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Proceedings 41st Annual Symposium on Foundations of Computer Science

12-14 Nov. 2000

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  • Proceedings 41st Annual Symposium on Foundations of Computer Science

    Publication Year: 2000
    Request permission for commercial reuse | PDF file iconPDF (259 KB)
    Freely Available from IEEE
  • Private quantum channels

    Publication Year: 2000, Page(s):547 - 553
    Cited by:  Papers (23)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (571 KB)

    We investigate how a classical private key can be used by two players, connected by an insecure one-way quantum channel, to perform private communication of quantum information. In particular, we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sufficient. This result may be viewed as the quantum analogue of the classical one-time pad encryption sc... View full abstract»

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  • Extracting randomness from samplable distributions

    Publication Year: 2000, Page(s):32 - 42
    Cited by:  Papers (44)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (952 KB)

    The standard notion of a randomness extractor is a procedure which converts any weak source of randomness into an almost uniform distribution. The conversion necessarily uses a small amount of pure randomness, which can be eliminated by complete enumeration in some, but not all, applications. We consider the problem of deterministically converting a weak source of randomness into an almost uniform... View full abstract»

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  • Opportunistic data structures with applications

    Publication Year: 2000, Page(s):390 - 398
    Cited by:  Papers (140)  |  Patents (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (844 KB)

    We address the issue of compressing and indexing data. We devise a data structure whose space occupancy is a function of the entropy of the underlying data set. We call the data structure opportunistic since its space occupancy is decreased when the input is compressible and this space reduction is achieved at no significant slowdown in the query performance. More precisely, its space occupancy is... View full abstract»

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  • Polynomial time approximation schemes for geometric k-clustering

    Publication Year: 2000, Page(s):349 - 358
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (624 KB)

    We deal with the problem of clustering data points. Given n points in a larger set (for example, Rd) endowed with a distance function (for example, L2 distance), we would like to partition the data set into k disjoint clusters, each with a “cluster center”, so as to minimize the sum over all data points of the distance between the point and the center of the clust... View full abstract»

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  • New data structures for orthogonal range searching

    Publication Year: 2000, Page(s):198 - 207
    Cited by:  Papers (24)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (840 KB)

    We present new general techniques for static orthogonal range searching problems in two and higher dimensions. For the general range reporting problem in R3, we achieve query time O(log n+k) using space O(n log1+ε n), where n denotes the number of stored points and k the number of points to be reported. For the range reporting problem on an n×n grid, we achieve que... View full abstract»

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  • Fully dynamic transitive closure: breaking through the O(n2 ) barrier

    Publication Year: 2000, Page(s):381 - 389
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (720 KB)

    We introduce a general framework for casting fully dynamic transitive closure into the problem of reevaluating polynomials over matrices. With this technique, we improve the best known bounds for fully dynamic transitive closure, in particular we devise a deterministic algorithm for general directed graphs that achieves O(n 2) amortized time for updates, while preserving unit worst-case... View full abstract»

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  • The online median problem

    Publication Year: 2000, Page(s):339 - 348
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (668 KB)

    We introduce a natural variant of the (metric uncapacitated) k-median problem that we call the online median problem. Whereas the k-median problem involves optimizing the simultaneous placement of k facilities, the on-line median problem imposes the following additional constraints: the facilities are placed one at a time; a facility cannot be moved once it is placed, and the total number of facil... View full abstract»

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  • Lower bounds on the efficiency of generic cryptographic constructions

    Publication Year: 2000, Page(s):305 - 313
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (652 KB)

    We present lower bounds on the efficiency of constructions for Pseudo-Random Generators (PRGs) and Universal One-Way Hash Functions (UOWHFs) based on black-box access to one-way permutations. Our lower bounds are tight as they match the efficiency of known constructions. A PRG (resp. UOWHF) construction based on black-box access is a machine that is given oracle access to a permutation. Whenever t... View full abstract»

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  • The randomness recycler: a new technique for perfect sampling

    Publication Year: 2000, Page(s):503 - 511
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (724 KB)

    For many probability distributions of interest, it is quite difficult to obtain samples efficiently. Often, Markov chains are employed to obtain approximately random samples from these distributions. The primary drawback to traditional Markov chain methods is that the mixing time of the chain is usually unknown, which makes it impossible to determine how close the output samples are to having the ... View full abstract»

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  • Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors

    Publication Year: 2000, Page(s):3 - 13
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (916 KB)

    The main contribution is a new type of graph product, which we call the zig-zag product. Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both. Iteration yields simple explicit constructions of constant-degree expanders of every size, starting from one constant-... View full abstract»

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  • Using expander graphs to find vertex connectivity

    Publication Year: 2000, Page(s):410 - 420
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (868 KB)

    The (vertex) connectivity κ of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. We present the fastest known algorithm for finding κ. For a digraph with n vertices, m edges and connectivity κ the time bound is O((n+min(κ5/2,κn3/4))m). This improves the previous best bound of O((n+min(κ3... View full abstract»

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  • On clusterings-good, bad and spectral

    Publication Year: 2000, Page(s):367 - 377
    Cited by:  Papers (55)  |  Patents (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (688 KB)

    We propose a new measure for assessing the quality of a clustering. A simple heuristic is shown to give worst-case guarantees under the new measure. Then we present two results regarding the quality of the clustering found by a popular spectral algorithm. One proffers worst case guarantees whilst the other shows that if there exists a “good” clustering then the spectral algorithm will ... View full abstract»

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  • The relationship between public key encryption and oblivious transfer

    Publication Year: 2000, Page(s):325 - 335
    Cited by:  Papers (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1060 KB)

    In this paper we study the relationships among some of the most fundamental primitives and protocols in cryptography: public-key encryption (i.e. trapdoor predicates), oblivious transfer (which is equivalent to general secure multi-party computation), key agreement and trapdoor permutations. Our main results show that public-key encryption and oblivious transfer are incomparable under black-box re... View full abstract»

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  • Extracting randomness via repeated condensing

    Publication Year: 2000, Page(s):22 - 31
    Cited by:  Papers (15)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (812 KB)

    On an input probability distribution with some (min-)entropy an extractor outputs a distribution with a (near) maximum entropy rate (namely the uniform distribution). A natural weakening of this concept is a condenser, whose output distribution has a higher entropy rate than the input distribution (without losing much of the initial entropy). We construct efficient explicit condensers. The condens... View full abstract»

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  • Straightening polygonal arcs and convexifying polygonal cycles

    Publication Year: 2000, Page(s):432 - 442
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (992 KB)

    Consider a planar linkage, consisting of disjoint polygonal arcs and cycles of rigid bars joined at incident endpoints (polygonal chains), with the property that no cycle surrounds another arc or cycle. We prove that the linkage can be continuously moved so that the arcs become straight, the cycles become convex, and no bars cross while preserving the bar lengths. Furthermore, our motion is piecew... View full abstract»

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  • Randomizing polynomials: A new representation with applications to round-efficient secure computation

    Publication Year: 2000, Page(s):294 - 304
    Cited by:  Papers (21)  |  Patents (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1008 KB)

    Motivated by questions about secure multi-party computation, we introduce and study a new natural representation of functions by polynomials, which we term randomizing polynomials. “Standard” low-degree polynomials over a finite field are easy to compute with a small number of communication rounds in virtually any setting for secure computation. However, most Boolean functions cannot b... View full abstract»

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  • “Soft-decision” decoding of Chinese remainder codes

    Publication Year: 2000, Page(s):159 - 168
    Cited by:  Papers (19)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (840 KB)

    Given n relatively prime integers p1<...<pn and an integer k<n, the Chinese Remainder Code, CRTp1,...,pnik, has as its message space M={0,...,Πi=1k,pi-1}, and encodes a message m ∈M as the vector ⟨m1,...,mn⟩, where mi=m(mod pi). The soft-decision decoding problem for the C... View full abstract»

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  • Sampling adsorbing staircase walks using a new Markov chain decomposition method

    Publication Year: 2000, Page(s):492 - 502
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (748 KB)

    Staircase walks are lattice paths from (0,0) to (2n,0) which take diagonal steps and which never fall below the x-axis. A path hitting the x-axis κ times is assigned a weight of λκ, where λ>0. A simple local Markov chain, which connects the state space and converges to the Gibbs measure (which normalizes these weights) is known to be rapidly mixing when &lam... View full abstract»

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  • Succinct quantum proofs for properties of finite groups

    Publication Year: 2000, Page(s):537 - 546
    Cited by:  Papers (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (808 KB)

    The article considers a quantum computational variant of nondeterminism based on the notion of a quantum proof, which is a quantum state that plays a role similar to a certificate in an NP-type proof. Specifically, we consider quantum proofs for properties of black-box groups, which are finite groups whose elements are encoded as strings of a given length and whose group operations are performed b... View full abstract»

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  • Stable distributions, pseudorandom generators, embeddings and data stream computation

    Publication Year: 2000, Page(s):189 - 197
    Cited by:  Papers (42)  |  Patents (19)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (568 KB)

    In this paper we show several results obtained by combining the use of stable distributions with pseudorandom generators for bounded space. In particular: we show how to maintain (using only O(log n/ε2) words of storage) a sketch C(p) of a point p∈l1n under dynamic updates of its coordinates, such that given sketches C(p) and C(q) one can estimate |p-q| View full abstract»

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  • Using upper confidence bounds for online learning

    Publication Year: 2000, Page(s):270 - 279
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (508 KB)

    We show how a standard tool from statistics, namely confidence bounds, can be used to elegantly deal with situations which exhibit an exploitation/exploration trade-off. Our technique for designing and analyzing algorithms for such situations is very general and can be applied when an algorithm has to make exploitation-versus-exploration decisions based on uncertain information provided by a rando... View full abstract»

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  • Hardness of approximate hypergraph coloring

    Publication Year: 2000, Page(s):149 - 158
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (852 KB)

    We introduce the notion of covering complexity of a probabilistic verifier. The covering complexity of a verifier on a given input is the minimum number of proofs needed to “satisfy” the verifier on every random string, i.e., on every random string, at least one of the given proofs must be accepted by the verifier. The covering complexity of PCP verifiers offers a promising route to ge... View full abstract»

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  • Fairness measures for resource allocation

    Publication Year: 2000, Page(s):75 - 85
    Cited by:  Papers (16)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (928 KB)

    In many optimization problems, one seeks to allocate a limited set of resources to a set of individuals with demands. Thus, such allocations can naturally be viewed as vectors, with one coordinate representing each individual. Motivated by work in network routing and bandwidth assignment, we consider the problem of producing solutions that simultaneously approximate all feasible allocations in a c... View full abstract»

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  • The product replacement algorithm is polynomial

    Publication Year: 2000, Page(s):476 - 485
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (696 KB)

    The product replacement algorithm is a heuristic designed to generate random group elements. The idea is to run a random walk on generating κ-tuples of the group, and then output a random component. The algorithm was designed by C.R. Leedham-Green, and further investigated by F. Cellar et al. (1995). It was found to have an outstanding performance, much better than the previously known algor... View full abstract»

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