Consider the following problem: If you want to sort n numbers in k (a constant) rounds then how many comparisons-per-round do you need? This problem has been studied carefully and there exist several algorithms and some lower bounds for it. Many of the algorithms are non-constructive. We have embarked on an empirical study of most of the algorithms in the literature, including the non-construct...

We focus on constant-time algorithms for graph problems in bounded degree model. We introduce several techniques to design constant-time approximation algorithms for problems such as Vertex Cover, Maximum Matching, Maximum Weighted Matching, Maximum Independent Set and Set Cover. Some of our techniques can also be applied to design constant-time testers for minor-closed properties. In Chapter 1...

We present a short review of the current quasar (QSO) absorption line constraints on possible variation of the fine structure constant, α ≡ e 2 /¯ hc. Particular attention is paid to recent optical Keck/HIRES spectra of 49 absorption systems which indicate a smaller α in the past [1, 2]. Here we present new preliminary results from 128 absorption systems: ∆α/α = (−0.57 ± 0.10) × 10 −5 over the ...

Introduction Stochastic representations of a problem domain can capture aspects that are otherwise difficult to model, such as errors, alternative outcomes of actions, and uncertainty about the world. Markov models (Bellman 1957) are a popular choice for constructing stochastic representations. The classic MDP, however, does not account for uncertainty in the process state. Often this state is ...

We introduce a technique to maintain a set of n elements from a universe of size u with membership and indel operations, so that elements are associated r-bit satellite data. We achieve constant worst-case time for all the operations, at the price of spending u + o(u) + O(nr + n log log log u) bits of space. Only the variant where the space is of the form O(nr + n log u) was exhaustively explor...

where C n(h) is the vertical profile of the refractive index structure constant, V (h) is the vertical profile of the modulus of the wind speed. In the following we always assume that τ0 refers to the wavelength λ0 = 0.5 μm. The differential-exposure scintillation index (DESI) is computed for the smallest 2-cm MASS aperture as a differential index between 1 ms and 3 ms exposures. Instead of bin...

The purpose of this paper is to demonstrate that the versatility of the reconngurable mesh can be exploited to devise constant-time algorithms for a number of important computational tasks relevant to robotics, computer graphics, image processing, and computer vision. In all our algorithms, we assume that one or two n-vertex (convex) polygons are pretiled, one vertex per processor, onto a recon...

We investigate the problem of storing a subset of the elements of a boundeduniverse so that searches can be performed in constant time and the space used is within a constant factor of the minimum required. Initially we focus on the static version of this problem and conclude with an enhancement that permits insertions and deletions.

Continuous, real-time mapping of an environment using a camera requires a constanttime estimation engine. This rules out optimal global solving such as bundle adjustment. In this article, we investigate the precision that can be achieved with only local estimation of motion and structure provided by a stereo pair. We introduce a simple but novel representation of the environment in terms of a s...

We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for approximating the partition function are Markov Chain Monte Carlo and Variational Methods. An impressive body of work in mathematics, physics and theoretical compute...