Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science

3-5 Nov. 1993

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  • Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science

    Publication Year: 1993
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    Freely Available from IEEE
  • Random sampling in matroids, with applications to graph connectivity and minimum spanning trees

    Publication Year: 1993, Page(s):84 - 93
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (788 KB)

    Random sampling is a powerful way to gather information about a group by considering only a small part of it. We give a paradigm for applying this technique to optimization problems, and demonstrate its effectiveness on matroids. Matroids abstractly model many optimization problems that can be solved by greedy methods, such as the minimum spanning tree (MST) problem. Our results have several appli... View full abstract»

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  • Exact learning via the Monotone theory

    Publication Year: 1993, Page(s):302 - 311
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (572 KB)

    We study the learnability of concept classes from membership and equivalence queries. We develop the Monotone theory that proves (1) Any boolean function is learnable as decision tree. (2) Any boolean function is either learnable as DNF or as CNF (or both). The first result solves the open problem of the learnability of decision trees and the second result gives more evidence that DNFs are not &ld... View full abstract»

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  • The complexity and distribution of hard problems

    Publication Year: 1993, Page(s):177 - 185
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (568 KB)

    Measure-theoretic aspects of the ⩽mP-reducibility structure of exponential time complexity classes E=DTIME(2linear) and E2=DTIME(2 polynomial) are investigated. Particular attention is given to the complexity (measured by the size of complexity cores) and distribution (abundance in the sense of measure) of languages that are ⩽m View full abstract»

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  • NP trees and Carnap's modal logic

    Publication Year: 1993, Page(s):42 - 51
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (712 KB)

    We consider problems and complexity classes definable by interdependent queries to an oracle in NP. How the queries depend on each other is specified by a directed graph G. We first study the class of problems where G is a general dag and show that this class coincides with Δ2P. We then consider the class where G is a tree. Our main result states that this class is iden... View full abstract»

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  • Simulated annealing for graph bisection

    Publication Year: 1993, Page(s):94 - 103
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (764 KB)

    We resolve in the affirmative a question of R.B. Boppana and T. Bui: whether simulated annealing can with high probability and in polynomial time, find the optimal bisection of a random graph an Gnpr when p-r=(ΘnΔ-2) for Δ⩽2. (The random graph model Gnpr specifies a “planted” bisection of density r, separating two n/2-vertex subset... View full abstract»

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  • Learning an intersection of k halfspaces over a uniform distribution

    Publication Year: 1993, Page(s):312 - 320
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (668 KB)

    We present a polynomial-time algorithm to learn an intersection of a constant number of halfspaces in n dimensions, over the uniform distribution on an n-dimensional ball. The algorithm we present in fact can learn an intersection of an arbitrary (polynomial) number of halfspaces over this distribution, if the subspace spanned by the normal vectors to the bounding hyperplanes has constant dimensio... View full abstract»

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  • Sensitive functions and approximate problems

    Publication Year: 1993, Page(s):186 - 193
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (560 KB)

    We investigate properties of functions that are good measures of the CRCW PRAM complexity of computing them. While the block sensitivity is known to be a good measure of the CREW PRAM complexity, no such measure is known for CRCW PRAMs. We show that the complexity of computing a function is related to its everywhere sensitivity, introduced by Vishkin and Wigderson (1985). Specifically we show that... View full abstract»

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  • Logical reducibility and monadic NP

    Publication Year: 1993, Page(s):52 - 61
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (512 KB)

    It is shown that, by choosing appropriate encodings of instances as relational structures, several known polynomial-time many-one reductions can he described in first-order logic, and furthermore they are monadic. As a corollary, several known NP-complete problems in monadic NP are shown not to be in monadic co-NP. It is further shown that there is no monadic first-order reduction from connectivit... View full abstract»

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  • Using difficulty of prediction to decrease computation: fast sort, priority queue and convex hull on entropy bounded inputs

    Publication Year: 1993, Page(s):104 - 112
    Cited by:  Papers (4)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (660 KB)

    Studies have indicated that sorting comprises about 20% of all computing on mainframes. Perhaps the largest use of sorting in computing (particularly business computing) is the sort required for large database operations (e.g. required by joint operations). In these applications the keys are many words long. Since our sorting algorithm hashes the key (rather than compare entire keys as in comparis... View full abstract»

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  • Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions

    Publication Year: 1993, Page(s):248 - 258
    Cited by:  Papers (9)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (920 KB)

    All algorithms below are optimal alphabet-independent parallel CRCW PRAM algorithms. In one dimension: Given a pattern string of length m for the string-matching problem, we design an algorithm that computes a deterministic sample of a sufficiently long substring in constant time. This problem used to be a bottleneck in the pattern preprocessing for one- and two-dimensional pattern matching. The b... View full abstract»

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  • On representations by low-degree polynomials

    Publication Year: 1993, Page(s):130 - 138
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (592 KB)

    In the first part of the paper we show that a subset S of a boolean cube Bn embedded in the projective space Pn can be approximated by a subset of Bn defined by nonzeroes of a low-degree polynomial only if the values of the Hilbert function of S are sufficiently small relative to the size of S. The use of this property provides a simple and direct technique for pro... View full abstract»

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  • On choosing a dense subgraph

    Publication Year: 1993, Page(s):692 - 701
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (696 KB)

    This paper concerns the problem of computing the densest k-vertex subgraph of a given graph, namely, the subgraph with the most edges, or with the highest edges-to-vertices ratio. A sequence of approximation algorithms is developed for the problem, with each step yielding a better ratio at the cost of a more complicated solution. The approximation ratio of our final algorithm is O˜(n0.3... View full abstract»

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  • Fast algorithms for constructing t-spanners and paths with stretch t

    Publication Year: 1993, Page(s):648 - 658
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (756 KB)

    The distance between two vertices in a weighted graph is the weight of a minimum-weight path between them. A path has stretch t if its weight is at most t times the distance between its end points. We consider a weighted undirected graph G=(V, E) and present algorithms that compute paths with stretch 2⩽t⩽log n. We present a O˜((m+k)n(2+ε/t)) time randomized algorithm ... View full abstract»

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  • Refining a triangulation of a planar straight-line graph to eliminate large angles

    Publication Year: 1993, Page(s):583 - 592
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (688 KB)

    We show that any planar straight line graph (PSLG) with v vertices can be triangulated with no angle larger than 7π/8 by adding O(v2log v) Steiner points in O(v2log2 v) time. We first triangulate the PSLG with an arbitrary constrained triangulation and then refine that triangulation by adding additional vertices and edges. We follow a lazy strategy of starting f... View full abstract»

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  • Better lower bounds on detecting affine and spherical degeneracies

    Publication Year: 1993, Page(s):528 - 536
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (688 KB)

    We show that in the worst case, Ω(nd) sidedness queries are required to determine whether a set of n points in Rd is affinely degenerate, i.e., whether it contains d+1 points on a common hyperplane. This matches known upper bounds. We give a straightforward adversary argument, based on the explicit construction of a point set containing Ω(nd) &... View full abstract»

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  • Faster algorithms for the generalized network flow problem

    Publication Year: 1993, Page(s):438 - 448
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (796 KB)

    We consider the generalized network flow problem. Each arc e in the network has a gain factor γ(e). If f(e) units of flow enter arc e, then f(e)γ(e) units arrive at the other end of e. The generalized network flow problem is to maximize the net flow into one specific node, the sink. We give an algorithm which solves this problem in O˜(m2(m+nloglog B)log B) time, where ... View full abstract»

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  • Primal-dual RNC approximation algorithms for (multi)-set (multi)-cover and covering integer programs

    Publication Year: 1993, Page(s):322 - 331
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (612 KB)

    We build on the classical greedy sequential set cover algorithm, in the spirit of the primal-dual schema, to obtain simple parallel approximation algorithms for the set cover problem and its generalizations. Our algorithms use randomization, and our randomized voting lemmas may be of independent interest. Fast parallel approximation algorithms were known before for set cover, though not for any of... View full abstract»

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  • Synchronization power depends on the register size

    Publication Year: 1993, Page(s):196 - 205
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (792 KB)

    Though it is common practice to treat synchronization primitives for multiprocessors as abstract data types, they are in reality machine instructions on registers. A crucial theoretical question with practical implications is the relationship between the size of the register and its computational power. The authors study this question and choose as a first target the popular compare and swap opera... View full abstract»

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  • Gates accept concurrent behavior

    Publication Year: 1993, Page(s):62 - 71
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (784 KB)

    We represent concurrent processes as Boolean propositions or gates, cast in the role of accepters of concurrent behavior. This properly extends other mainstream representations of concurrent behavior such as event structures, yet is defined more simply. It admits an intrinsic notion of duality that permits processes to be viewed as either schedules or automata. Its algebraic structure is essential... View full abstract»

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  • General bounds on statistical query learning and PAC learning with noise via hypothesis boosting

    Publication Year: 1993, Page(s):282 - 291
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (856 KB)

    We derive general bounds on the complexity of learning in the statistical query model and in the PAC model with classification noise. We do so by considering the problem of boosting the accuracy of weak learning algorithms which fall within the statistical query model. This new model was introduced by M. Kearns (1993) to provide a general framework for efficient PAC learning in the presence of cla... View full abstract»

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  • Approximating shortest superstrings

    Publication Year: 1993, Page(s):158 - 165
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (500 KB)

    The Shortest Superstring Problem is to find a shortest possible string that contains every string in a given set as substrings. This problem has applications to data compression and DNA sequencing. As the problem is NP-hard and MAX SNP-hard, approximation algorithms are of interest. We present a new algorithm which always finds a superstring that is at most 2.89 times as long as the shortest super... View full abstract»

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  • The hardness of approximate optima in lattices, codes, and systems of linear equations

    Publication Year: 1993, Page(s):724 - 733
    Cited by:  Papers (34)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (784 KB)

    We prove the following about the Nearest Lattice Vector Problem (in any lp norm), the Nearest Code-word Problem for binary codes, the problem of learning a halfspace in the presence of errors, and some other problems. 1. Approximating the optimum within any constant factor is NP-hard. 2. If for some ε>0 there exists a polynomial time algorithm that approximates the optimum withi... View full abstract»

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  • The shrinkage exponent is 2

    Publication Year: 1993, Page(s):114 - 123
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (632 KB)

    We prove that if we hit a formula of size L with a random restriction from Rp then the expected remaining size is at most O(p2(log p)3/2L). As a corollary we obtain a R(n3-O(1)) formula size lower bound for an explicit function in NP View full abstract»

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  • An O(nlog3 n) algorithm for the real root problem

    Publication Year: 1993, Page(s):626 - 635
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (752 KB)

    Given a univariate complex polynomial f(x) of degree n with rational coefficients expressed as a ratio of two integers <2m , the root problem is to find all the roots of f(x) up to specified precision 2-μ. In this paper we assume the arithmetic model for computation. We give an algorithm for the real root problem: where all the roots of the polynomial are real. Our real... View full abstract»

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