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.
7295712
The minimum area spanning tree problem
Motivated by optimization problems in sensor coverage, we formulate and study the Minimum-Area Spanning Tree (MAST) problem: Given a set P of n points in the plane, find a spanning tree of P of minimum "area", where the area of a spanning tree T is the area of the union of the n - 1 disks whose diameters are the edges in T. We prove that the Euclidean minimum spanning tree of P is a constant-factor approximation for MAST. We then apply this result to obtain constant-factor approximations for the Minimum-Area Range Assignment (MARA) problem, for the Minimum-Area Connected Disk Graph (MACDG) problem, and for the Minimum-Area Tour (MAT) problem. The first problem is a variant of the power assignment problem in radio networks, the second problem is a related natural problem, and the third problem is a variant of the traveling salesman problem.
20253449
Approximating Polygons and Subdivisions with Minimum Link Paths
We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate objects with the minimum number of line segments, or with near the minimum, by using efficient greedy algorithms. We give some variants that have linear or O(n log n) algorithms approximating polygonal chains of n segments. We also show that approximating subdivisions and approximating with chains with. no self-intersections are NP-hard.
17335559
Finding Optimal Bipartitions of Points and Polygons
We give efficient algorithms to compute an optimal bipartition of a set of points or a set of simple polygons in the plane. We examine various criteria involving the perimeter and the area of the convex hulls of the two subsets.
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.
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.
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.
7766101
A linguistic characterization of bounded oracle computation and probabilistic polynomial time
We present a higher-order functional notation for polynomial-time computation with an arbitrary 0, 1-valued oracle. This formulation provides a linguistic characterization for classes such as NP and BPP, as well as a notation for probabilistic polynomial-time functions. The language is derived from Hofmann's adaptation of Bellantoni-Cook safe recursion, extended to oracle computation via work derived from that of Kapron and Cook. Like Hofmann's language, ours is an applied typed lambda calculus with complexity bounds enforced by a type system. The type system uses a modal operator to distinguish between two sorts of numerical expressions. Recursion can take place on only one of these sorts. The proof that the language captures precisely oracle polynomial time is model-theoretic, using adaptations of various techniques from category theory.
5227025
Curved PN triangles
To improve the visual quality of existing triangle-based art in realtime entertainment, such as computer games, we propose replacing flat triangles with curved patches and higher-order normal variation. At the hardware level, based only on the three vertices and three vertex normals of a given flat triangle, we substitute the geometry of a three-sided cubic Bezier patch for the triangle’s flat geometry, and a quadratically varying normal for Gouraud shading. These curved point-normal triangles, or PN triangles, require minimal or no change to existing authoring tools and hardware designs while providing a smoother, though not necessarily everywhere tangent continuous, silhouette and more organic shapes. CR Categories: I.3.5 [surface representation, splines]: I.3.6— graphics data structures
53232540
Architectural Support for Copy and Tamper Resistant Software
31091998
Tree Automata with One Memory, Set Constraints, and Ping-Pong Protocols
We introduce a class of tree automata that perform tests on a memory that is updated using function symbol application and projection. The language emptiness problem for this class of tree automata is shown to be in DEXPTIME. We also introduce a class of set constraints with equality tests and prove its decidability by completion techniques and a reduction to tree automata with one memory. Set constraints with equality tests may be used to decide secrecy for a class of cryptographic protocols that properly contains a class of memoryless "ping-pong protocols" introduced by Dolev and Yao.