A crucial issue in wireless networks is to support efficiently communication patterns that are typical in traditional (wired) networks. These include broadcasting, multicasting, and gossiping (all-to-all communication...
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A crucial issue in wireless networks is to support efficiently communication patterns that are typical in traditional (wired) networks. These include broadcasting, multicasting, and gossiping (all-to-all communication). In this work we study such problems in static ad hoc networks. Since, in ad hoc networks, energy is a scarce resource, the important engineering question to be solved is to guarantee a desired communication pattern minimizing the total energy consumption. Motivated by this question, we study a series of wireless network design problems and present new approximation algorithms and inapproximability results.
We consider the generalized minimum Manhattan network problem (GMMN). The input to this problem is a set R of n pairs of terminals, which are points in . The goal is to find a minimum-length rectilinear network that c...
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We consider the generalized minimum Manhattan network problem (GMMN). The input to this problem is a set R of n pairs of terminals, which are points in . The goal is to find a minimum-length rectilinear network that connects every pair in R by a Manhattan path, that is, a path of axis-parallel line segments whose total length equals the pair's Manhattan distance. This problem is a natural generalization of the extensively studied minimum Manhattan network problem (MMN) in which R consists of all possible pairs of terminals. Another important special case is the well-known rectilinear Steiner arborescence problem (RSA). As a generalization of these problems, GMMN is NP-hard. No approximation algorithms are known for general GMMN. We obtain an -approximation algorithm for GMMN. Our solution is based on a stabbing technique, a novel way of attacking Manhattan network problems. Some parts of our algorithm generalize to higher dimensions, yielding a simple -approximation algorithm for the problem in arbitrary fixed dimension d. As a corollary, we obtain an exponential improvement upon the previously best -ratio for MMN in d dimensions (ESA 2011). En route, we show that an existing -approximation algorithm for 2D-RSA generalizes to higher dimensions.
Given dissimilarity data on pairs of objects in a set, we study the problem of fitting a tree metric to this data so as to minimize additive error (i.e., some measure of the difference between the tree metric and the ...
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Given dissimilarity data on pairs of objects in a set, we study the problem of fitting a tree metric to this data so as to minimize additive error (i.e., some measure of the difference between the tree metric and the given data). This problem arises in constructing an M-level hierarchical clustering of objects (or an ultrametric on objects) so as to match the given dissimilarity data-a basic problem in statistics. Viewed in this way, the problem is a generalization of the correlation clustering problem (which corresponds to M - 1). We give a very simple randomized combinatorial algorithm for the M-level hierarchical clustering problem that achieves an approximation ratio of M+2. This is a generalization of a previous factor 3 algorithm for correlation clustering on complete graphs. The problem of fitting tree metrics also arises in phylogeny where the objective is to learn the evolution tree by fitting a tree to dissimilarity data on taxa. The quality of the fit is measured by taking the l(p) norm of the difference between the tree metric constructed and the given data. Previous results obtained a factor 3 approximation for finding the closest tree metric under the l(infinity) norm. No nontrivial approximation for general l(p) norms was known before. We present a novel linear program formulation for this problem and obtain an O((log n log log n)(1/p))-approximation to the closest ultrametric under the l(p) norm using this. Our techniques are based on representing and viewing an ultrametric as a hierarchy of clusterings and may be useful in other contexts.
The goal of the project described in this paper is to build a prototype of an operational system, which will provide registration within subpixel accuracy of multitemporal Landsat data, acquired by either Landsat-5 or...
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The goal of the project described in this paper is to build a prototype of an operational system, which will provide registration within subpixel accuracy of multitemporal Landsat data, acquired by either Landsat-5 or Landsat-7 Thematic Mapper instruments. Integrated within an automated mass processing system for Landsat data, the input to our registration system consists of scenes that have been geometrically and radiometrically corrected, as well as preprocessed for detection of clouds and cloud shadows. Such preprocessed scenes are then georegistered relative to a database of Landsat chips. This paper describes the entire registration process, including the use of landmark chips, feature extraction performed by an overcomplete wavelet representation, and feature matching using statistically robust techniques. Knowing the approximate longitudes and latitudes or the UTM coordinates of the four corners of each incoming scene, a subset of the chips that represent landmarks included in the scene are selected to perform the registration. For each of these selected landmark chips, a corresponding window is extracted from the incoming scene, and each chip-window pair is registered using a robust wavelet feature-matching methodology. Based on the transformations from the chip-window pairs, a global transformation is then computed for the entire scene using a variant of a robust least median of squares estimator. Empirical results of this registration process, which provided subpixel accuracy for several multitemporal scenes from different study areas, are presented and discussed.
We consider a problem in which it is required to find a cyclic tour and a vehicle loading plan maximizing the total profit realized from purchasing and selling commodities loaded at vertices of the tour. It is shown t...
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We consider a problem in which it is required to find a cyclic tour and a vehicle loading plan maximizing the total profit realized from purchasing and selling commodities loaded at vertices of the tour. It is shown that the problem reduces to the metric traveling salesman problem. We present polynomial-time approximation algorithms with proven performance guarantees for solving some variants of the problem corresponding to different loading schemes. We also identify special cases where our algorithms find either optimal or asymptotically optimal solutions. (C) 2002 Elsevier B.V. All rights reserved.
Let P and Q be two simple polygons in the plane of total complexity n, each of which can be decomposed into at most k convex parts. We present a (1 - epsilon )-approximation algorithm, for finding the translation of Q...
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Let P and Q be two simple polygons in the plane of total complexity n, each of which can be decomposed into at most k convex parts. We present a (1 - epsilon )-approximation algorithm, for finding the translation of Q, which maximizes its area of overlap with P. Our algorithm runs in O (cn) time, where c is a constant that depends only on k and e. This suggests that for polygons that are "close" to being convex, the problem can be solved (approximately), in near linear time.
We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph G that ad...
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We investigate problems addressing combined connectivity augmentation and orientations settings. We give a polynomial-time 6-approximation algorithm for finding a minimum cost subgraph of an undirected graph G that admits an orientation covering a nonnegative crossing G-supermodular demand function, as defined by Frank [J. Comb. Theory Ser. B, 28 (1980), pp. 251-261]. An important example is (k, t)-edge-connectivity, a common generalization of global and rooted edge-connectivity. Our algorithm is based on a nonstandard application of the iterative rounding method. We observe that the standard linear program with cut constraints is not amenable and use an alternative linear program with partition and copartition constraints instead. The proof requires a new type of uncrossing technique on partitions and copartitions. We also consider the problem setting when the cost of an edge can be different for the two possible orientations. The problem becomes substantially more difficult already for the simpler requirement of k-edge-connectivity. Khanna, Naor, and Shepherd [SIAM J. Discrete Math., 19 (2005), pp. 245-257] showed that the integrality gap of the natural linear program is at most 4 when k = 1 and conjectured that it is constant for all fixed k. We disprove this conjecture by showing an Omega(vertical bar V vertical bar) integrality gap even when k = 2.
This paper considers a joint multi-graph inference and clustering problem for simultaneous inference of node centrality and association of graph signals with their graphs. We study a mixture model of filtered low pass...
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This paper considers a joint multi-graph inference and clustering problem for simultaneous inference of node centrality and association of graph signals with their graphs. We study a mixture model of filtered low pass graph signals with excitation driven by a sparse matrix. While the mixture model is motivated from practical scenarios, it presents significant challenges to prior graph learning methods. As a remedy, we consider an inference problem focusing on the node centrality of graphs. We design an expectation-maximization (EM) algorithm with a unique low-rank plus sparse prior derived from low pass signal property. We propose a novel online EM algorithm for inference from streaming data. As an example, we extend the online algorithm to detect if the signals are generated from an abnormal graph. We show that the proposed algorithms converge to a stationary point of the maximum-a-posterior (MAP) problem. Numerical experiments support our analysis.
It is of central interest in information theory to determine whether a given vector in the entropy space is an almost entropic vector. This problem can be answered if all the information inequalities are known, but th...
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It is of central interest in information theory to determine whether a given vector in the entropy space is an almost entropic vector. This problem can be answered if all the information inequalities are known, but this is an extremely challenging problem. On the other hand, we can establish that a given vector is an entropy vector if we can show the existence of distribution such that the corresponding entropy vector is the same as the given vector. However, there is no known algorithm to solve this problem. Only for the simplest case of binary entropy vectors, an algorithm is known to solve this problem. In this paper, we present a recursive algorithm to determine whether a given vector is a quasi-uniform entropy vector and, if it is, to return a consistent quasi-uniform distribution. We also present two applications of the recursive procedure: (i) to generate all quasi-uniform distributions motivated by the problem of finding the smallest quasi-uniform distribution such that its entropy vector violates the well known Ingleton inequality and (ii) to obtain an entropy vector (not necessarily quasi-uniform) near to a target vector in the entropy space for random variables with given alphabet size.
This brief studies an energy management (EM) problem with unknown dynamics of consumer appliances. A two-level optimization model is established between the utility company and the consumers. In this model, the utilit...
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This brief studies an energy management (EM) problem with unknown dynamics of consumer appliances. A two-level optimization model is established between the utility company and the consumers. In this model, the utility company maximizes its profit by setting the electricity price, and the consumers respond to the price by regulating power usage to minimize their costs. The aforementioned process is performed in multiple stages. In each stage, the consumer response is formulated as a constrained optimization problem, which can be transformed into an unconstrained optimization problem using the penalty function method, and then an extremum seeking control (ESC) algorithm is developed to search for the quasi-optimal power consumption of the consumers. The ESC algorithm has noncontinuous first and second derivatives with respect to the variables. We propose an approximation method to make the ESC algorithm continuous and prove that the algorithm is semiglobally practically asymptotically (SPA) stable. After the consumer response in the same stage, the utility company updates the electricity price by the particle swarm optimization (PSO) algorithm. Then, we give an EM algorithm that integrates the ESC with PSO. In simulations, the algorithm is applied to achieve EM of heating, ventilation, and air conditioning (HVAC) systems, and the results show that the algorithm can converge to a neighborhood of the optimal solution and reduce the peak load and daily load.
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