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
  • Scale-sensitive dimensions, uniform convergence, and learnability

    Publication Year: 1993, Page(s):292 - 301
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (624 KB)

    Learnability in Valiant's PAC learning model has been shown to be strongly related to the existence of uniform laws of large numbers. These laws define a distribution-free convergence property of means to expectations uniformly over classes of random variables. Classes of real-valued functions enjoying such a property are also known as uniform Gliveako-Cantelli classes. In this paper we prove, thr... 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 union of convex polyhedra in three dimensions

    Publication Year: 1993, Page(s):518 - 527
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (772 KB)

    We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k3+knlog2 k). This bound is almost tight in the worst case. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k3+knlog3 k) expected time View full abstract»

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  • Near-linear cost sequential and distributed constructions of sparse neighborhood covers

    Publication Year: 1993, Page(s):638 - 647
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (708 KB)

    This paper introduces the first near-linear (specifically, O(Elog n+nlog2 n)) time algorithm for constructing a sparse neighborhood cover in sequential and distributed environments. This automatically implies analogous improvements (from quadratic to near-linear) to all the results in the literature that rely on network decompositions, both in sequential and distributed domains, includi... 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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  • 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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  • 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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  • A Chernoff bound for random walks on expander graphs

    Publication Year: 1993, Page(s):680 - 691
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (888 KB)

    We consider a finite random walk on a weighted graph G; we show that the sample average of visits to a set of vertices A converges to the stationary probability π(A) with error probability exponentially small in the length of the random walk and the square of the size of the deviation from π(A). The exponential bound is in terms of the expansion of G and improves previous results. We show th... View full abstract»

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  • A randomized time-space tradeoff of O˜(mRˆ) for USTCON

    Publication Year: 1993, Page(s):238 - 246
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (644 KB)

    We present a randomized time space tradeoff of O˜(mRˆ) for undirected S-T-connectivity, where Rˆ ΣυεV 1/dυ is the virtual resistance of the graph. This solves an open question of Broder et al. (1989) (implicit also in Aleliunas et al. (1979)) who asked whether a tradeoff of O˜(mn) is achievable, and also improves upon a tradeoff of O... View full abstract»

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  • A weak version of the Blum, Shub and Smale model

    Publication Year: 1993, Page(s):486 - 495
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (728 KB)

    We propose a weak version of the Blum-Shub-Smale model (1989) of computation over the real numbers. In this weak model only a “moderate” usage of multiplications and divisions is allowed. The class of languages recognizable in polynomial time as shown to be the complexity class P/poly. This implies under a standard complexity-theoretic assumption that P≠NP in the weak model, and tha... 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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  • A tight lower bound for k-set agreement

    Publication Year: 1993, Page(s):206 - 215
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (788 KB)

    We prove tight bounds on the time needed to solve k-set agreement, a natural generalization of consensus. We analyze this problem in a synchronous, message-passing model where processors fail by crashing. We prove a lower bound of [f/k]+1 rounds of communication for solutions to k-set agreement that tolerate f failures. This bound is tight, and shows that there is an inherent tradeoff between the ... 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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  • What can we sort in o(nlog n) time?

    Publication Year: 1993, Page(s):538 - 546
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (628 KB)

    We define two conditions on a random access machine (RAM) with arithmetic and Boolean instructions and possible bounds on word and memory sizes. One condition asserts that we either restrict attention to short words or allow non-uniform programs. The second asserts that we either allow a large memory or a double-precision multiplication. Our main theorem shows that the RAM can sort in o(nlog n) ti... 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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  • 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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  • 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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  • Quantum circuit complexity

    Publication Year: 1993, Page(s):352 - 361
    Cited by:  Papers (23)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (556 KB)

    We propose a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomial-size quantum circuit. This result also enables us to construct a universal quantum computer which can simulate, with a polynomial factor slowdown, a broader class of quantum machines tha... View full abstract»

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  • A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed

    Publication Year: 1993, Page(s):566 - 572
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (428 KB)

    We prove that for any dimension d there exists a polynomial time algorithm for counting integral points in polyhedra in the d-dimensional Euclidean space. Previously such algorithms were known for dimensions d=1,2,3, and 4 only 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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  • A polynomial-time algorithm for the perfect phylogeny problem when the number of character states is fixed

    Publication Year: 1993, Page(s):140 - 147
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (528 KB)

    We present a polynomial-time algorithm for determining whether a set of species, described by the characters they exhibit, has a perfect phylogeny, assuming the maximum number of possible states for a character is fixed. This solves a longstanding open problem. Our result should be contrasted with the proof by Steel and Bodlaender, Fellows, and Warnow that the perfect phylogeny problem is NP-compl... View full abstract»

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  • The complexity of the theory of p-adic numbers

    Publication Year: 1993, Page(s):412 - 421
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (740 KB)

    This paper addresses the question of the complexity of the decision problem for the theory Th(Qp) of p-adic numbers. The best known lower bound for the theory is double exponential alternating time with a linear number of alternations. I have designed an algorithm that determines the truth value of sentences of the theory requiring double exponential space. My algorithm is based on tech... View full abstract»

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  • Almost tight upper bounds for lower envelopes in higher dimensions

    Publication Year: 1993, Page(s):498 - 507
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (816 KB)

    We show that the combinatorial complexity of the lower envelope of n surfaces or surface patches in d-space (d⩾3), all algebraic of constant maximum degree, and bounded by algebraic surfaces of constant maximum degree, is O(nd-1+ε), for any ε>0; the constant of proportionality depends on ε, d, and the shape and degree of the surface patches and of their boundaries.... 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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