2022 Nov. 1994
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Proceedings 35th Annual Symposium on Foundations of Computer Science
Publication Year: 1994 PDF (87 KB) 
On monotone formula closure of SZK
Publication Year: 1994, Page(s):454  465
Cited by: Papers (13)We investigate structural properties of statistical zero knowledge (SZK) both in the interactive and in the noninteractive model. Specifically, we look into the closure properties of SZK languages under monotone logical formula composition. This gives rise to new protocol techniques. We show that interactive SZK for random self reducible languages (RSR) (and for coRSR) is closed under monotone B... View full abstract»

On the complexity of boundedinteraction and noninteractive zeroknowledge proofs
Publication Year: 1994, Page(s):466  477
Cited by: Papers (1)We consider the basic cryptographic primitive known as zeroknowledge proofs on committed bits. In this primitive, a prover P commits to a set of bits, and then at a later time convinces a verifier V that some property 𝒫 holds for a subset of these bits. It is known how to implement this primitive based on an ordinary bitcommittal primitive, but the standard implementations involve a great d... View full abstract»

Reducibility and completeness in multiparty private computations
Publication Year: 1994, Page(s):478  489
Cited by: Papers (1)  Patents (1)We define the notions of reducibility and completeness in multiparty private computations. Let g be an nargument function. We say that a function f is reducible to g if n honestbutcurious players can compute the function f nprivately, given a blackbox for g (for which they secretly give inputs and get the result of operating g on these inputs). We say that g is complete (for multiparty priv... View full abstract»

Computing with very weak random sources
Publication Year: 1994, Page(s):264  275
Cited by: Papers (7)  Patents (2)For any fixed ε>0, we show how to simulate RP algorithms in time n^{O(log n}) using the output of a δsource with minentropy R(ε). Such a weak random source is asked once for R(ε) bits; it outputs an Rbit string such that any string has probability at most 2^{R(ε}). If ε>11/(k+1), our BPP simulations take time n^{O(log(k} n)) (log... View full abstract»

A spectral approach to lower bounds
Publication Year: 1994, Page(s):674  682
Cited by: Papers (2)We establish a nonlinear lower bound for halfplane range searching over a group. Specifically, we show that summing up the weights of n (weighted) points within n halfplanes requires Ω(n log n) additions and subtractions. This is the first nontrivial lower bound for range searching over a group. By constrast, range searching over a semigroup (which forbids subtractions) is almost completely ... View full abstract»

“Go with the winners” algorithms
Publication Year: 1994, Page(s):492  501
Cited by: Papers (13)  Patents (1)We can view certain randomized optimization algorithms as rules for randomly moving a particle around in a state space; each state might correspond to a distinct solution to the optimization problem, or more generally, the state space might express some other structure underlying the optimization algorithm. In this setting, a general paradigm for designing heuristics is to run several simulations ... View full abstract»

Randomnessefficient oblivious sampling
Publication Year: 1994, Page(s):276  287
Cited by: Papers (26)We introduce a natural notion of obliviousness of a sampling procedure, and construct a randomnessefficient oblivious sampler. Our sampler uses O(l+log δ^{1}·log l) coins to output m=poly(ε^{1}, log δ^{1}, log l) sample points x_{1}, …, x_{m}, ∈ {0, 1}^{1} such that Pr[1/mΣ_{i=1}^{m}f(x... View full abstract»

Parallel algorithms for higherdimensional convex hulls
Publication Year: 1994, Page(s):683  694
Cited by: Papers (12)We give fast randomized and deterministic parallel methods for constructing convex hulls in
R ^{d}, for any fixed d. Our methods are for the weakest sharedmemory model, the EREW PRAM, and have optimal work bounds (with high probability for the randomized methods). In particular, we show that the convex hull of n points inR ^{d} can be constructed in O(log n) time ... View full abstract» 
Randomized simplex algorithms on KleeMinty cubes
Publication Year: 1994, Page(s):502  510We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the KleeMinty cubes (1972) and similar linear programs with exponential decreasing paths. The analysis of two most natural randomized pivot rules on the KleeMinty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random ... View full abstract»

On the robustness of functional equations
Publication Year: 1994, Page(s):288  299
Cited by: Papers (2)Given a functional equation, such as ∀x, y f(x)+f(y)=f(x+y), we study the following general question: When can the “for all” quantifiers be replaced by “for most” quantifiers without essentially changing the functions that are characterized by the property? When “for most” quantifiers are sufficient, we say that the functional equation is robust. We show ... View full abstract»

More outputsensitive geometric algorithms
Publication Year: 1994, Page(s):695  702
Cited by: Papers (15)A simple idea for speeding up the computation of extrema of a partially ordered set turns out to have a number of interesting applications in geometric algorithms; the resulting algorithms generally replace an appearance of the input size n in the running time by an output size A⩽n. In particular, the A coordinatewise minima of a set of n points in R^{d} can be found by an algorithm n... View full abstract»

Finding separator cuts in planar graphs within twice the optimal
Publication Year: 1994, Page(s):14  23
Cited by: Papers (2)Building on the works of S.B. Rao (1987, 1992) and J.K. Park and C.A. Phillips (1993), we present a factor 2 approximation algorithm for the problem of finding a minimum cost bbalanced cut in planar graphs, for b⩽1/3, if the vertex weights are given in unary (using scaling, a psuedoapproximation algorithm is also presented for the case of binary vertex weights). This problem is of considerab... View full abstract»

Motion planning on a graph
Publication Year: 1994, Page(s):511  520
Cited by: Papers (12)We are given a connected, undirected graph G on n vertices. There is a mobile robot on one of the vertices; this vertex is labeled s. Each of several other vertices contains a single movable obstacle. The robot and the obstacles may only reside at vertices, although they may be moved across edges. A vertex may never contain more than one object (robot/obstacle). In one step, we may move either the... View full abstract»

Lower bounds on Hilbert's Nullstellensatz and propositional proofs
Publication Year: 1994, Page(s):794  806
Cited by: Papers (7)The weak form of the Hilbert's Nullstellensatz says that a system of algebraic equations over a field, Q_{i}(x¯)=0, does not have a solution in the algebraic closure iff 1 is in the ideal generated by the polynomials Q_{i}(x¯). We shall prove a lower bound on the degrees of polynomials P_{i}(x¯) such that Σ _{i} P_{i}(x¯)Q... View full abstract»

Optimizing static calendar queues
Publication Year: 1994, Page(s):732  743
Cited by: Papers (1)The calendar queue is an important implementation of a priority queue which is particularly useful in discrete event simulators. In this paper we present an analysis of the static calendar queue which maintains N active events. A step of the discrete event simulator removes and processes the event with the smallest associated time and inserts a new event whose associated time is the time of the re... View full abstract»

A lower bound for the monotone depth of connectivity
Publication Year: 1994, Page(s):302  308
Cited by: Papers (6)We show that any monotone circuit for computing graph connectivity must have a depth greater than Ω((log n)^{3/2}/ log log n). This proves that UCONN_{n} is not in monotone NC^{1}. The proof technique, which is an adaptation of Razborov's approximation method, is also used to derive lower bounds for a general class of graph problems View full abstract»

On the combinatorial and algebraic complexity of quantifier elimination
Publication Year: 1994, Page(s):632  641
Cited by: Papers (12)In this paper we give a new algorithm for performing quantifier elimination from first order formulae over real closed fields. This algorithm improves the complexity of the asymptotically fastest algorithm for this problem, known to this date. A new feature of our algorithm is that the role of the algebraic part (the dependence on the degrees of the input polynomials) and the combinatorial part (t... View full abstract»

Randomized and deterministic algorithms for geometric spanners of small diameter
Publication Year: 1994, Page(s):703  712
Cited by: Papers (10)Let S be a set of n points in IR^{d} and let t>1 be a real number. A tspanner for S is a directed graph having the points of S as its vertices, such that for any pair p and q of points there is a path from p to q of length at most t times the Euclidean distance between p and p. Such a path is called a tspanner path. The spanner diameter of such a spanner is defined as the smallest int... View full abstract»

Polynomial time randomised approximation schemes for the Tutte polynomial of dense graphs
Publication Year: 1994, Page(s):24  35
Cited by: Papers (3)The TutteGrothendieck polynomial T(G; x, y) of a graph G encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (x,y) plane gave the number of spanning forests of the graph, the number of its strongly connected orientations, the number of its proper kcolorings, the (all terminal) reliability probability of the graph, and various o... View full abstract»

On learning discretized geometric concepts
Publication Year: 1994, Page(s):54  63
Cited by: Papers (3)We present a polynomial time online learning algorithm that learns any discretized geometric concept generated from any number of halfspaces with any number of known (to the learner) slopes in a constant dimensional space. In particular, our algorithm learns (from equivalence queries only) unions of discretized axisparallel rectangles in a constant dimensional space in polynomial time. The algori... View full abstract»

The localization problem for mobile robots
Publication Year: 1994, Page(s):521  531
Cited by: Papers (17)  Patents (72)A fundamental task for an autonomous mobile robot is that of localizationdetermining its location in a known environment. This problem arises in settings that range from the computer analysis of aerial photographs to the design of autonomous Mars rovers. L. Guibas et al. ((1992) have given geometric algorithms for the problem of enumerating locations for a robot consistent with a given view of th... View full abstract»

Fast and feasible periodic sorting networks of constant depth
Publication Year: 1994, Page(s):369  380
Cited by: Papers (2)A periodic comparator network has depth (or period) k, if for every t>k, the compareexchange operations performed at step t are executed between exactly the same registers as at step tk. We introduce a general method that converts an arbitrary comparator network that sorts n items in time T(n) and that has layout area A into a periodic sorting network of depth 5 that sorts Θ(n·T(... View full abstract»

Measure on small complexity classes, with applications for BPP
Publication Year: 1994, Page(s):807  818
Cited by: Papers (15)We present a notion of resourcebounded measure for P and other subexponentialtime classes. This generalization is based on Lutz's notion of measure, but overcomes the limitations that cause Lutz's definitions to apply only to classes at least as large as E. We present many of the basic properties of this measure, and use it to explore the class of sets that are hard for BPP. Bennett and Gill sho... View full abstract»

Fully dynamic cycleequivalence in graphs
Publication Year: 1994, Page(s):744  755Two edges e_{1} and e_{2} of an undirected graph are cycleequivalent iff all cycles that contain e_{1} also contain e_{2}, i.e., iff e_{1} and e_{2} are a cutedge pair. The cycleequivalence classes of the controlflow graph are used in optimizing compilers to speed up existing controlflow and dataflow algorithms. While the cycleequivalence clas... View full abstract»