Proceedings 38th Annual Symposium on Foundations of Computer Science

20-22 Oct. 1997

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  • Proceedings 38th Annual Symposium on Foundations of Computer Science

    Publication Year: 1997
    Request permission for commercial reuse | PDF file iconPDF (277 KB)
    Freely Available from IEEE
  • Beyond the flow decomposition barrier

    Publication Year: 1997, Page(s):2 - 11
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (925 KB)

    We introduce a new approach to the maximum flow problem. This approach is based on assigning arc lengths based on the residual flow value and the residual are capacities. Our approach leads to an O(min(n/sup 2/3/, m/sup 1/2/)m log(n/sup 2//m) log U) time bound for a network with n vertices, m arcs, and integral arc capacities in the range [1,...,U]. This is a fundamental improvement over the previ... View full abstract»

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  • Undirected single source shortest paths in linear time

    Publication Year: 1997, Page(s):12 - 21
    Cited by:  Papers (13)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1017 KB)

    The single source shortest paths problem (SSSP) is one of the classic problems in algorithmic graph theory: given a weighted graph G with a source vertex s, find the shortest path from s to all other vertices in the graph. Since 1959 all theoretical developments in SSSP have been based on Dijkstra's algorithm, visiting the vertices in order of increasing distance from s. Thus, any implementation o... View full abstract»

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  • A faster deterministic algorithm for minimum spanning trees

    Publication Year: 1997, Page(s):22 - 31
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (960 KB)

    A deterministic algorithm for computing a minimum spanning tree of a connected graph is presented. Its running time is O(m /spl alpha/ log /spl alpha/), where /spl alpha/=/spl alpha/(m,n) is a functional inverse of Ackermann's function and n (resp. m) is the number of vertices (resp. edges). This improves on the previous, ten-year old bound of (roughly) O(m log log* m). View full abstract»

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  • Flows in undirected unit capacity networks

    Publication Year: 1997, Page(s):32 - 34
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (288 KB)

    We describe an O(min(m, n/sup 3/2/)m/sup 1/2/)-time algorithm for finding maximum flows in undirected networks with unit capacities and no parallel edges. This improves upon the previous bound of Karzanov and Even and Tarjan when m=/spl omega/(n/sup 3/2/), and upon a randomized bound of Karger when /spl upsi/=/spl Omega/(n/sup 7/4//m/sup 1/2/). View full abstract»

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  • Randomized and deterministic algorithms for the dimension of algebraic varieties

    Publication Year: 1997, Page(s):36 - 45
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (945 KB)

    We prove old and new results on the complexity of computing the dimension of algebraic varieties. In particular, we show that this problem is NP-complete in the Blum-Shub-Smale model of computation over C, that it admits a s/sup O(1)/D/sup O(n)/ deterministic algorithm, and that for systems with integer coefficients it is in the Arthur-Merlin class under the Generalized Riemann Hypothesis. The fir... View full abstract»

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  • Deciding properties of polynomials without factoring

    Publication Year: 1997, Page(s):46 - 55
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (988 KB)

    The polynomial time algorithm of Lenstra, Lenstra, and Lovasz (1982) for factoring integer polynomials and variants thereof have been widely used to show that various computational problems in number theory have polynomial time solutions. Among them is the problem of factoring polynomials over algebraic number fields, which is used itself as a major subroutine for several other algorithms. Althoug... View full abstract»

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  • An improved algorithm for quantifier elimination over real closed fields

    Publication Year: 1997, Page(s):56 - 65
    Cited by:  Papers (8)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (958 KB)

    We give a new algorithm for quantifier elimination in the first order theory of real closed fields that improves the complexity of the best known algorithm for this problem till now. Unlike previously known algorithms the combinatorial part of the complexity of this new algorithm is independent of the number of free variables. Moreover, under the assumption that each polynomial in the input depend... View full abstract»

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  • On the power of quantum finite state automata

    Publication Year: 1997, Page(s):66 - 75
    Cited by:  Papers (80)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (905 KB)

    In this paper, we introduce 1-way and 2-way quantum finite state automata (1qfa's and 2qfa's), which are the quantum analogues of deterministic, nondeterministic and probabilistic 1-way and 2-way finite state automata. We prove the following facts regarding 2qfa's. 1. For any /spl epsiv/>0, there is a 2qfa M which recognizes the non-regular language L={a/sup m/b/sup m/|m/spl ges/1} with (one-si... View full abstract»

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  • Two Decades of Temporal Logic: Achievements and Challenges

    Publication Year: 1997, Page(s): 78
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  • Computable obstructions to wait-free computability

    Publication Year: 1997, Page(s):80 - 89
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1040 KB)

    Effectively computable obstructions are associated to a distributed decision task (/spl Iscr/,/spl Oscr/,/spl Delta/) in the asynchronous, wait-free, read-write shared-memory model. The key new ingredient of this work is the association of a simplicial complex /spl Tscr/, the task complex, to the input-output relation d. The task determines a simplicial map /spl alpha/ from /spl Tscr/ to the input... View full abstract»

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  • Reliable cellular automata with self-organization

    Publication Year: 1997, Page(s):90 - 99
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1029 KB)

    In a noisy cellular automaton, even if it is infinite, it is non-trivial to keep a bit of information for more than a constant number of steps. A clever solution in 2 dimensions has been applied to a simple 3-dimensional fault-tolerant cellular automaton. This technique did not solve the following problems: remembering a bit of information in 1 dimension; computing in dimensions lower than 3, or w... View full abstract»

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  • Alternating-time temporal logic

    Publication Year: 1997, Page(s):100 - 109
    Cited by:  Papers (58)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1097 KB)

    Temporal logic comes in two varieties: linear-time temporal logic assumes implicit universal quantification over all paths that are generated by system moves; branching-time temporal logic allows explicit existential and universal quantification over all paths. We introduce a third, more general variety of temporal logic: alternating-time temporal logic offers selective quantification over those p... View full abstract»

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  • On the complexity of a set-union problem

    Publication Year: 1997, Page(s):110 - 115
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (622 KB)

    We consider a simple data structure supporting the following operations: (i) create a new singleton set; (ii) create a new set which is the union of two pre-existing sets; (iii) determine whether a given element is in a particular set. We prove both lower and upper bounds for an implementation of such a data structure. In a restricted model we show that no deterministic implementation can be bette... View full abstract»

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  • Succinct representation of balanced parentheses, static trees and planar graphs

    Publication Year: 1997, Page(s):118 - 126
    Cited by:  Papers (18)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (962 KB)

    We consider the implementation of abstract data types for the static objects: binary tree, rooted ordered tree and balanced parenthesis expression. Our representations use an amount of space within a lower order term of the information theoretic minimum and support, in constant time, a richer set of navigational operations than has previously been considered in similar work. In the case of binary ... View full abstract»

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  • Deterministic superimposed coding with applications to pattern matching

    Publication Year: 1997, Page(s):127 - 136
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (817 KB)

    A superimposed code is a set of binary vectors having the property that no vector is contained in a boolean sum (i.e. bitwise OR) of a small number of others. Such codes are used in information retrieval for constructing so-called signature files; they also have applications in other areas. In this paper we introduce a new notion of data-dependent superimposed codes and give a deterministic algori... View full abstract»

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  • Optimal suffix tree construction with large alphabets

    Publication Year: 1997, Page(s):137 - 143
    Cited by:  Papers (77)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (594 KB)

    The suffix tree of a string is the fundamental data structure of combinatorial pattern matching. Weiner (1973), who introduced the data structure, gave an O(n)-time algorithm for building the suffix tree of an n-character string drawn from a constant size alphabet. In the comparison model, there is a trivial /spl Omega/(n log n)-time lower bound based on sorting, and Weiner's algorithm matches thi... View full abstract»

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  • Pattern matching with swaps

    Publication Year: 1997, Page(s):144 - 153
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (918 KB)

    Let a text string T of n symbols and a pattern string P of m symbols from alphabet /spl Sigma/ be given. A swapped version T' of T is a length n string derived from T by a series of local swaps, (i.e. t/sup '//sub l//spl larr/t/sub l+1/ and t'/sub l+1//spl larr/t/sub l/) where each element can participate in no more than one swap. The Pattern Matching with Swaps problem is that of finding all loca... View full abstract»

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  • Improved bounds on planar k-sets and k-levels

    Publication Year: 1997, Page(s):156 - 161
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (539 KB)

    We prove an O(nk/sup 1/3/) upper bound for planar k-sets. This is the first considerable improvement on this bound after its early solutions approximately twenty seven years ago. Our proof technique also applies to improve the current bounds on the combinatorial complexities of k-levels in arrangements of line segments, k convex polygons in the union of n lines, parametric minimum spanning trees a... View full abstract»

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  • Computing integral points in convex semi-algebraic sets

    Publication Year: 1997, Page(s):162 - 171
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (810 KB)

    Let Y be a convex set in R/sup k/ defined by polynomial inequalities and equations of degree at most d/spl ges/2 with integer coefficients of binary length l. We show that if Y/spl cap/Z/sup k//spl ne//spl theta/, then Y contains an integral point of binary length ld/sup O/((k/sup 4/)). For fixed k, our bound implies a polynomial-time algorithm for computing an integral point y/spl isin/Y. In part... View full abstract»

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  • The computational complexity of knot and link problems

    Publication Year: 1997, Page(s):172 - 181
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1015 KB)

    We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted (that is, whether it is capable of being continuously deformed without self-intersection so that it lies in a plane). We show that this problem, UNKNOTTING PROBLEM, is in NP. We also consider the problem, SPLITTING PROBLEM, of determining whether two or more such polygons can be split (that i... View full abstract»

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  • Approximating shortest paths on a nonconvex polyhedron

    Publication Year: 1997, Page(s):182 - 191
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1146 KB)

    We present an approximation algorithm that, given the boundary P of a simple, nonconvex polyhedron in R/sup 3/, and two points s and t on P, constructs a path on P between s and t whose length is at most 7(1+/spl epsi/)d/sub P/(s,t), where d/sub P/(s,t) is the length of the shortest path between s and t on P, and /spl epsi/>0 is an arbitrarily small positive constant. The algorithm runs in O(n/... View full abstract»

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  • Randomized allocation processes

    Publication Year: 1997, Page(s):194 - 203
    Cited by:  Papers (10)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1045 KB)

    We investigate various randomized processes allocating balls into bins that arise in applications in dynamic resource allocation and on-line load balancing. We consider the scenario when m balls arriving sequentially are to be allocated into n bins on-line and without using a global controller. Traditionally, the main aim of allocation processes is to place the balls into bins to minimize the maxi... View full abstract»

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  • The analysis of a list-coloring algorithm on a random graph

    Publication Year: 1997, Page(s):204 - 212
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (788 KB)

    We introduce a natural k-coloring algorithm and analyze its performance on random graphs with constant expected degree c (G/sub n,p=c/n/). For k=3 our results imply that almost all graphs with n vertices and 1.923 n edges are 3-colorable. This improves the lower bound on the threshold for random 3-colorability significantly and settles the last case of a long-standing open question of Bollobas. We... View full abstract»

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  • Contention resolution with guaranteed constant expected delay

    Publication Year: 1997, Page(s):213 - 222
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (976 KB)

    We study contention resolution in multiple-access channels such as the Ethernet. Under a stochastic model of continuous packet generation from a set of n processors, we construct a protocol which guarantees constant expected delay for generation rates up to a fixed constant /spl lambda//sub 0/<1. Previous protocols which are stable for constant arrival rates do not guarantee constant expected d... View full abstract»

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