30 Oct.1 Nov. 1989
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30th Annual Symposium on Foundations of Computer Science (Cat. No.89CH28084)
Publication Year: 1989 PDF (78 KB) 
Simulating (log/sup c/n)wise independence in NC
Publication Year: 1989, Page(s):2  7
Cited by: Papers (3)A general framework is developed for removing randomness from randomized NC algorithms whose analysis uses only polylogarithmic independence. Previously, no techniques were known to determinize those RNC algorithms depending on more than constant independence. One application of the techniques is an NC algorithm for the set discrepancy problem, which can be used to obtain many other NC algorithms,... View full abstract»

The probabilistic method yields deterministic parallel algorithms
Publication Year: 1989, Page(s):8  13
Cited by: Papers (6)A method is provided for converting randomized parallel algorithms into deterministic parallel algorithms. The approach is based on a parallel implementation of the method of conditional probabilities. Results obtained by applying the method to the set balancing problem, lattice approximation, edgecoloring graphs, random sampling, and combinatorial constructions are presented. The general form in... View full abstract»

Dispersers, deterministic amplification, and weak random sources
Publication Year: 1989, Page(s):14  19
Cited by: Papers (38)The use of highly expanding bipartite multigraphs (called dispersers) to reduce greatly the error of probabilistic algorithms at the cost of few additional random bits is treated. Explicit constructions of such graphs are generalized and used to obtain the following results: (1) The error probability of any RP (BPP) algorithm can be made exponentially small at the cost of only a constant factor in... View full abstract»

On universal classes of fast high performance hash functions, their timespace tradeoff, and their applications
Publication Year: 1989, Page(s):20  25
Cited by: Papers (12)A mechanism is provided for constructing lognwiseindependent hash functions that can be evaluated in O(1) time. A probabilistic argument shows that for fixed epsilon <1, a table of n/sup epsilon / random words can be accessed by a small O(1)time program to compute one important family of hash functions. An explicit algorithm for such a family, which achieves comparable performance for all p... View full abstract»

The strength of weak learnability
Publication Year: 1989, Page(s):28  33
Cited by: Papers (14)The problem of improving the accuracy of a hypothesis output by a learning algorithm in the distributionfree learning model is considered. A concept class is learnable (or strongly learnable) if, given access to a source of examples from the unknown concept, the learner with high probability is able to output a hypothesis that is correct on all but an arbitrarily small fraction of the instances. ... View full abstract»

A theory of learning simple concepts under simple distributions and average case complexity for the universal distribution
Publication Year: 1989, Page(s):34  39
Cited by: Papers (6)It is pointed out that in L.G. Valiant's learning model (Commun. ACM, vol.27, p.113442, 1984) many concepts turn out to be too hard to learn, whereas in practice, almost nothing we care to learn appears to be not learnable. To model the intuitive notion of learning more closely, it is assumed that learning happens under an arbitrary distribution, rather than under an arbitrary simple distribution... View full abstract»

Generalizing the PAC model: sample size bounds from metric dimensionbased uniform convergence results
Publication Year: 1989, Page(s):40  45
Cited by: Papers (21)The probably approximately correct (PAC) model of learning from examples is generalized. The problem of learning functions from a set X into a set Y is considered, assuming only that the examples are generated by independent draws according to an unknown probability measure on X*Y. The learner's goal is to find a function in a given hypothesis space of functions from X into Y that on average give ... View full abstract»

Learning binary relations and total orders
Publication Year: 1989, Page(s):46  51
Cited by: Papers (3)The problem of designing polynomial prediction algorithms for learning binary relations is studied for an online model in which the instances are drawn by the learner, by a helpful teacher, by an adversary, or according to a probability distribution on the instance space. The relation is represented as an n*m binary matrix, and results are presented when the matrix is restricted to have at most k ... View full abstract»

Efficient NC algorithms for set cover with applications to learning and geometry
Publication Year: 1989, Page(s):54  59
Cited by: Papers (9)NC approximation algorithms are given for the unweighted and weighted set cover problems. The algorithms use a linear number of processors and give a cover that has at most log n times the optimal size/weight, thus matching the performance of the best sequential algorithms. The set cover algorithm is applied to learning theory, providing an NC algorithm for learning the concept class obtained by t... View full abstract»

Fast matching algorithms for points on a polygon
Publication Year: 1989, Page(s):60  65
Cited by: Papers (2)The complete graph induced by a set of 2n points on the boundary of a polygon is considered. The edges are assigned weights equal to the Euclidean distance between their endpoints if the endpoints see each other in the polygon, and + infinity otherwise. An O(n log n)time algorithm is obtained for finding a minimumweight perfect matching in this graph if the polygon is convex, and an O(n log/sup ... View full abstract»

Ensemble motion planning in trees
Publication Year: 1989, Page(s):66  71
Cited by: Papers (1)The problem of transporting a set of objects between the vertices of a tree by a unit capacity vehicle that travels along the edges of the tree is considered. For the case in which any object can be dropped at intermediate vertices along its route and picked up later, the authors present algorithms for finding a minimum cost transportation that run in O(k+qn) time and in O(k+n log n) time, where n... View full abstract»

An upper bound on the number of planar ksets
Publication Year: 1989, Page(s):72  79
Cited by: Papers (4)Given a set S of n points, a subset X of size k is called a kset if there is a hyperplane II that separates X from X/sup c/. It is proved that O(n square root k/log/sub */k) is an upper bound for the number of ksets in the plane, thus improving the previous bound of P. Erdos et al. (A Survey of Combinatorial Theory, NorthHolland, 1983, p.13949) by a factor of log/sub */k. The method can be ext... View full abstract»

The inverse of an automorphism in polynomial time
Publication Year: 1989, Page(s):82  87
Cited by: Papers (1)The first known polynomialtime algorithm for computing the inverse of a Kalgebra automorphism is presented. The algorithm works over a commutative ring K and is based on a polynomial decomposition algorithm. A polynomialtime algorithm for computing the left composition factor of a multivariate decomposition is also presented. Two related open problems are stated.<<ETX>> View full abstract»

Testing permutation polynomials
Publication Year: 1989, Page(s):88  92The simple test for determining whether an arbitrary polynomial is a permutation polynomial, by producing its list of values, is considered, and it is found that offtheshelf techniques from computer algebra improve the running time slightly, without requiring any new insights into the problem. A probabilistic variant of the Hermite test that reduces its running time is given. A criterion for per... View full abstract»

Computing irreducible representations of finite groups
Publication Year: 1989, Page(s):93  98The bit complexity of computing irreducible representations of finite groups is considered. Exact computations in algebraic number fields are performed symbolically. A polynomialtime algorithm for finding a complete set of inequivalent irreducible representations over the field of complex numbers of a finite group given by its multiplication table is presented. It follows that some representative... View full abstract»

Galois groups and factoring polynomials over finite fields
Publication Year: 1989, Page(s):99  104
Cited by: Papers (2)Let p be a prime and F be a polynomial with integer coefficients. Suppose that the discriminant of F is not divisible by p, and denote by m the degree of the splitting field of F over Q and by L the maximal size of the coefficients of F. Then, assuming the generalized Riemann hypothesis (GRH), it is shown that the irreducible factors of F modulo p can be found in deterministic time polynomial in d... View full abstract»

Efficient algorithms for independent assignment on graphic and linear matroids
Publication Year: 1989, Page(s):106  111
Cited by: Papers (5)Efficient algorithms are presented for the matroid intersection problem and generalizations. The algorithm for weighted intersection works by scaling the weights. The cardinality algorithm is a special case that takes advantage of greater structure. Efficiency of the algorithms is illustrated by several implementations. On graphic matroids the algorithms run close to the best bounds for trivial ma... View full abstract»

Flow in planar graphs with multiple sources and sinks
Publication Year: 1989, Page(s):112  117
Cited by: Papers (7)  Patents (1)Given a planar network with many sources and sinks, the problem of computing the maximum flow from the sources to the sinks is investigated. An algorithm that runs in O(log/sup 2/n) time using O(n/sup 1.5/) processors on an exclusivereadexclusivewrite parallel randomaccess machine (EREW PRAM) is obtained, when the amount of flow (demand) at each source and sink is assumed as input. When the de... View full abstract»

A randomized maximumflow algorithm
Publication Year: 1989, Page(s):118  123
Cited by: Papers (3)The authors present a randomized maximumflow algorithm, called the PLED (prudent linking excess diminishing) algorithm, whose expected running time is O(nm+n/sup 2/(log n)/sup 3/); this is O(nm) for all except relatively sparse networks. The algorithm is always correct, and in the worst case, which occurs with negligible probability, it take O(nm log n) time. The approach taken is to maintain a p... View full abstract»

Graph products and chromatic numbers
Publication Year: 1989, Page(s):124  128
Cited by: Papers (14)The problem of computing the chromatic number of a graph is considered. No known approximation algorithm can guarantee a better than O(n/sup 0.4/) coloring on a threechromatic graph with n vertices. Evidence is provided that it is inherently impossible to achieve a better than n/sup epsilon / ratio in polynomial time by showing that 'breaking the n/sup epsilon / barrier' will automatically lead t... View full abstract»

Lower bounds for the stable marriage problem and its variants
Publication Year: 1989, Page(s):129  133
Cited by: Papers (1)An instance of the stable marriage problem of size n involves n men and n women. Each participant ranks all members of the opposite sex in order of preference. A stable marriage is a complete matching M=((m/sub 1/, w/sub i1/), (m/sub 2/, w/sub i2/), . . ., (m/sub n/, w/sub in/)) such that no unmatched man and woman prefer each other to their partners in M. A pair (m/sub i/, w/sub j/) is stable if ... View full abstract»

Approximation schemes for constrained scheduling problems
Publication Year: 1989, Page(s):134  139
Cited by: Papers (30)Several constrained scheduling problems are considered. The first polynomial approximation schemes for the problem of minimizing maximum completion time in a twomachine flow shop with release dates and for the problem of minimizing maximum lateness for the single and parallelmachine problem with release dates are described. All of these algorithms are based upon the notion of an outline, a set o... View full abstract»

Datalog vs. firstorder logic
Publication Year: 1989, Page(s):142  147
Cited by: Papers (9)The relation between the expressive power of datalog and that of firstorder languages, is clarified. It is then proved that every firstorder expressible datalog query is bounded. A form of compactness theorem for finite structure implied by this result is examined, and counterexamples to natural generalizations of the above result are given.<<ETX>> View full abstract»

Decidability and expressiveness for firstorder logics of probability
Publication Year: 1989, Page(s):148  153
Cited by: Papers (1)Decidability and expressiveness issues for two firstorder logics of probability are considered. In one the probability is on possible worlds, whereas in the other it is on the domain. It turns out that in both cases it takes very little to make reasoning about probability highly undecidable. It is shown that, when the probability is on the domain, if the language contains only unary predicates, t... View full abstract»