Proceedings., 33rd Annual Symposium on Foundations of Computer Science

24-27 Oct. 1992

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  • Proceedings 33rd Annual Symposium on Foundations of Computer Science (Cat. No.92CH3188-0)

    Publication Year: 1992
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    Freely Available from IEEE
  • Randomized consensus in expected O(n log2 n) operations per processor

    Publication Year: 1992, Page(s):137 - 146
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (776 KB)

    The paper presents a new randomized algorithm for achieving consensus among asynchronous processors that communicate by reading and writing shared registers. The fastest previously known algorithm requires a processor to perform an expected O(n2 log n) read and write operations in the worst case. In the algorithm, each processor executes at most an expected <... View full abstract»

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  • Zero-knowledge proofs of knowledge without interaction

    Publication Year: 1992, Page(s):427 - 436
    Cited by:  Papers (12)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (776 KB)

    A zero-knowledge proof system of knowledge is a protocol between two parties called the prover and the verifier. The prover wants to convince the verifier that he `knows' the proof of a given theorem without revealing any additional information. This is different from a zero-knowledge proof system of membership where the prover convinces the verifier only of the veridicity of the statement. Zero-k... View full abstract»

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  • Markov paging

    Publication Year: 1992, Page(s):208 - 217
    Cited by:  Papers (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (700 KB)

    This paper considers the problem of paging under the assumption that the sequence of pages accessed is generated by a Markov chain. The authors use this model to study the fault-rate of paging algorithms, a quantity of interest to practitioners. They first draw on the theory of Markov decision processes to characterize the paging algorithm that achieves optimal fault-rate on any Markov chain. They... View full abstract»

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  • Sparsification-a technique for speeding up dynamic graph algorithms

    Publication Year: 1992, Page(s):60 - 69
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (788 KB)

    The authors provide data structures that maintain a graph as edges are inserted and deleted, and keep track of the following properties: minimum spanning forests, best swap, graph connectivity, and graph 2-edge-connectivity, in time O(n1/2log(m/n)) per change; 3-edge-connectivity, in time O(n2/3) per change; 4-edge-connect... View full abstract»

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  • Fast unimodular reduction: planar integer lattices

    Publication Year: 1992, Page(s):437 - 446
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (580 KB)

    The author shows that a shortest basis for the 2-dimensional lattice Λ(u, v) generated by an input pair u, v∈Z 2 can be computed in O(M(n) log n) where n is the bit-size of the input numbers and M(n) is the complexity of multiplying two n-bit integers. This generalizes Schonhage's technique (1971) for fast integer GCD to a higher dimension View full abstract»

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  • On-line load balancing

    Publication Year: 1992, Page(s):218 - 225
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (444 KB)

    The setup for the authors' problem consists of n servers that must complete a set of tasks. Each task can be handled only by a subset of the servers, requires a different level of service, and once assigned can not be re-assigned. They make the natural assumption that the level of service is known at arrival time, but that the duration of service is not. The on-line load balancing problem... View full abstract»

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  • The algorithmic aspects of the regularity lemma

    Publication Year: 1992, Page(s):473 - 481
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (520 KB)

    The regularity lemma of Szemeredi (1978) is a result that asserts that every graph can be partitioned in a certain regular way. This result has numerous applications, but its known proof is not algorithmic. The authors first demonstrate the computational difficulty of finding a regular partition; they show that deciding if a given partition of an input graph satisfies the properties guaranteed by ... View full abstract»

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  • Quadratic dynamical systems

    Publication Year: 1992, Page(s):304 - 313
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (864 KB)

    The paper promotes the study of computational aspects, primarily the convergence rate, of nonlinear dynamical systems from a combinatorial perspective. The authors identify the class of symmetric quadratic systems. Such systems have been widely used to model phenomena in the natural sciences, and also provide an appropriate framework for the study of genetic algorithms in combinatorial optimisatio... View full abstract»

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  • Amplification and percolation [probabilistic Boolean functions]

    Publication Year: 1992, Page(s):258 - 267
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (664 KB)

    The authors extend R.B. Boppana's results (1989) in two ways. They first show that his two lower bounds hold for general read-once formulae, not necessarily monotone, that may even include exclusive-or gates. They are then able to join his two lower bounds together and show that any read-once, not necessarily monotone, formula that amplifies ( p-1/n,p+1... View full abstract»

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  • On four-connecting a triconnected graph

    Publication Year: 1992, Page(s):70 - 79
    Cited by:  Papers (6)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (776 KB)

    The author considers the problem of finding a smallest set of edges whose addition four-connects a triconnected graph. This is a fundamental graph-theoretic problem that has applications in designing reliable networks. He presents an O(nα(m,n)+m) time sequential algorithm for four-connecting an undirected graph G that is triconnected by adding the smallest number of edges, where n and m are ... View full abstract»

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  • How to denest Ramanujan's nested radicals

    Publication Year: 1992, Page(s):447 - 456
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (684 KB)

    The author presents a simple condition when nested radical expressions of depth two can be denested using real radicals or radicals of some bounded degree. He describes the structure of these denestings and determines an upper bound on the maximum size of a denesting. Also for depth two radicals he describes an algorithm that will find such a denesting whenever one exists. Unlike all previous dene... View full abstract»

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  • Improved lower bounds for Shellsort

    Publication Year: 1992, Page(s):226 - 235
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (808 KB)

    The authors give improved lower bounds for Shellsort based on a new and relatively simple proof idea. The lower bounds obtained are both stronger and more general than the previously known bounds. In particular, they hold for nonmonotone increment sequences and adaptive Shellsort algorithms, as well as for some recently proposed variations of Shellsort View full abstract»

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  • Tiling a polygon with rectangles

    Publication Year: 1992, Page(s):610 - 619
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (440 KB)

    The authors study the problem of tiling a simple polygon of surface n with rectangles of given types (tiles). They present a linear time algorithm for deciding if a polygon can be tiled with 1 × m and k × 1 tiles (and giving a tiling when it exists), and a quadratic algorithm for the same problem when the tile types are m × k and k × m View full abstract»

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  • On the randomized complexity of volume and diameter

    Publication Year: 1992, Page(s):482 - 492
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (676 KB)

    The authors give an O(n7log2 n) randomised algorithm to approximate the volume of a convex body, and an O(n6log n) algorithm to sample a point from the uniform distribution over a convex body. For convex polytopes the algorithm runs in O(n 7log4n) steps. Several t... View full abstract»

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  • On the bit extraction problem

    Publication Year: 1992, Page(s):314 - 319
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (412 KB)

    Consider a coloring of the n-dimensional Boolean cube with c=2s colors in such a way that every k-dimensional subcube is equicolored, i.e. each color occurs the same number of times. The author shows that for such a coloring one necessarily has (k-1)/n⩾θ c=(c/2-1)/(c-1). This resolves the `bit extraction' or `t-resilient functions' problem (also a special case of th... View full abstract»

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  • Algebraic decision trees and Euler characteristics

    Publication Year: 1992, Page(s):268 - 277
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (592 KB)

    For any set S⊆Rn, let χ(S) denote its Euler characteristic. The author shows that any algebraic computation tree or fixed-degree algebraic decision tree must have height Ω(log|χ(S)|)for deciding the membership question of a compact semi-algebraic set S. This extends a result by A. Bjorner, L. Lovasz and A. Yao where it was ... View full abstract»

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  • The complexity of parallel prefix problems on small domains

    Publication Year: 1992, Page(s):638 - 647
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (660 KB)

    The authors study the complexity of some prefix problems in the CRCW PRAM model. The main result is an Ω(α(n)) lower bound for chaining, matching a previous upper bound and solving an open problem. They give reductions to show an Ω(α(n)) lower bound on the complexity of the prefix maxima and range maxima problems even when the domain is {1,...,n}. An interesting consequence... View full abstract»

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  • Fault-tolerant wait-free shared objects

    Publication Year: 1992, Page(s):157 - 166
    Cited by:  Papers (5)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (728 KB)

    The authors classify object failures into two broad categories: responsive and non-responsive. They require that wait-free objects subject to responsive failures continue to respond (in finite time) to operation invocations. The responses may be incorrect. In contrast, wait-free objects subject to non-responsive failures are exempt from responding to operation invocations. Such objects may `hang' ... View full abstract»

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  • Towards a computational theory of statistical tests

    Publication Year: 1992, Page(s):406 - 416
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (868 KB)

    The authors initiate a computational theory of statistical tests. Loosely speaking, an algorithm is a statistical test if it rejects a `negligible' fraction of strings. A statistical test is universal for a class of algorithms if it rejects all (but finitely many) of the strings rejected by each algorithm in the class. They consider the existence and efficiency of universal statistical tests for v... View full abstract»

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  • Dynamic half-space reporting, geometric optimization, and minimum spanning trees

    Publication Year: 1992, Page(s):80 - 89
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (732 KB)

    The authors describe dynamic data structures for half-space range reporting and for maintaining the minima of a decomposable function. Using these data structures, they obtain efficient dynamic algorithms for a number of geometric problems, including closest/farthest neighbor searching, fixed dimension linear programming, bi-chromatic closest pair, diameter, and Euclidean minimum spanning tree View full abstract»

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  • Data structural bootstrapping, linear path compression, and catenable heap ordered double ended queues

    Publication Year: 1992, Page(s):40 - 49
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (712 KB)

    The authors provide an efficient implementation of catenable mindeques. To prove that the resulting data structure achieves constant amortized time per operation, they consider order preserving path compression. They prove a linear bound on deque ordered spine-only path compression, a case of order persevering path compression employed by the data structure View full abstract»

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  • On efficient band matrix arithmetic

    Publication Year: 1992, Page(s):457 - 463
    Cited by:  Papers (1)  |  Patents (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (528 KB)

    An efficient parallel Las Vegas algorithm is presented for computation of the determinant of a non-singular band matrix and for the solution of a system of linear equations with a band matrix as coefficient matrix. The algorithm can be implemented using time polylogarithmic in n with O(nmω-1) processors, in order to process an input matrix with order n and band width m, provided t... View full abstract»

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  • The asymptotic complexity of merging networks

    Publication Year: 1992, Page(s):236 - 246
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (620 KB)

    Let M(m,n) be the minimum number of comparators needed in a comparator network that merges m elements x1⩽x2⩽. . .⩽xm and n elements y1 ⩽y2. . .⩽yn, where n⩾m. Batcher's odd-even merge yields th... View full abstract»

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  • Mick gets some (the odds are on his side) [satisfiability]

    Publication Year: 1992, Page(s):620 - 627
    Cited by:  Papers (38)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (472 KB)

    Consider a randomly generated boolean formula F (in the conjunctive normal form) with m clauses of size k over n variables; k is fixed at any value greater than 1, but n tends to infinity and m = (1 + o(1))cn for some c depending only on k. It is easy to see that F is unsatisfiable with probability 1-o(1) whenever c>(ln 2)2k; the authors complement this observation by proving that F ... View full abstract»

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