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Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)

8-11 Nov. 1998

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  • Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)

    Publication Year: 1998
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    Freely Available from IEEE
  • Geometric computation and the art of sampling (tutorial)

    Publication Year: 1998, Page(s): 2
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (7 KB)

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  • A tutorial on theoretical issues in probabilistic artificial intelligence

    Publication Year: 1998, Page(s): 4
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  • Author index

    Publication Year: 1998, Page(s):744 - 745
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    Freely Available from IEEE
  • Pattern matching for spatial point sets

    Publication Year: 1998, Page(s):156 - 165
    Cited by:  Papers (9)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (156 KB)

    Two sets of points in d-dimensional space are given: a data set D consisting of N points, and a pattern set or probe P consisting of k points. We address the problem of determining whether there is a transformation, among a specified group of transformations of the space, carrying P into or near (meaning at a small directed Hausdorff distance of) D. The groups we consider are translations and rigi... View full abstract»

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  • Approximation of diameters: randomization doesn't help

    Publication Year: 1998, Page(s):244 - 251
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (136 KB)

    We describe a deterministic polynomial-time algorithm which, for a convex body K in Euclidean n-space, finds upper and lower bounds on K's diameter which differ by a factor of O(√n/logn). We show that this is, within a constant factor, the best approximation to the diameter that a polynomial-time algorithm can produce even if randomization is allowed. We also show that the above results hold... View full abstract»

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  • A divide-and-conquer algorithm for min-cost perfect matching in the plane

    Publication Year: 1998, Page(s):320 - 329
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (180 KB)

    Given a set V of 2n points in the plane, the min-cost perfect matching problem is to pair up the points (into n pairs) so that the sum of the Euclidean distances between the paired points is minimized. We present an O(n3/2log5 n)-time algorithm for computing a min-cost perfect matching in the plane, which is an improvement over the previous best algorithm of Vaidya [1989) by ... View full abstract»

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  • On approximate nearest neighbors in non-Euclidean spaces

    Publication Year: 1998, Page(s):148 - 155
    Cited by:  Papers (3)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (128 KB)

    The nearest neighbor search (NNS) problem is the following: Given a set of n points P={p1,...,pn} in some metric space X, preprocess P so as to efficiently answer queries which require finding a point in P closest to a query point q∈X. The approximate nearest neighbor search (c-NNS) is a relaxation of NNS which allows to return any point within c times the distance to th... View full abstract»

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  • The security of individual RSA bits

    Publication Year: 1998, Page(s):510 - 519
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (132 KB)

    We study the security of individual bits in an RSA encrypted message EN(X). We show that given EN(X), predicting any single bit in x with only a non-negligible advantage over the trivial guessing strategy is (through a polynomial time reduction) as hard as breaking RSA. We briefly discuss a related result for bit security of the discrete logarithm View full abstract»

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  • A tight characterization of NP with 3 query PCPs

    Publication Year: 1998, Page(s):8 - 17
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (168 KB)

    It is known that there exists a PCP characterization of NP where the verifier makes 3 queries and has a one-sided error that is bounded away from 1; and also that 2 queries do not suffice for such a characterization. Thus PCPs with 3 queries possess non-trivial verification power and motivate the task of determining the lowest error that can be achieved with a 3-query PCP. Recently, Hastad (1997) ... View full abstract»

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  • Which problems have strongly exponential complexity?

    Publication Year: 1998, Page(s):653 - 662
    Cited by:  Papers (23)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (168 KB)

    For several NP-complete problems, there have been a progression of better but still exponential algorithms. In this paper we address the relative likelihood of sub-exponential algorithms for these problems. We introduce a generalized reduction which we call sub-exponential reduction family (SERF) that preserves sub-exponential complexity. We show that Circuit-SAT is SERF-complete for all NP-search... View full abstract»

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  • 1-way quantum finite automata: strengths, weaknesses and generalizations

    Publication Year: 1998, Page(s):332 - 341
    Cited by:  Papers (26)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (124 KB)

    We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFAs can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversibl... View full abstract»

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  • Randomness vs. time: de-randomization under a uniform assumption

    Publication Year: 1998, Page(s):734 - 743
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (212 KB)

    We prove that if BPP≠EXP, then every problem in BPP can be solved deterministically in subexponential time on almost every input (on every samplable ensemble for infinitely many input sizes). This is the first derandomization result for BPP based on uniform, noncryptographic hardness assumptions. It implies the following gap in the average-instance complexities of problems in BPP: either these ... View full abstract»

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  • Algorithms to tile the infinite grid with finite clusters

    Publication Year: 1998, Page(s):137 - 145
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    We say that a subset T of Z2, the two dimensional infinite grid, tiles Z2 if we can cover Z2 with non-overlapping translates of T. No algorithm is known to decide whether a finite T⊆Z2 tiles Z2. Here we present two algorithms, one for the case when |T| is prime, and another for the case when |T|=4. Both algorithms generalize to the case, ... View full abstract»

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  • Geometric separator theorems and applications

    Publication Year: 1998, Page(s):232 - 243
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (336 KB)

    We find a large number of “geometric separator theorems” such as: I: Given N disjoint isooriented squares in the plane, there exists a rectangle with ⩽2N/3 squares inside, ⩽2N/3 squares outside, and ⩽(4+0(1))√N partly in & out. II: There exists a rectangle that is crossed by the minimal spanning tree of N sites in the plane at ⩽(4·31/4+0(1))&... View full abstract»

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  • Quantum cryptography with imperfect apparatus

    Publication Year: 1998, Page(s):503 - 509
    Cited by:  Papers (25)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (104 KB)

    Quantum key distribution, first proposed by C.H. Bennett and G. Brassard (1984), provides a possible key distribution scheme whose security depends only on the quantum laws of physics. So far the protocol has been proved secure even under channel noise and detector faults of the receiver but is vulnerable if the photon source used is imperfect. In this paper we propose and give a concrete design f... View full abstract»

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  • Testing monotonicity

    Publication Year: 1998, Page(s):426 - 435
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (180 KB)

    We present a (randomized) test for monotonicity of Boolean functions. Namely, given the ability to query an unknown function f: {0, 1}n-{0, 1} at arguments of its choice, the test always accepts a monotone f, and rejects f with high probability if it is ε-far from being monotone (i.e., every monotone function differs from f on more than an ε fraction of the domain). The comple... View full abstract»

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  • Optimal time-space trade-offs for sorting

    Publication Year: 1998, Page(s):264 - 268
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (92 KB)

    We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem. P. Beame (1991) has shown a lower bound of Ω(n2) for this product leaving a gap of a logarithmic factor up to the previously best known upper bound of O(n2 log n) due to G.N. Frederickson (1987... View full abstract»

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  • Informatin Retrieval on the Web

    Publication Year: 1998, Page(s): 6
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  • All pairs shortest paths in weighted directed graphs-exact and almost exact algorithms

    Publication Year: 1998, Page(s):310 - 319
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (172 KB)

    We present two new algorithms for solving the All Pairs Shortest Paths (APSP) problem for weighted directed graphs. Both algorithms use fast matrix multiplication algorithms. The first algorithm solves the APSP problem for weighted directed graphs in which the edge weights are integers of small absolute value in O˜(n2+μ) time, where μ satisfies the equation ω(1,μ,1)... View full abstract»

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  • Tseitin's tautologies and lower bounds for Nullstellensatz proofs

    Publication Year: 1998, Page(s):648 - 652
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (148 KB)

    We use the known linear lower bound for Tseitin's tautologies for establishing linear lower bounds on the degree of Nullstellensatz proofs (in the usual boolean setting) for explicitly constructed systems of polynomials of a constant (in our construction 6) degree. It holds over any field of characteristic distinct from 2. Previously, a linear lower bound was proved for an explicitly constructed s... View full abstract»

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  • Marked ancestor problems

    Publication Year: 1998, Page(s):534 - 543
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (100 KB)

    Consider a rooted tree whose nodes can be in two states: marked or unmarked. The marked ancestor problem is to maintain a data structure with the following operations: mark(v) marks node v: unmark(v) removes any marks from node v; firstmarked(v) returns the first marked node on the path from v to the root. We show tight upper and lower bounds for the marked ancestor problem. The lower bounds are p... View full abstract»

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  • Heuristics for finding large independent sets, with applications to coloring semi-random graphs

    Publication Year: 1998, Page(s):674 - 683
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (160 KB)

    We study a semi-random graph model for finding independent sets. For α>0, an n-vertex graph with an independent set S of site αn is constructed by blending random and adversarial decisions. Randomly and independently with probability p, each pair of vertices, such that one is in S and the other is not, is connected by an edge. An adversary can then add edges arbitrarily (provided th... View full abstract»

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  • The minimum equivalent DNF problem and shortest implicants

    Publication Year: 1998, Page(s):556 - 563
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (124 KB)

    We prove that the Minimum Equivalent DNF problem is Σ2 p-complete, resolving a conjecture due to L.J. Stockmeyer (1976). The proof involves as an intermediate step a variant of a related problem in logic minimization, namely, that of finding the shortest implicant of a Boolean function. We also obtain certain results concerning the complexity of the shortest implicant p... View full abstract»

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  • Perfect information leader election in log*n+O(1) rounds

    Publication Year: 1998, Page(s):576 - 583
    Cited by:  Papers (6)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (124 KB)

    In the leader election problem, n players wish to elect a random leader. The difficulty is that some coalition of players may conspire to elect one of its own members. We adopt the perfect information model: all communication is by broadcast, and the bad players have unlimited computational power. Within a round, they may also wait to see the inputs of the good players. A protocol is called resili... View full abstract»

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