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.
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.
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.
16824358
On Minimum-Area Hulls
Abstract. We study some minimum-area hull problems that generalize the notion of convex hull to star-shaped and monotone hulls. Specifically, we consider the minimum-area star-shaped hull problem: Given an n -vertex simple polygon P , find a minimum-area, star-shaped polygon P* containing P . This problem arises in lattice packings of translates of multiple, nonidentical shapes in material layout problems (e.g., in clothing manufacture), and has been recently posed by Daniels and Milenkovic. We consider two versions of the problem: the restricted version, in which the vertices of P* are constrained to be vertices of P , and the unrestricted version, in which the vertices of P* can be anywhere in the plane. We prove that the restricted problem falls in the class of ``3sum-hard'' (sometimes called ``n2 -hard'') problems, which are suspected to admit no solutions in o(n2) time. Further, we give an O(n2) time algorithm, improving the previous bound of O(n5) . We also show that the unrestricted problem can be solved in O(n2 p(n)) time, where p(n) is the time needed to find the roots of two equations in two unknowns, each a polynomial of degree O(n) . We also consider the case in which P* is required to be monotone, with respect to an unspecified direction; we refer to this as the minimum-area monotone hull problem. We give a matching lower and upper bound of Θ(n log n) time for computing P* in the restricted version, and an upper bound of O(n q(n)) time in the unrestricted version, where q(n) is the time needed to find the roots of two polynomial equations in two unknowns with degrees 2 and O(n) .
31926003
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 $\mathcal{P}$ of n points in the plane, find a spanning tree of $\mathcal{P}$ of minimum “area,” where the area of a spanning tree $\mathcal{T}$ is the area of the union of the n–1 disks whose diameters are the edges in $\mathcal{T}$. We prove that the Euclidean minimum spanning tree of $\mathcal{P}$ 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.
1174606
Optimal covering tours with turn costs
We give the first algorithmic study of a class of “covering tour” problems related to the geometric Traveling Salesman Problem: Find a polygonal tour for a cutter so that it sweeps out a specified region (“pocket”), in order to minimize a cost that depends not only on the length of the tour but also on the number of turns. These problems arise naturally in manufacturing applications of computational geometry to automatic tool path generation and automatic inspection systems, as well as arc routing (“postman”) problems with turn penalties. We prove lower bounds (NP-completeness of minimum-turn milling) and give efficient approximation algorithms for several natural versions of the problem, including a polynomial-time approximation scheme based on a novel adaptation of the m-guillotine method.
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.
14302964
A formal framework for the Java bytecode language and verifier
This paper presents a sound type system for a large subset of the Java bytecode language including classes, interfaces, constructors, methods, exceptions, and bytecode subroutines. This work serves as the foundation for developing a formal specification of the bytecode language and the Java Virtual Machine's bytecode verifier. We also describe a prototype implementation of a type checker for our system and discuss some of the other applications of this work. For example, we show how to extend our work to examine other program properties, such as the correct use of object locks.
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.
14607433
Lower bounds on type inference with subtypes
We investigate type inference for programming languages with subtypes. As described in previous work, there are several type inference problems for any given expression language, depending on the form of the subtype partial order and the ability to define new subtypes in programs. Our first main result is that for any specific subtype partial order, the problem of determining whether a lambda term is typable is algorithmically (polynomial-time) equivalent to a form of satisfiability problem over the same partial order. This gives the first exact characterization of the problem that is independent of the syntax of expressions. In addition, since this form of satisfiability problem is PSPACE-hard over certain partial orders, this equivalence strengthens the previous lower bound of NP-hard to PSPACE-hard. Our second main result is a lower bound on the length of most general types when the subtype hierarchy may change as a result of additional type declarations within the program. More specifically, given any input expression, a type inference algorithm tries to find a most general (or principal) typing. The property of a most general typing is that it has all other possible typings as instances. However, there are several sound notions of instance in the presence of subtyping. Our lower bound is that no sound definition of instance would allow the set of additional subtyping hypotheses about a term to grow less than linearly in the size of the term.
6478208
Chemistry in Bioinformatics
AbstractChemical information is now seen as critical for most areas of life sciences. But unlike Bioinformatics, where data is openly available and freely re-usable, most chemical information is closed and cannot be re-distributed without permission. This has led to a failure to adopt modern informatics and software techniques and therefore paucity of chemistry in bioinformatics. New technology, however, offers the hope of making chemical data (compounds and properties) free during the authoring process. We argue that the technology is already available; we require a collective agreement to enhance publication protocols.