495062
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. A typical worker's objective is to minimize the amount of work he does (he is "lazy"), or more generally, to schedule as inefficiently (in some sense) as possible. The worker is subject to the constraint that he must be busy when there is work that he can do; we make this notion precise both in the preemptive and nonpreemptive settings. The resulting class of "perverse" scheduling preblems, which we denote "Lazy Bureaucrat Problems," gives rise to a rich set of new questions that explore the distinction between maximization and minimization in computing optimal schedules.
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.
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.
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.
57900050
Computational Geometry Column 42
A compendium of thirty previously published open problems in computational geometry is presented.
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.
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.
5528932
On the Relationship Between Classes, Objects, and Data Abstraction
While most object-oriented programming is done in class-based languages, the trend in theoretical study has been to develop formal systems that are object-based, without classes and often without explicit inheritance mechanisms. This paper studies the correspondence between object primitives and class constructs of the form found in C++, Eiffel, and Java. The main qualitative insight is that such classes require both an extensible aggregate, to serve as the basis for inheritance, and a non-extensible form of object to support subtyping. We compare three approaches to modeling classes, the first using records of object components called “premethods” and the latter two using an extensible form of object called a “prototype.” While the first approach uses fewer primitive operations on objects, it does not provide several important features of class-based languages. In the latter two approaches, we overcome these deficiencies by combining prototypes with standard abstraction mechanisms. All three treatments of classes use translations into provably sound object calculi.
23474411
Finite-state analysis of two contract signing protocols
Optimistic contract signing protocols allow two parties to commit to a previously agreed upon contract, relying on a third party to abort or confirm the contract if needed. These protocols are relatively subtle, since there may be interactions between the subprotocols used for normal signing without the third party, aborting the protocol through the third party, or requesting confirmation from the third party. With the help of Mur, a finite-state verification tool, we analyze two related contract signing protocols: the optimistic contract signing protocol of Asokan, Shoup, and Waidner, and the abuse-free contract signing protocol of Garay, Jakobsson, and MacKenzie. For the first protocol, we discover that a malicious participant can produce inconsistent versions of the contract or mount a replay attack. For the second protocol, we discover that negligence or corruption of the trusted third party may allow abuse or unfairness. In this case, contrary to the intent of the protocol, the cheated party is not able to hold the third party accountable. We present and analyze modifications to the protocols that avoid these problems and discuss the basic challenges involved in formal analysis of fair exchange protocols.
7468814
Coupled optimization in protein docking
Here, we introduce a new approach to macromolecular docking which combines the continuous global optimization algorithm CGU [6, 21] with the grid-based conformational search engine DOT [23]. We also detail the use of this method to dock acetylcholine into the fasciculin-acetylcholinesterase complex. Fasciculin blocks access to the long, narrow pathway leading to the active site, which is located in the interior of the acetylcholinesterase. For this reason, flnding the location computationally is rather non-trivial. We not only successfully identifled the optimal docking conflguration, but were able to do so in a matter of hours.