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
  • 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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  • 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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  • Asymptotically fast algorithms for spherical and related transforms

    Publication Year: 1989, Page(s):344 - 349
    Cited by:  Papers (2)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (476 KB)

    The problem of computing the convolution of two functions on the sphere by means of a spherical transform is considered. Such convolutions are applicable to surface recognition and the location of both rotated and translated patterns in an image. The authors give convolution theorems that relate the spherical transform to convolution, sampling theorems that allow the exact computation of the trans... View full abstract»

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  • Lower bounds for the stable marriage problem and its variants

    Publication Year: 1989, Page(s):129 - 133
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (332 KB)

    An instance of the stable marriage problem of size n involves n men and n women. Each participant ranks all members of the opposite sex in order of preference. A stable marriage is a complete matching M={(m1, wi1), (m2, wi2 ), . . ., (mn, win)}... View full abstract»

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  • Expanders might be practical: fast algorithms for routing around faults on multibutterflies

    Publication Year: 1989, Page(s):384 - 389
    Cited by:  Papers (37)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (592 KB)

    Simple deterministic O(log N)-step algorithms for routing packets on a multibutterfly are described. The algorithms are shown to be robust against faults, even in the worst case, and to be efficient from a practical point of view. As a consequence, the multibutterfly is shown to be an excellent candidate for a high-bandwidth, low-diameter switching network underlying a distribute... View full abstract»

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  • A new algorithm for minimizing convex functions over convex sets

    Publication Year: 1989, Page(s):338 - 343
    Cited by:  Papers (34)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (400 KB)

    An algorithm for minimizing a convex function over a convex set is given. The notion of a volumetric center of a polytope and a related ellipsoid of maximum volume inscribable in the polytope is central to the algorithm. The algorithm has a much better rate of global convergence than the ellipsoid algorithm. A by-product of the algorithm is an algorithm for solving linear programming problems that... View full abstract»

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  • Graph products and chromatic numbers

    Publication Year: 1989, Page(s):124 - 128
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (348 KB)

    The problem of computing the chromatic number of a graph is considered. No known approximation algorithm can guarantee a better than O(n0.4) coloring on a three-chromatic graph with n vertices. Evidence is provided that it is inherently impossible to achieve a better than nε ratio in polynomial time by showing that `breaking the n<... View full abstract»

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  • The synchronization of nonuniform networks of finite automata

    Publication Year: 1989, Page(s):376 - 381
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (548 KB)

    The generalized firing squad synchronization problem (GFSSP) is the well-known firing squad synchronization problem extended to arbitrarily connected networks of finite automata. When the transmission delays associated with the links of a network are allowed to be arbitrary nonnegative integers, the problem is called GFSSP-NUD (GFSSP with nonuniform delays). A solution of GFSSP-NUD is given for th... View full abstract»

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  • Approximation algorithms for geometric embeddings in the plane with applications to parallel processing problems

    Publication Year: 1989, Page(s):604 - 609
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (540 KB)

    Given an undirected graph G with N vertices and a set P of N points in the plane, the geometric embedding problem consists of finding a bijection from the vertices of G to the points in the plane which minimize the sum total of edge lengths of the embedded graph. Fast approximation algorithms are given for embedding d-dimensional grids in the p... View full abstract»

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  • The equivalence and learning of probabilistic automata

    Publication Year: 1989, Page(s):268 - 273
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (412 KB)

    It is proved that the equivalence problem for probabilistic automata is solvable in time O((n1+n 2)4), where n1 and n 2 are numbers of states of two given probabilistic automata. This result improves the best previous upper bound of coNP. The algorithm has some interesting applications, for example,... View full abstract»

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  • Speeding-up linear programming using fast matrix multiplication

    Publication Year: 1989, Page(s):332 - 337
    Cited by:  Papers (29)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (420 KB)

    The author presents an algorithm for solving linear programming problems that requires O((m+n)1.5 nL) arithmetic operations in the worst case, where m is the number of constraints, n the number of variables, and L a parameter defined in the paper. This result improves on the best known time complexity for linear programming ... View full abstract»

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  • Multiparty computation with faulty majority

    Publication Year: 1989, Page(s):468 - 473
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (576 KB)

    The problem of performing a multiparty computation when more than half of the processors are cooperating Byzantine faults is addressed. It is shown how to compute any Boolean function of n inputs distributively, preserving the privacy of inputs held by nonfaulty processors and ensuring that faulty processors obtain the function value if and only if the nonfaulty processors do. If the nonf... View full abstract»

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  • Using cellular graph embeddings in solving all pairs shortest paths problems

    Publication Year: 1989, Page(s):448 - 453
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (496 KB)

    An algorithm for generating a succinct encoding of all-pairs shortest path information in an n-vertex directed planar G with O(n) edges is presented. The edges have real-valued costs, but the graph contains no negative cycles. The time complexity is given in terms of a topological embedding measure defined in the paper. The algorithm uses a decomposition of the... View full abstract»

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  • A randomized maximum-flow algorithm

    Publication Year: 1989, Page(s):118 - 123
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (488 KB)

    The authors present a randomized maximum-flow algorithm, called the PLED (prudent linking excess diminishing) algorithm, whose expected running time is O(nm+n2(log n )3); this is O(nm) for all except relatively sparse networks. The algorithm is always correct, and in the worst case, which occurs with negligible probability... View full abstract»

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  • The inverse of an automorphism in polynomial time

    Publication Year: 1989, Page(s):82 - 87
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (408 KB)

    The first known polynomial-time algorithm for computing the inverse of a K-algebra automorphism is presented. The algorithm works over a commutative ring K and is based on a polynomial decomposition algorithm. A polynomial-time algorithm for computing the left composition factor of a multivariate decomposition is also presented. Two related open problems are stated View full abstract»

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  • Upper and lower bounds for routing schemes in dynamic networks

    Publication Year: 1989, Page(s):370 - 375
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (504 KB)

    An algorithm and two lower bounds are presented for the problem of constructing and maintaining routing schemes in dynamic networks. The algorithm distributively assigns addresses to nodes and constructs routing tables in a dynamically growing tree. The resulting scheme routes data messages over the shortest path between any source and destination, assigns addresses of O(log2 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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  • 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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  • Output-sensitive hidden surface removal

    Publication Year: 1989, Page(s):598 - 603
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (544 KB)

    Several output-sensitive algorithms for hidden surface removal in a collection of n horizontal triangles, viewed from a point at z=-∞, are derived. If k is the combinatorial complexity of the output visibility map, then the result is a simple (deterministic) algorithm that runs in time O(n√ k log n) and several improved and... View full abstract»

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  • On the complexity of learning from counterexamples

    Publication Year: 1989, Page(s):262 - 267
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (472 KB)

    The complexity of learning concepts belonging to various concrete concept classes C⊆2X over a finite domain X is analyzed in terms of the number of counterexamples that are needed in the worst case. It turns out that for many interesting concept classes there exist exponential differences between the number of counterexamples that are required by a `naive' learni... View full abstract»

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  • The complexity of approximating the square root

    Publication Year: 1989, Page(s):325 - 330
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (508 KB)

    The authors prove upper and lower bounds for approximately computing the square root using a given set of operations. The bounds are extended to hold for approximating the kth root, for any fixed k. Several tools from approximation theory are used to prove the lower bound. These include Markoff inequality, Chebyshev polynomials, and a theorem that relates the degree of a rational... View full abstract»

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  • Structure in locally optimal solutions

    Publication Year: 1989, Page(s):216 - 221
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (432 KB)

    A class of local search problems, PLS (polynomial-time local search), as defined by D.S. Johnson et al. (see J. Comput. Syst. Sci., vol.37, no.1, p.79-100 (1988)) is considered. PLS captures much of the structure of NP problems at the level of their feasible solutions and neighborhoods. It is first shown that CNF (conjunctive normal form) satisfiability is PLS-complete, even with simultaneously bo... View full abstract»

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  • Randomized search trees

    Publication Year: 1989, Page(s):540 - 545
    Cited by:  Papers (22)  |  Patents (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (468 KB)

    A randomized strategy for maintaining balance in dynamically changing search trees that has optimal expected behavior is presented. In particular, in the expected case an update takes logarithmic time and requires fewer than two rotations. Moreover, the update time remains logarithmic, even if the cost of a rotation is taken to be proportional to the size of the rotated subtree. The approach gener... View full abstract»

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  • On the complexity of space bounded interactive proofs

    Publication Year: 1989, Page(s):462 - 467
    Cited by:  Papers (18)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (420 KB)

    Two results on interactive proof systems with two-way probabilistic finite-state verifiers are proved. The first is a lower bound on the power of such proof systems if they are not required to halt with high probability on rejected inputs: it is shown that they can accept any recursively enumerable language. The second is an upper bound on the power of interactive proof systems that halt with high... View full abstract»

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