30th Annual Symposium on Foundations of Computer Science

Oct. 30 1989-Nov. 1 1989

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  • 30th Annual Symposium on Foundations of Computer Science (Cat. No.89CH2808-4)

    Publication Year: 1989
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    Freely Available from IEEE
  • Lower bounds for constant depth circuits in the presence of help bits

    Publication Year: 1989, Page(s):532 - 537
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (292 KB)

    The problem of how many extra bits of `help' a constant depth circuit needs in order to compute m functions is considered. Each help bit can be an arbitrary Boolean function. An exponential lower bound on the size of the circuit computing m parity functions in the presence of m-1 help bits is proved. The proof is carried out using the algebraic machinery of A. Razborov (... View full abstract»

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  • Generalizing the continued fraction algorithm to arbitrary dimensions

    Publication Year: 1989, Page(s):320 - 324
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (304 KB)

    A higher dimensional continued fraction algorithm (CFA) that produces diophantine approximations of more than linear goodness is given. The algorithm is also ideally convergent and detects integer relations View full abstract»

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  • Conductance and convergence of Markov chains-a combinatorial treatment of expanders

    Publication Year: 1989, Page(s):526 - 531
    Cited by:  Papers (29)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (400 KB)

    A direct combinatorial argument is given to bound the convergence rate of Markov chains in terms of their conductance (these are statements of the nature `random walks on expanders converge fast'). In addition to showing that the linear algebra in previous arguments for such results on time-reversible Markov chains was unnecessary, the direct analysis applies to general irreversible Markov chains View full abstract»

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  • Subquadratic simulations of circuits by branching programs

    Publication Year: 1989, Page(s):568 - 573
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (332 KB)

    Boolean circuits and their simulations by bounded-width branching programs are considered. It is shown that every NC1 circuit of size s can be simulated by a constant-width branching program of length s1.811. . .. Some related group-theoretic results are presented View full abstract»

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  • Simplification of nested radicals

    Publication Year: 1989, Page(s):314 - 319
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (428 KB)

    Radical simplification is a fundamental mathematical question, as well as an important part of symbolic computation systems. The general denesting problem had not been known to be decidable. Necessary and sufficient conditions for a radical α over a field k to be denested, as well as the first algorithm to decide whether the expression can be denested, are given. The algorithm compu... View full abstract»

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  • An analogue of the Myhill-Nerode theorem and its use in computing finite-basis characterizations

    Publication Year: 1989, Page(s):520 - 525
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (448 KB)

    A theorem that is a graph-theoretic analog of the Myhill-Nerode characterization of regular languages is proved. The theorem is used to establish that for many applications obstruction sets are computable by known algorithms. The focus is exclusively on what is computable (by a known algorithm) in principle, as opposed to what is computable in practice View full abstract»

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  • Probabilistic communication complexity of Boolean relations

    Publication Year: 1989, Page(s):562 - 567
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (352 KB)

    The authors demonstrate an exponential gap between deterministic and probabilistic complexity and between the probabilistic complexity of monotonic and nonmonotonic relations. They then prove, as their main result, an Ω((log n)2) bound on the probabilistic communication complexity of monotonic st-connectivity. From this they deduce that every nonmonotonic NC... View full abstract»

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  • Power of fast VLSI models is insensitive to wires' thinness

    Publication Year: 1989, Page(s):402 - 407
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (500 KB)

    VLSI f-models which allow the switching time to decrease to f(D) when the length of all wires is restricted by D are called `fast' if the decrease is slightly superlinear. The fast models are so strong and robust that their computational power cannot be increased by and combination of the following: (1) making zero the width of each wire of length d, ex... View full abstract»

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  • Lower bounds for algebraic computation trees with integer inputs

    Publication Year: 1989, Page(s):308 - 313
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (420 KB)

    A proof is given of a general theorem showing that for certain sets W a certain topological lower bound is valid in the algebraic computation tree model, even if the inputs are restricted to be integers. The theorem can be used to prove tight lower bounds for the integral-constrained form of many basic problems, such as element distinctness, set disjointness, and finding the convex hull. ... View full abstract»

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  • On the computational power of PP and ⊕P

    Publication Year: 1989, Page(s):514 - 519
    Cited by:  Papers (48)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (344 KB)

    Two complexity classes, PP and ⊕P, are compared with PH (the polynomial-time hierarchy). The main results are as follows: (1) every set in PH is reducible in a certain sense to a set in PP, an (2) every set in PH is reducible to a set in ⊕P under randomized polynomial-time reducibility with two-sided bounded error probability. It follows from these results that neither PP nor ⊕P ... View full abstract»

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  • Twists, turns, cascades, deque conjecture, and scanning theorem

    Publication Year: 1989, Page(s):555 - 559
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (356 KB)

    Nearly tight upper and lower bounds on the maximum number of various rotational operations that can be performed on a binary tree are proved. One of the lower bound results refutes D.E. Sleator's turn conjecture for binary trees (see R.E. Tarjan, SIAM J. Alg. Disc. Meth., vol.2, p.306-318, 1985). The upper bound results are used to derive an inverse Ackerman bound for Tarjan's deque conjecture on ... View full abstract»

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  • On the network complexity of selection

    Publication Year: 1989, Page(s):396 - 401
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (544 KB)

    The sequential complexity of determining the kth largest out of a given set of n keys is known to be linear. Thus, given a p-processor parallel machine, it is asked whether or not an O(n/p) selection algorithm can be devised for that machine. An Ω((n/p) log log p+log p) lower bound is obtained for selec... View full abstract»

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  • Processor efficient parallel algorithms for the two disjoint paths problem, and for finding a Kuratowski homeomorph

    Publication Year: 1989, Page(s):300 - 305
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (520 KB)

    Given a graph G and two pairs of vertices s1, t1 and s2, t2, the two disjoint paths problem asks for vertex-disjoint paths connecting si with ti, i=1, 2. A fast parallel (NC) algorithm is given for this problem, which has applications in certain routing situatio... View full abstract»

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  • Sorting on a parallel pointer machine with applications to set expression evaluation

    Publication Year: 1989, Page(s):190 - 195
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (564 KB)

    Optimal algorithms for sorting on parallel CREW (concurrent read, exclusive write) and EREW (exclusive read, exclusive write) versions of the pointer machine model are presented. Intuitively, these methods can be viewed as being based on the use of linked lists rather than arrays (the usual parallel data structure). It is shown how to exploit the `locality' of the approach to solve a problem with ... View full abstract»

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  • Area-optimal three-layer channel routing

    Publication Year: 1989, Page(s):506 - 511
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (400 KB)

    The channel routing problem in the knock-knee mode is considered. The algorithm presented always constructs a correct layout in a channel of bounded size, if there is one, and guarantees that it is wirable with only three conducting layers; that is, the layout is optimal with respect to the area and to the number of layers. The algorithm thus improves all previously known layout algorithms, which ... View full abstract»

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  • Space-efficient static trees and graphs

    Publication Year: 1989, Page(s):549 - 554
    Cited by:  Papers (127)  |  Patents (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (380 KB)

    Data structures that represent static unlabeled trees and planar graphs are developed. The structures are more space efficient than conventional pointer-based representations, but (to within a constant factor) they are just as time efficient for traversal operations. For trees, the data structures described are asymptotically optimal: there is no other structure that encodes n-node trees ... View full abstract»

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  • Solvability in asynchronous environments

    Publication Year: 1989, Page(s):422 - 427
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (440 KB)

    The authors present necessary and sufficient combinatorial conditions that determine membership in SMt (respectively, MPt), the class of distributed decision tasks that are solvable in the shared memory (resp. message passing) model by a t-resilient randomized protocol, which never errs and works in the presence of a strong adversary. The sufficienc... View full abstract»

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  • The probabilistic method yields deterministic parallel algorithms

    Publication Year: 1989, Page(s):8 - 13
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (524 KB)

    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, edge-coloring graphs, random sampling, and combinatorial constructions are presented. The general form in... View full abstract»

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  • Generating random spanning trees

    Publication Year: 1989, Page(s):442 - 447
    Cited by:  Papers (50)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (364 KB)

    The author describes a probabilistic algorithm that, given a connected, undirected graph G with n vertices, produces a spanning tree of G chosen uniformly at random among the spanning trees of G. The expected running time is O(n log n) per generated tree for almost all graphs, and O(n3) for the worst graphs... View full abstract»

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  • Flow in planar graphs with multiple sources and sinks

    Publication Year: 1989, Page(s):112 - 117
    Cited by:  Papers (5)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (504 KB)

    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(log2n ) time using O(n1.5) processors on an exclusive-read-exclusive-write parallel random-access machine (EREW PRAM) is obtained, when the amount of flow (demand) at each s... View full abstract»

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  • Efficient simulations of small shared memories on bounded degree networks

    Publication Year: 1989, Page(s):390 - 395
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (452 KB)

    The problem of simulating a parallel random-access machine (PRAM) with n processors and memory size m⩾n on an n-node bounded degree network (BDN) is considered. Since many of the more efficient PRAM algorithms use an amount of shared memory not much larger than the number of processors, the case in which m=o(n1+ε) i... View full abstract»

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  • The parallel complexity of the subgraph connectivity problem

    Publication Year: 1989, Page(s):294 - 299
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (384 KB)

    It is shown that the problem of testing whether a graph G contains a vertex- (edge-) connected induced subgraph of cardinality k is P-complete for any fixed k⩾3. Moreover, it is shown that approximating within a factor c>1/2 the maximum d for which there is a d-vertex-(d-edge-) connected induced subgraph of G is not in NC, unles... View full abstract»

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  • One-way functions are essential for complexity based cryptography

    Publication Year: 1989, Page(s):230 - 235
    Cited by:  Papers (39)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (496 KB)

    It is shown that many of the standard cryptographic tasks are equivalent to the usual definition of a one-way function. In particular, it is shown that for some of the standard cryptographic tasks any secure protocol for the task can be converted into a one-way function in the usual sense, and thus the security of any proposed protocol for these tasks is implicitly based on a function being `one-w... View full abstract»

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  • Pipelining computations in a tree of processors

    Publication Year: 1989, Page(s):184 - 189
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract |PDF file iconPDF (432 KB)

    The computational power of a tree of processors is investigated. It is demonstrated that a tree of processors can solve certain problems impressively fast by exploiting the internal pipelining capabilities. Efficient tree algorithms are designed for two different problems: selection and maintaining dictionaries. It is shown that an O(log n)-height tree of processors can find the ... View full abstract»

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