2426 Oct. 1988
Filter Results

29th Annual Symposium on Foundations of Computer Science (IEEE Cat. No.88CH26526)
Publication Year: 1988 PDF (251 KB) 
Results on learnability and the VapnikChervonenkis dimension
Publication Year: 1988, Page(s):120  129
Cited by: Papers (3)The problem of learning a concept from examples in a distributionfree model is considered. The notion of dynamic sampling, wherein the number of examples examined can increase with the complexity of the target concept, is introduced. This method is used to establish the learnability of various concept classes with an infinite VapnikChervonenkis (VC) dimension. An important variation on the probl... View full abstract»

On the complexity of kinodynamic planning
Publication Year: 1988, Page(s):306  316
Cited by: Papers (35)The following problem, is considered: given a robot system find a minimaltime trajectory from a start position and velocity to a goal position and velocity, while avoiding obstacles and respecting dynamic constraints on velocity and acceleration. The simplified case of a point mass under Newtonian mechanics together with velocity and acceleration bounds is considered. The point must be flown from... View full abstract»

Covering polygons is hard
Publication Year: 1988, Page(s):601  611
Cited by: Papers (8)It is shown that the following minimum cover problems are NPhard, even for polygons without holes: (1) covering an arbitrary polygon with convex polygons; (2) covering the boundary of an arbitrary polygon with convex polygons; (3) covering an orthogonal polygon with rectangles; and (4) covering the boundary of an orthogonal polygon with rectangles. It is noted that these results hold even if the ... View full abstract»

An optimal algorithm for intersecting line segments in the plane
Publication Year: 1988, Page(s):590  600
Cited by: Papers (25)The authors present the first optimal algorithm for the following problem: given
n line segments in the plane, compute allk pairwise intersections in O(n logn +k ) time. Within the same asymptotic cost the algorithm will also compute the adjacencies of the planar subdivision induced by the segments, which is a useful data structure for contourfilling ... View full abstract» 
A fast planar partition algorithm. I
Publication Year: 1988, Page(s):580  589
Cited by: Papers (17)  Patents (1)A fast randomized algorithm is given for finding a partition of the plane induced by a given set of linear segments. The algorithm is ideally suited for a practical use because it is extremely simple and robust, as well as optimal; its expected running time is O(
m +n logn ) wheren is the number of input segments andm is the number of points of interse... View full abstract» 
Speeding up dynamic programming
Publication Year: 1988, Page(s):488  496
Cited by: Papers (3)A number of important computational problems in molecular biology, geology, speech recognition, and other areas can be expressed as recurrences which have typically been solved with dynamic programming. By using more sophisticated data structures, and by taking advantage of further structure from the applications, the authors speed up the computation of several of these recurrences by one or two o... View full abstract»

Combinatorial complexity bounds for arrangements of curves and surfaces
Publication Year: 1988, Page(s):568  579
Cited by: Papers (9)The authors study both the incidence counting and the manyfaces problem for various kinds of curves, including lines, pseudolines, unit circles, general circles, and pseudocircles. They also extend the analysis to three dimensions, where they concentrate on the case of spheres, which is relevant for the threedimensional unitdistance problem. They obtain upper bounds for certain quantities. The ... View full abstract»

Constructive results from graph minors: linkless embeddings
Publication Year: 1988, Page(s):398  409
Cited by: Papers (5)A formal study of threedimensional topological graph theory is initiated. The problem of deciding whether a graph can be embedded in 3space so that no collection of vertexdisjoint cycles is topologically linked is considered first. The RobertsonSeymour Theory of Graph Minors is applicable to this problem and guarantees the existence of an O(
n ^{3}) algorithm for the decision p... View full abstract» 
Bounds on the cover time
Publication Year: 1988, Page(s):479  487
Cited by: Papers (3)A particle that moves on a connected unidirected graph
G withn vertices is considered. At each step the particle goes from the current vertex to one of its neighbors, chosen uniformly at random. The cover time is the first time when the particle has visited all the vertices in the graph, starting from a given vertex. Upper and lower bounds are presented that relate the expected ... View full abstract» 
Fully dynamic techniques for point location and transitive closure in planar structures
Publication Year: 1988, Page(s):558  567
Cited by: Papers (3)It is shown that a planar
st graphG admits two total orders on the setV ∪E ∪F , whereV ,E , andF are, respectively, the sets of vertices, edges and faces ofG , with V =n . An O(n ) space data structure for the maintenance of the two orders is exhibited that supports an update of ... View full abstract» 
On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines
Publication Year: 1988, Page(s):387  397
Cited by: Papers (8)  Patents (2)A model for computation over an arbitrary (ordered) ring
R is presented. In this general setting, universal machines, partial recursive functions, and NPcomplete problems are obtained. While the theory reflects of classical overZ (e.g. the computable functions are the recursive functions), it also reflects the special mathematical character of the underlying ringR (e.... View full abstract» 
Take a walk, grow a tree
Publication Year: 1988, Page(s):469  478
Cited by: Papers (5)A simple randomized algorithm is presented for maintaining dynamically evolving binary trees on hypercube networks. The algorithm guarantees that: (1) nodes adjacent in the tree are within distance O(log log
N ) in anN processor hypercube, and (2) with overwhelming probability, no hypercube processor is assigned more than O(1+M /N ) tree nodes, whereM is... View full abstract» 
New upper bounds in Klee's measure problem
Publication Year: 1988, Page(s):550  556
Cited by: Papers (12)New upper bounds are given for the measure problem of V. Klee (1977) that significantly improve the previous bounds for dimensions greater than 2. An O(
n ^{d/2} logn ,n ) timespace upper bound to compute the measure of a set ofn boxes in Euclideand space is obtained. The solution requires several novel ideas including application of the inclus... View full abstract» 
Nonexpressibility of fairness and signaling
Publication Year: 1988, Page(s):377  386
Cited by: Papers (1)Expressiveness results for indeterminate data flow primitives are established. Choice primitives with three differing fairness assumptions are considered, and it is shown that they are strictly inequivalent in expressive power. It is also shown that the ability to announce choices enhances the expressive power of two of the primitives. These results are proved using a very crude semantics and will... View full abstract»

Learning via queries
Publication Year: 1988, Page(s):130  137
Cited by: Papers (1)The power of various query languages is compared along two dimensions, namely the inherent power of the language and the number of alternations of quantizers. Learning by asking questions is compared to learning by passively reading data. It is found that the extent of what can be learned by queries is largely dependent on the language used by the inference mechanism to formulate questions to ask ... View full abstract»

Lower bounds for integer greatest common divisor computations
Publication Year: 1988, Page(s):54  63
Cited by: Papers (3)An Ω(log log
n ) lower bound is proved on the depth of any computation tree with operations {+, , /, mod, ⩽} that computes the greatest common divisor (GCD) of all pairs ofn bit integers. A novel technique for handling the truncation operation is implicit in the proof. Also proved is a Θ(n ) bound on the depth of any algebraic computation trees with opera... View full abstract» 
Genus
Publication Year: 1988, Page(s):458  468g graphs have pagenumber O(√g )A book embedding of a graph consists of a linear ordering of the vertices along the spine of a book and an assignment of edges to pages so that edges on the same page do not intersect. The minimum number of pages in which a graph can be embedded is its pagenumber. The following results are presented: (1) any graph of genus
g has pagenumber O(√g ); and (2) mostn ver... View full abstract» 
A faster PSPACE algorithm for deciding the existential theory of the reals
Publication Year: 1988, Page(s):291  295
Cited by: Papers (7)The decision problem for the existential theory of the reals is the problem of deciding if the set {
x ∈R ^{n };P (x ) is nonempty, whereP (x ) is a predicate which is a Boolean function of atomic predicates either of which is a Boolean function of atomic predicates either of the formf _{i}(x )⩾0 or ... View full abstract» 
A deterministic view of random sampling and its use in geometry
Publication Year: 1988, Page(s):539  549
Cited by: Papers (7)A number of efficient probabilistic algorithms based on the combination of divideandconquer and random sampling have been recently discovered. It is shown that all those algorithms can be derandomized with only polynomial overhead. In the process. results of independent interest concerning the covering of hypergraphs are established, and various probabilistic bounds in geometry complexity are im... View full abstract»

Optimal parallel algorithm for the Hamiltonian cycle problem on dense graphs
Publication Year: 1988, Page(s):186  193
Cited by: Papers (1)G.A. Dirac's classical theorem (1952) asserts that if every vertex of a graph
G onn vertices has degree at leastn /2, theG has a Hamiltonian cycle. A fast parallel algorithm on a concurrentreadexclusivewrite parallel randomaccess machine (CREW PRAM) is given to find a Hamiltonian cycle in such graphs. The algorithm uses a linear number of processors and i... View full abstract» 
Fully abstract models of the lazy lambda calculus
Publication Year: 1988, Page(s):368  376
Cited by: Papers (2)Much of what is known about the model theory and proof theory of the λcalculus is sensible in nature, i.e. only head normal forms are semantically meaningful. However, most functional languages are lazy, i.e. programs are evaluated in normal order to weak head normal forms. The author develops a theory of lazy or strongly sensible λcalculus that corresponds to practice. A general m... View full abstract»

Achieving oblivious transfer using weakened security assumptions
Publication Year: 1988, Page(s):42  52
Cited by: Papers (50)  Patents (1)The authors present some general techniques for establishing the cryptographic strength of a wide variety of games. As case studies, they analyze some weakened versions of the standard forms of oblivious transfer. They also consider variants of oblivious transfer that are motivated by coding theory and physics. Among their results, they show that a noisy telephone line is in fact a very sophistica... View full abstract»

Hardness vs. randomness
Publication Year: 1988, Page(s):2  11
Cited by: Papers (27)A simple construction for a pseudorandom bit generator is presented. It stretches a short string of truly random bits into a long string that looks random to any algorithm from a complexity class C (e.g. P, NC, PSPACE, etc.), using an arbitrary function that is hard for C. This generator reveals an equivalence between the problems of proving lower bounds and the problem of generating good pseudora... View full abstract»

A Las Vegas algorithm for linear programming when the dimension is small
Publication Year: 1988, Page(s):452  456
Cited by: Papers (13)  Patents (1)An algorithm for solving linear programming problems is given. The expected number of arithmetic operations required by the algorithm is given. The expectation is with respect to the random choices made by the algorithm, and the bound holds for any given input. The technique can be extended to other convex programming problems View full abstract»