysis of subroutines and object initialization reveals a previously unpublished bug in the Sun JDK bytecode verifier.
12997315
PER models of subtyping, recursive types and higher-order polymorphism
We relate standard techniques for solving recursive domain equations to previous models with types interpreted as partial equivalence relations (per's) over a Dm lambda model. This motivates a particular choice of type functions, which leads to an extension of, such models to higher-order polymorphism. The resulting models provide natural interpretations for function spaces, records, recursively defined types, higher-order type functions, and bounded polymor-phic types Y-X <: Y. A where the bound may be of a higher kind. In particular, we may combine recursion and polymorphism in a way that allows the bound Y in VX <: Y. A to be recursive y defined. The model may also be used to interpret so-called " F-bounded polymorphism. " Together, these features allolv us to represent several forms of type and type functions that seem to arise naturally in typed object-oriented programming. 1 Introduction In type systems aimed towards object-oriented programming , several typing ideas naturally arise. The most basic are subtyping, the fact that values of one type may be treated as values of another, polymor-phism, and recursively defined types. the Powell Foundation. t s~lpported in part by an NSF PYI Award, matching funds from Digital Equipment Corporation, the Powell Foundation, and Xerox Corporation NSF grant CCR-881 4921 and the Wal-lace F. and Lucille M. Davis Faculty Scholarship. Pennksion to copy without fee all or part of this material is granted provided that tie copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of tbe publication and its date appear, and notice is given that copying is by permission of tbe Association for Computing Machinery. To copy otherwise , or to republish, requires a fee sad/or specific permission. the existing, implemented type systems for object-oriented languages have notable errors (see, [CO089]), it is important to prove the soundness of these type systems. The primary technique for doing so is by constructing a selmantic model. A class of semantic models for languages with subtyp-ing, polymorphism and recursion are developed in [Cop85, Ama91, Car89, AP90]. These models all interpret types as partial equivalence relations (per's) over suitable Dm structures obtained by the so-called " inverse limit') construction. The main contributions of this paper are to provide a general framework for understanding type recursion in these models and to extend per models to higher-order type functions and additional forms of polymorphism. Since the use of per's over …