15153556
Analysis of Heuristics for the Freeze-Tag Problem
In the Freeze Tag Problem (FTP) we are given a swarm of n asleep (frozen or inactive) robots and a single awake (active) robot, and we want to awaken all robots in the shortest possible time. A robot is awakened when an active robot "touches" it. The goal is to compute an optimal awakening schedule such that all robots are awake by time t*, for the smallest possible value of t*. We devise and test heuristic strategies on geometric and network datasets. Our experiments show that all of the strategies perform well, with the simple greedy strategy performing particularly well. A theoretical analysis of the greedy strategy gives a tight approximation bound of ?(?logn) for points in the plane. We show more generally that the (tight) performance bound is ?((log n)1-1/d) in d dimensions. This is in contrast to general metric spaces, where greedy is known to have a ?(log n) approximation factor, and no method is known to achieve an approximation bound of o(log n).
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.
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.
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.
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.
2870926
Protecting browser state from web privacy attacks
Through a variety of means, including a range of browser cache methods and inspecting the color of a visited hyperlink, client-side browser state can be exploited to track users against their wishes. This tracking is possible because persistent, client-side browser state is not properly partitioned on per-site basis in current browsers. We address this problem by refining the general notion of a "same-origin" policy and implementing two browser extensions that enforce this policy on the browser cache and visited links.We also analyze various degrees of cooperation between sites to track users, and show that even if long-term browser state is properly partitioned, it is still possible for sites to use modern web features to bounce users between sites and invisibly engage in cross-domain tracking of their visitors. Cooperative privacy attacks are an unavoidable consequence of all persistent browser state that affects the behavior of the browser, and disabling or frequently expiring this state is the only way to achieve true privacy against colluding parties.
26562844
Understanding SPKI/SDSI using first-order logic
SPKI/SDSI is a language for expressing distributed access control policy, derived from SPKI and SDSI. We provide a first-order logic (FOL) semantics for SDSI, and show that it has several advantages over previous semantics. For example, the FOL semantics is easily extended to additional policy concepts and gives meaning to a larger class of access control and other policy analysis queries. We prove that the FOL semantics is equivalent to the string rewriting semantics used by SDSI designers, for all queries associated with the rewriting semantics. We also provide a FOL semantics for SPKI/SDSI. This reveals some problems. For example, the standard proof procedure in RFC 2693 is semantically incomplete. In addition, as noted before by other authors, authorization tags in SPKI/SDSI are algorithmically problematic, making a complete proof procedure unlikely. We compare SPKI/SDSI with RT/sub 1//sup C/, which is a language in the RT role-based trust-management framework that can be viewed as an extension of SDSI. The constraint feature of /sub 1//sup C/, based on constraint datalog, provides an alternative mechanism that is expressively similar to SPKI/SDSI tags, semantically natural, and algorithmically tractable.
3038947
Beyond proof-of-compliance: safety and availability analysis in trust management
Trust management is a form of distributed access control using distributed policy. statements. Since one party may delegate partial control to another party, it is natural to ask what permissions may be granted as the result of policy changes by other parties. We study security properties such as safety, and availability for a family of trust management languages, devising algorithms for deciding the possible consequences of certain changes in policy. While trust management is more powerful in certain ways than mechanisms in the access matrix model, and the security properties considered are more than simple safety, we find that in contrast to the classical HRU undecidability of safety properties, our primary security properties are decidable. In particular, most properties we studied are decidable in polynomial time. Containment, the most complicated security property we studied, is decidable in polynomial time for the simplest TM language in the family. The problem becomes co-NP-hard when intersection or linked roles are added to the language.
1653333
A derivation system for security protocols and its logical formalization
Many authentication and key exchange protocols are built using an accepted set of standard concepts such as Diffie-Hellman key exchange, nonces to avoid replay, certificates from an accepted authority, and encrypted or signed messages. We introduce a basic framework for deriving security protocols from such simple components. As a case study, we examine the structure of a family of key exchange protocols that includes station-to-station (STS), ISO-9798-3, just fast keying (JFK), IKE and related protocols, deriving all members of the family from two basic protocols using a small set of refinements and protocol transformations. As initial steps toward associating logical derivations with protocol derivations, we extend a previous security protocol logic with preconditions and temporal assertions. Using this logic, we prove the security properties of the standard signature based challenge-response protocol and the Diffie-Hellman key exchange protocol. The ISO-9798-3 protocol is then proved correct by composing the correctness proofs of these two simple protocols.