Sharif Digital Repository

In this paper, we address recovery of sparse signals from compressed measurements, and sparse signal approximation, which have received considerable attention over the last decade. First, we revisit smoothed L0 (SL0), a well-known sparse recovery algorithm, and give some insights into it that have not been noticed previously. Specifically, we re-derive the SL0 algorithm based on proximal methods, and using recent results in solving nonconvex problems by proximal algorithms, we provide a convergence guarantee for it. In addition, inspired by this derivation, we propose a general family of algorithms, which we call iterative sparsification-projection (ISP), having SL0 as a special member. Our... 

In this paper, based on a successively accuracy-increasing approximation of the ℓ0 norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the ℓ0 norm can be controlled. We prove that the series of the approximations asymptotically coincides with the ℓ1 and ℓ0 norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed that leads to a number of weighted ℓ1 minimization programs, whereas, in the presence of noise, we propose... 

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  

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a continuous region ({Imprecise} model) or a finite set of points ({Indecisive} model). Given a set of inexact points in one of {Imprecise} or {Indecisive} models, we wish to provide a lower-bound on the diameter of the real points. In the first part of the paper, we focus on {Indecisive} model. We present an (formula presented) time approximation algorithm of factor (1+epsilon) for finding minimum diameter of a set of points in d dimensions. This improves the previously proposed algorithms for this... 

We study the problem of causal structure learning when the experimenter is limited to perform at most k non-adaptive experiments of size 1. We formulate the problem of finding the best intervention target set as an optimization problem, which aims to maximize the average number of edges whose directions are resolved. We prove that the corresponding objective function is submodular and a greedy algorithm suffices to achieve (1 - approximation of the optimal value. We further present an accelerated variant of the greedy algorithm, which can lead to orders of magnitude performance speedup. We validate our proposed approach on synthetic and real graphs. The results show that compared to the... 

In recent decades, multistate two-terminal reliability problem has attracted several researchers, and accordingly many exact and approximation approaches have been proposed in the literature in terms of minimal cuts (MCs) or minimal paths (MPs) to address this problem. Here, an MP-based approximation approach is developed based on exact algorithms. With all the MPs at hand, the approach rearranges the MPs ascendingly with respect to their lengths and then sets the flow on some MPs to be zero which turns to reduce the computing cost in solving the problem. We provide the complexity results, and by employing some benchmarks and one thousand randomly generated networks illustrate that not only... 

The purpose of dictionary learning problem is to learn a dictionary D from a training data matrix Y such that Y ≈ DX and the coefficient matrix X is sparse. Many algorithms have been introduced to this aim, which minimize the representation error subject to a sparseness constraint on X. However, the dictionary learning problem is non-convex with respect to the pair (D,X). In a previous work [Sadeghi et al., 2013], a convex approximation to the non-convex term DX has been introduced which makes the whole DL problem convex. This approach can be almost applied to any existing DL algorithm and obtain better algorithms. In the current paper, it is shown that a simple modification on that approach... 

We study the problem of preclustering a set B of imprecise points in Rd: we wish to cluster the regions specifying the potential locations of the points such that, no matter where the points are located within their regions, the resulting clustering approximates the optimal clustering for those locations. We consider k-center, k-median, and k-means clustering, and obtain the following results. Let B := {b1, . . ., bn} be a collection of disjoint balls in Rd, where each ball bi specifies the possible locations of an input point pi. A partition C of B into subsets is called an (f(k), α)preclustering (with respect to the specific k-clustering variant under consideration) if (i) C consists of... 

We study a weighted balanced version of the k-center problem, where each center has a fixed capacity, and each element has an arbitrary demand. The objective is to assign demands of the elements to the centers, so as the total demand assigned to each center does not exceed its capacity, while the maximum distance between centers and their assigned elements is minimized. We present a deterministic O(1)-approximation algorithm for this generalized version of the k-center problem in the distributed setting, where data is partitioned among a number of machines. Our algorithm substantially improves the approximation factor of the current best randomized algorithm available for the problem. We... 

The objective of this article is to study the estimation of an overall heat transfer coefficient in a partially filled rotating cylinder. Herein is an inverse analysis for estimating the overall heat transfer coefficient in an arbitrary cross-section of the aforementioned system from the temperatures measured on the shell. The material employs the finite-volume method to solve the direct problem. The hybrid effective algorithm applied here contains the local optimization algorithm to estimate the unknown parameter by minimizing the objective function. The data measured here are simulated by adding random errors to the exact solution. An investigation is made of the impact of the measurement... 

A decade has passed since the first appearance of the superconvergent patch recovery (SPR) method introduced by Zienkiewicz and Zhu [The superconvergence patch recovery and a posteriori error estimates, part I: the recovery techniques, Int. J. Numer. Methods Eng. 33 (1992) 1331-1364; The superconvergence patch recovery and a posteriori error estimates, part II: error estimates and adaptivity, Int. J. Numer. Methods Eng. 33 (1992) 1365-1380; Superconvergence and the superconvergent patch recovery, Finite Elem. Anal. Des. 19 (1995) 11-23]. The method is now widely used in engineering practices for its robustness and efficiency in computer implementation. This paper presents an extension of the... 

We give approximation algorithms and inapproximability results for a class of movement problems. In general, these problems involve planning the coordinated motion of a large collection of objects (representing anything from a robot swarm or firefighter team to map labels or network messages) to achieve a global property of the network while minimizing the maximum or average movement. In particular, we consider the goals of achieving connectivity (undirected and directed), achieving connectivity between a given pair of vertices, achieving independence (a dispersion problem), and achieving a perfect matching (with applications to multicasting). This general family of movement problems... 

Given a translating and rotating rod robot in a plane in the presence of polygonal obstacles with the initial and final placements of the rod known, the d1-optimal motion planning problem is defined as finding a collision-free motion of the rod such that the orbit length of a fixed but arbitrary point F on the rod is minimized. In this paper we study a special case of this problem in which the rod can translate freely, but can only rotate by some pre-specified given angles around F. We first characterize the d1-optimal motion of the robot under the given conditions and then present a (1 + ε)-approximation algorithm for finding the optimal path. The running time of the algorithm is bounded by... 

The spread of influence in social networks is studied in two main categories: the progressive model and the non-progressive model (see e.g. the seminal work of Kempe, Kleinberg, and Tardos in KDD 2003). While the progressive models are suitable for modeling the spread of influence in monopolistic settings, non-progressive are more appropriate for modeling non-monopolistic settings, e.g., modeling diffusion of two competing technologies over a social network. Despite the extensive work on the progressive model, non-progressive models have not been studied well. In this paper, we study the spread of influence in the nonprogressive model under the strict majority threshold: given a graph G with... 

In the (k, λ)-subgraph problem, we are given an undirected graph G = (V,E) with edge costs and two positive integers k and λ, and the goal is to find a minimum cost simple λ-edge-connected subgraph of G with at least k nodes. This generalizes several classical problems, such as the minimum cost k-spanning tree problem, or k-MST (which is a (k, 1)-subgraph), and the minimum cost λ-edge-connected spanning subgraph (which is a (|V(G)|, λ)-subgraph). The only previously known results on this problem [L. C. Lau, J. S. Naor, M. R. Salavatipour, and M. Singh, SIAM J. Comput., 39 (2009), pp. 1062-1087], [C. Chekuri and N. Korula, in Proceedings of the IARCS Annual Conference on Foundations of...