Sharif Digital Repository

Motivated by the bus escape routing problem in printed circuit boards (PCBs), we study the following optimization problem: given a set of rectangles attached to the boundary of a rectangular region, find a subset of nonoverlapping rectangles with maximum total weight. We present an efficient algorithm that solves this problem optimally in O(n4) time, where n is the number of rectangles in the input instance. This improves over the best previous O(n6) -time algorithm available for the problem. We also present two efficient approximation algorithms for the problem that find near-optimal solutions with guaranteed approximation factors. The first algorithm finds a 2-approximate solution in O(n2)... 

We study the 2-center problem with outliers in high-dimensional data streams. Given a stream of points in arbitrary d dimensions, the goal is to find two congruent balls of minimum radius covering all but at most z points. We present a (1.8+ε)-approximation streaming algorithm, improving over the previous (4+ε)-approximation algorithm available for the problem. The space complexity and update time of our algorithm are poly(d,z,1/ε), independent of the size of the stream. © 2016 Elsevier B.V  

Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a Hermitean bundle on M with connection. We define a coarse multi-partitioned index of the spin Dirac operator on M twisted by E. Our main result is the computation of this multi-partitioned index as the Fredholm index of the Dirac operator on the compact manifold N, twisted by the restriction of E to N. We establish the following main application: if the scalar curvature of M is bounded below by a positive constant everywhere (or even if this happens only on one of... 

The main motivation behind compressive sensing is to reduce the sampling rate at the input of a digital signal processing system. However, if for processing the sensed signal one requires to reconstruct the corresponding Nyquist samples, then the data rate will be again high in the processing stages of the overall system. Therefore, it is preferred that the desired processing task is done directly on the compressive measurements, without the need for the reconstruction of the Nyquist samples. This paper addresses the case in which the processing task is “detection” (the existence) of a sparse signal in additive white Gaussian noise, with applications e.g. in radar systems. Moreover, we will... 

Given a set P of n points in the plane, the all nearest neighbors problem asks for finding the closest point in P for each point in the set. The following folklore algorithm is used for the problem in practice: Pick a line in a random direction, project all points onto the line, and then search for the nearest neighbor of each point in a small vicinity of that point on the line. It is widely believed that the expected number of points needed to be checked by the algorithm in the vicinity of each point is O(pn) on average. We confirm this conjecture in affirmative by providing a careful analysis on the expected number of comparisons made by the algorithm. We also present a matching lower... 

Given a set P of n points in the plane, the all nearest neighbors problem asks for finding the closest point in P for each point in the set. The following folklore algorithm is used for the problem in practice: Pick a line in a random direction, project all points onto the line, and then search for the nearest neighbor of each point in a small vicinity of that point on the line. It is widely believed that the expected number of points needed to be checked by the algorithm in the vicinity of each point is O(pn) on average. We confirm this conjecture in affirmative by providing a careful analysis on the expected number of comparisons made by the algorithm. We also present a matching lower... 

This paper presents efficient algorithms for learning low-coherence dictionaries. First, a new algorithm based on proximal methods is proposed to solve the dictionary learning (DL) problem regularized with the mutual coherence of dictionary. This is unlike the previous approaches that solve a regularized problem where an approximate incoherence promoting term, instead of the mutual coherence, is used to encourage low-coherency. Then, a new solver is proposed for constrained low-coherence DL problem, i.e., a DL problem with an explicit constraint on the mutual coherence of the dictionary. As opposed to current methods, which follow a suboptimal two-step approach, the new algorithm directly... 

The copper/copper (Cu/Cu) interface has an important role in wafer-to-wafer hybrid bonding for 3D integration applications. Reports indicate the possibility of the formation of post-bonding interfacial voids and cracks which must be avoided. Here, we use molecular dynamics simulations to investigate the effect of annealing-induced tensions on the strength and deformation mechanisms of Cu/Cu interfaces. We perform tensile tests on the pristine and defective Cu/Cu interfaces including a prototypical interfacial grain boundary in two defective limits: the presence of a single (isolated) void, and an array of multiple voids. The latter resembles interfacial nanoscale roughness as a result of... 

This paper is a survey of semi-blind source separation approaches. Since Gaussian iid signals are not separable, simplest priors suggest to assume non Gaussian iid signals, or Gaussian non iid signals. Other priors can also been used, for instance discrete or bounded sources, positivity, etc. Although providing a generic framework for semi-blind source separation, Sparse Component Analysis and Bayesian ICA will just sketched in this paper, since two other survey papers develop in depth these approaches. © 2006 i6doc.com publication. All rights reserved  

In this paper, a nonparametric "gradient" of the mutual information is first introduced. It is used for showing that mutual information has no local minima. Using the introduced "gradient", two general gradient based approaches for minimizing mutual information in a parametric model are then presented. These approaches are quite general, and principally they can be used in any mutual information minimization problem. In blind source separation, these approaches provide powerful tools for separating any complicated (yet separable) mixing model. In this paper, they are used to develop algorithms for separating four separable mixing models: linear instantaneous, linear convolutive, post...