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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
    Request permission for commercial reuse | PDF file iconPDF (93 KB)
    Freely Available from IEEE
  • 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 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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  • Signal propagation, with application to a lower bound on the depth of noisy formulas

    Publication Year: 1993, Page(s):594 - 603
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (676 KB)

    We study the decay of an information signal propagating through a series of noisy channels. We obtain exact bounds on such decay, and as a result provide a new lower bound on the depth of formulas with noisy components. This improves upon previous work of N. Pippenger (1988) and significantly decreases the gap between his lower bound and the classical upper bound of von Neumann. We also discuss co... View full abstract»

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  • A quantum bit commitment scheme provably unbreakable by both parties

    Publication Year: 1993, Page(s):362 - 371
    Cited by:  Papers (19)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (592 KB)

    We describe a complete protocol for bit commitment based on the transmission of polarized photons. We show that under the laws of quantum physics, this protocol cannot be cheated by either party except with exponentially small probability (exponential in the running time needed to implement the honest protocol). A more thorough analysis is required to adjust all the constants used in this paper to... View full abstract»

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  • Space bounds for graph connectivity problems on node-named JAGs and node-ordered JAGs

    Publication Year: 1993, Page(s):218 - 227
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (712 KB)

    Two new models, NO-JAG and NN-JAG in order of increasing computation power, are introduced as extensions to the conventional JAG model. A space lower bound of Ω(log2 n/log log n) is proved for the problem of directed st-connectivity on a probabilistic NN-JAG and a space upper bound of O(log n) is proved for the problem of directed st-nonconnectivity on a nondeterministic NO-JAG. I... View full abstract»

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  • Directed vs. undirected monotone contact networks for threshold functions

    Publication Year: 1993, Page(s):604 - 613
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (692 KB)

    We consider the problem of computing threshold functions using directed and undirected monotone contact networks. Our main results are the following. First, we show that there exist directed monotone contact networks that compute Tkn, 2⩽k⩽n-1, of size O(k(n-k+2)log(n-k+2)). This bound is almost optimal for small thresholds, since there exists an Ω(knlog (n/(k-1)... View full abstract»

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  • A framework for cost-scaling algorithms for submodular flow problems

    Publication Year: 1993, Page(s):449 - 458
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (820 KB)

    The submodular flow problem includes such problems as minimum-cost network flow, dijoin, edge-connectivity orientation and others. We present a cost-scaling algorithm for submodular flow problems. The algorithm applies to these problems in general; we also examine its efficiency for the dijoin and edge-connectivity orientation problems. A minimum-cost dijoin is found in time O(min{m1/2,... 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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  • Simulated annealing for graph bisection

    Publication Year: 1993, Page(s):94 - 103
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (764 KB)

    We resolve in the affirmative a question of R.B. Boppana and T. Bui: whether simulated annealing can with high probability and in polynomial time, find the optimal bisection of a random graph an Gnpr when p-r=(ΘnΔ-2) for Δ⩽2. (The random graph model Gnpr specifies a “planted” bisection of density r, separating two n/2-vertex subset... View full abstract»

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  • Solving systems of set constraints with negated subset relationships

    Publication Year: 1993, Page(s):372 - 380
    Cited by:  Papers (6)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (660 KB)

    We present a decision procedure, based on tree automata techniques, for satisfiability of systems of set constraints including negated subset relationships. This result extends all previous works on set constraints solving and solves a problem which was left open by L. Bachmair et al. (1993). We prove in a constructive way that a non empty set of solutions always contains a regular solution, that ... View full abstract»

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  • Highly efficient asynchronous execution of large-grained parallel programs

    Publication Year: 1993, Page(s):271 - 280
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (828 KB)

    An n-thread parallel program p is large-grained if in every parallel step the computations on each of the threads are complex procedures requiring numerous processor instructions. This practically relevant style of programs differs from PRAM programs in its large granularity and the possibility that within a parallel step the computations on different threads may considerably vary in size. Let M b... View full abstract»

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  • A sub-linear time distributed algorithm for minimum-weight spanning trees

    Publication Year: 1993, Page(s):659 - 668
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (688 KB)

    This paper considers the question of identifying the parameters governing the behavior of fundamental global network problems. Many papers on distributed network algorithms consider the task of optimizing the running time successful when an O(n) bound is achieved on an n-vertex network. We propose that a more sensitive parameter is the network's diameter Diam. This is demonstrated in the paper by ... View full abstract»

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  • Optimal parallel all-nearest-neighbors using the well-separated pair decomposition

    Publication Year: 1993, Page(s):332 - 340
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (652 KB)

    We present an optimal parallel algorithm to construct the well-separated pair decomposition of a point set P in Rd. We show how this leads to a deterministic optimal O(log n) time parallel algorithm for finding the k nearest neighbors of each point in P, where k is a constant. We discuss several additional applications of the well-separated pair decomposition for which we can derive fas... View full abstract»

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  • Parallel computable higher type functionals

    Publication Year: 1993, Page(s):72 - 81
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (664 KB)

    The primary aim of this paper is to introduce higher type analogues of some familiar parallel complexity classes, and to show that these higher type classes can be characterised in significantly different ways. Recursion-theoretic, proof-theoretic and machine-theoretic characterisations are given for various classes, providing evidence of their naturalness 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 (7)  |  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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  • 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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  • Time-space lower bounds for directed s-t connectivity on JAG models

    Publication Year: 1993, Page(s):228 - 237
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (788 KB)

    Directed s-t connectivity is the problem of detecting whether there is a path from a distinguished vertex s to a distinguished vertex t in a directed graph. We prove time-space lower bounds of ST=Ω(n 2/log n) and S1/2T Ω(mn1/2) for Cook and Rackoff's JAG model (1980), where n is the number of vertices and m the number of edges in the input graph, and S ... View full abstract»

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  • Counting rational points on curves over finite fields

    Publication Year: 1993, Page(s):616 - 625
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (764 KB)

    We consider the problem of counting the number of points on a plane curve, given by a homogeneous polynomial F∈Fp [x, y, z], which is rational over the ground field Fp. More precisely, we show that if we are given a projective plane curve C of degree n, and if C has only ordinary multiple points, then one can compute the number of Fp 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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  • Efficient computation of Euclidean shortest paths in the plane

    Publication Year: 1993, Page(s):508 - 517
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (896 KB)

    We propose a new algorithm for a classical problem in plane computational geometry: computing a shortest path between two points in the presence of polygonal obstacles. Our algorithm runs in worst-case time O(nlog2 n) and requires O(nlog n) space, where n is the total number of vertices in the obstacle polygons. Our algorithm actually computes a planar map that encodes shortest paths fr... 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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  • The complexity and distribution of hard problems

    Publication Year: 1993, Page(s):177 - 185
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (568 KB)

    Measure-theoretic aspects of the ⩽mP-reducibility structure of exponential time complexity classes E=DTIME(2linear) and E2=DTIME(2 polynomial) are investigated. Particular attention is given to the complexity (measured by the size of complexity cores) and distribution (abundance in the sense of measure) of languages that are ⩽m View full abstract»

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  • Testing equalities of multiplicative representations in polynomial time

    Publication Year: 1993, Page(s):422 - 426
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (200 KB)

    For multiplicative representations Πi=1kαin(i) and Πj=1lβjm(j) where αi, βj are non-zero elements of some algebraic number field K and ni, mj are rational integers, we present a deterministic polynomial time algorithm that decides whether &... View full abstract»

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  • A simple local-control approximation algorithm for multicommodity flow

    Publication Year: 1993, Page(s):459 - 468
    Cited by:  Papers (31)  |  Patents (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (688 KB)

    In this paper, we describe a very simple (1+ε)-approximation algorithm for the multicommodity flow problem. The algorithm runs in time that is polynomial in N (the number of nodes in the network) and ε-1 (the closeness of the approximation to optimal). The algorithm is remarkable in that it is much simpler than all known polynomial time flow algorithms (including algorithms fo... View full abstract»

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