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Proceedings 35th Annual Symposium on Foundations of Computer Science

20-22 Nov. 1994

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  • Proceedings 35th Annual Symposium on Foundations of Computer Science

    Publication Year: 1994
    Request permission for commercial reuse | PDF file iconPDF (87 KB)
    Freely Available from IEEE
  • On monotone formula closure of SZK

    Publication Year: 1994, Page(s):454 - 465
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (940 KB)

    We investigate structural properties of statistical zero knowledge (SZK) both in the interactive and in the non-interactive model. Specifically, we look into the closure properties of SZK languages under monotone logical formula composition. This gives rise to new protocol techniques. We show that interactive SZK for random self reducible languages (RSR) (and for co-RSR) is closed under monotone B... View full abstract»

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  • On the complexity of bounded-interaction and noninteractive zero-knowledge proofs

    Publication Year: 1994, Page(s):466 - 477
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (916 KB)

    We consider the basic cryptographic primitive known as zero-knowledge proofs on committed bits. In this primitive, a prover P commits to a set of bits, and then at a later time convinces a verifier V that some property 𝒫 holds for a subset of these bits. It is known how to implement this primitive based on an ordinary bit-committal primitive, but the standard implementations involve a great d... View full abstract»

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  • Reducibility and completeness in multi-party private computations

    Publication Year: 1994, Page(s):478 - 489
    Cited by:  Papers (1)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1040 KB)

    We define the notions of reducibility and completeness in multi-party private computations. Let g be an n-argument function. We say that a function f is reducible to g if n honest-but-curious players can compute the function f n-privately, given a black-box for g (for which they secretly give inputs and get the result of operating g on these inputs). We say that g is complete (for multi-party priv... View full abstract»

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  • Computing with very weak random sources

    Publication Year: 1994, Page(s):264 - 275
    Cited by:  Papers (7)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (904 KB)

    For any fixed ε>0, we show how to simulate RP algorithms in time nO(log n) using the output of a δ-source with min-entropy R(ε). Such a weak random source is asked once for R(ε) bits; it outputs an R-bit string such that any string has probability at most 2-R(ε). If ε>1-1/(k+1), our BPP simulations take time nO(log(k n)) (log... View full abstract»

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  • A spectral approach to lower bounds

    Publication Year: 1994, Page(s):674 - 682
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (584 KB)

    We establish a nonlinear lower bound for halfplane range searching over a group. Specifically, we show that summing up the weights of n (weighted) points within n halfplanes requires Ω(n log n) additions and subtractions. This is the first nontrivial lower bound for range searching over a group. By constrast, range searching over a semigroup (which forbids subtractions) is almost completely ... View full abstract»

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  • “Go with the winners” algorithms

    Publication Year: 1994, Page(s):492 - 501
    Cited by:  Papers (13)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (620 KB)

    We can view certain randomized optimization algorithms as rules for randomly moving a particle around in a state space; each state might correspond to a distinct solution to the optimization problem, or more generally, the state space might express some other structure underlying the optimization algorithm. In this setting, a general paradigm for designing heuristics is to run several simulations ... View full abstract»

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  • Randomness-efficient oblivious sampling

    Publication Year: 1994, Page(s):276 - 287
    Cited by:  Papers (26)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (784 KB)

    We introduce a natural notion of obliviousness of a sampling procedure, and construct a randomness-efficient oblivious sampler. Our sampler uses O(l+log δ-1·log l) coins to output m=poly(ε-1, log δ-1, log l) sample points x1, …, xm, ∈ {0, 1}1 such that Pr[|1/mΣi=1mf(x... View full abstract»

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  • Parallel algorithms for higher-dimensional convex hulls

    Publication Year: 1994, Page(s):683 - 694
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1028 KB)

    We give fast randomized and deterministic parallel methods for constructing convex hulls in Rd, for any fixed d. Our methods are for the weakest shared-memory model, the EREW PRAM, and have optimal work bounds (with high probability for the randomized methods). In particular, we show that the convex hull of n points in Rd can be constructed in O(log n) time ... View full abstract»

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  • Randomized simplex algorithms on Klee-Minty cubes

    Publication Year: 1994, Page(s):502 - 510
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (612 KB)

    We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the Klee-Minty cubes (1972) and similar linear programs with exponential decreasing paths. The analysis of two most natural randomized pivot rules on the Klee-Minty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random ... View full abstract»

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  • On the robustness of functional equations

    Publication Year: 1994, Page(s):288 - 299
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (884 KB)

    Given a functional equation, such as ∀x, y f(x)+f(y)=f(x+y), we study the following general question: When can the “for all” quantifiers be replaced by “for most” quantifiers without essentially changing the functions that are characterized by the property? When “for most” quantifiers are sufficient, we say that the functional equation is robust. We show ... View full abstract»

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  • More output-sensitive geometric algorithms

    Publication Year: 1994, Page(s):695 - 702
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (572 KB)

    A simple idea for speeding up the computation of extrema of a partially ordered set turns out to have a number of interesting applications in geometric algorithms; the resulting algorithms generally replace an appearance of the input size n in the running time by an output size A⩽n. In particular, the A coordinate-wise minima of a set of n points in Rd can be found by an algorithm n... View full abstract»

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  • Finding separator cuts in planar graphs within twice the optimal

    Publication Year: 1994, Page(s):14 - 23
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (660 KB)

    Building on the works of S.B. Rao (1987, 1992) and J.K. Park and C.A. Phillips (1993), we present a factor 2 approximation algorithm for the problem of finding a minimum cost b-balanced cut in planar graphs, for b⩽1/3, if the vertex weights are given in unary (using scaling, a psuedo-approximation algorithm is also presented for the case of binary vertex weights). This problem is of considerab... View full abstract»

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  • Motion planning on a graph

    Publication Year: 1994, Page(s):511 - 520
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (708 KB)

    We are given a connected, undirected graph G on n vertices. There is a mobile robot on one of the vertices; this vertex is labeled s. Each of several other vertices contains a single movable obstacle. The robot and the obstacles may only reside at vertices, although they may be moved across edges. A vertex may never contain more than one object (robot/obstacle). In one step, we may move either the... View full abstract»

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  • Lower bounds on Hilbert's Nullstellensatz and propositional proofs

    Publication Year: 1994, Page(s):794 - 806
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (916 KB)

    The weak form of the Hilbert's Nullstellensatz says that a system of algebraic equations over a field, Qi(x¯)=0, does not have a solution in the algebraic closure iff 1 is in the ideal generated by the polynomials Qi(x¯). We shall prove a lower bound on the degrees of polynomials Pi(x¯) such that Σ i Pi(x¯)Q... View full abstract»

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  • Optimizing static calendar queues

    Publication Year: 1994, Page(s):732 - 743
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (756 KB)

    The calendar queue is an important implementation of a priority queue which is particularly useful in discrete event simulators. In this paper we present an analysis of the static calendar queue which maintains N active events. A step of the discrete event simulator removes and processes the event with the smallest associated time and inserts a new event whose associated time is the time of the re... View full abstract»

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  • A lower bound for the monotone depth of connectivity

    Publication Year: 1994, Page(s):302 - 308
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (384 KB)

    We show that any monotone circuit for computing graph connectivity must have a depth greater than Ω((log n)3/2/ log log n). This proves that UCONNn is not in monotone NC1. The proof technique, which is an adaptation of Razborov's approximation method, is also used to derive lower bounds for a general class of graph problems View full abstract»

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  • On the combinatorial and algebraic complexity of quantifier elimination

    Publication Year: 1994, Page(s):632 - 641
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (712 KB)

    In this paper we give a new algorithm for performing quantifier elimination from first order formulae over real closed fields. This algorithm improves the complexity of the asymptotically fastest algorithm for this problem, known to this date. A new feature of our algorithm is that the role of the algebraic part (the dependence on the degrees of the input polynomials) and the combinatorial part (t... View full abstract»

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  • Randomized and deterministic algorithms for geometric spanners of small diameter

    Publication Year: 1994, Page(s):703 - 712
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (764 KB)

    Let S be a set of n points in IRd and let t>1 be a real number. A t-spanner for S is a directed graph having the points of S as its vertices, such that for any pair p and q of points there is a path from p to q of length at most t times the Euclidean distance between p and p. Such a path is called a t-spanner path. The spanner diameter of such a spanner is defined as the smallest int... View full abstract»

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  • Polynomial time randomised approximation schemes for the Tutte polynomial of dense graphs

    Publication Year: 1994, Page(s):24 - 35
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (584 KB)

    The Tutte-Grothendieck polynomial T(G; x, y) of a graph G encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (x,y) plane gave the number of spanning forests of the graph, the number of its strongly connected orientations, the number of its proper k-colorings, the (all terminal) reliability probability of the graph, and various o... View full abstract»

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  • On learning discretized geometric concepts

    Publication Year: 1994, Page(s):54 - 63
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (720 KB)

    We present a polynomial time online learning algorithm that learns any discretized geometric concept generated from any number of halfspaces with any number of known (to the learner) slopes in a constant dimensional space. In particular, our algorithm learns (from equivalence queries only) unions of discretized axis-parallel rectangles in a constant dimensional space in polynomial time. The algori... View full abstract»

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  • The localization problem for mobile robots

    Publication Year: 1994, Page(s):521 - 531
    Cited by:  Papers (17)  |  Patents (72)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (832 KB)

    A fundamental task for an autonomous mobile robot is that of localization-determining its location in a known environment. This problem arises in settings that range from the computer analysis of aerial photographs to the design of autonomous Mars rovers. L. Guibas et al. ((1992) have given geometric algorithms for the problem of enumerating locations for a robot consistent with a given view of th... View full abstract»

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  • Fast and feasible periodic sorting networks of constant depth

    Publication Year: 1994, Page(s):369 - 380
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (956 KB)

    A periodic comparator network has depth (or period) k, if for every t>k, the compare-exchange operations performed at step t are executed between exactly the same registers as at step t-k. We introduce a general method that converts an arbitrary comparator network that sorts n items in time T(n) and that has layout area A into a periodic sorting network of depth 5 that sorts Θ(n·T(... View full abstract»

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  • Measure on small complexity classes, with applications for BPP

    Publication Year: 1994, Page(s):807 - 818
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (856 KB)

    We present a notion of resource-bounded measure for P and other subexponential-time classes. This generalization is based on Lutz's notion of measure, but overcomes the limitations that cause Lutz's definitions to apply only to classes at least as large as E. We present many of the basic properties of this measure, and use it to explore the class of sets that are hard for BPP. Bennett and Gill sho... View full abstract»

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  • Fully dynamic cycle-equivalence in graphs

    Publication Year: 1994, Page(s):744 - 755
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1040 KB)

    Two edges e1 and e2 of an undirected graph are cycle-equivalent iff all cycles that contain e1 also contain e2, i.e., iff e1 and e2 are a cut-edge pair. The cycle-equivalence classes of the control-flow graph are used in optimizing compilers to speed up existing control-flow and data-flow algorithms. While the cycle-equivalence clas... View full abstract»

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