Browsing by Subject "Approximation algorithms"

Now showing 1 - 20 of 25

Open Access
Algebraic acceleration and regularization of the source reconstruction method with the recompressed adaptive cross approximation
(IEEE, 2014) Kazempour, Mahdi; Gürel, Levent
We present a compression algorithm to accelerate the solution of source reconstruction problems that are formulated with integral equations and defined on arbitrary three-dimensional surfaces. This compression technique benefits from the adaptive cross approximation (ACA) algorithm in the first step. A further error-controllable recompression is applied after the ACA. The numerical results illustrate the efficiency and accuracy of the proposed method. © 2014 IEEE.
Open Access
An algorithm and a core set result for the weighted euclidean one-center problem
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2009) Kumar, P.; Yıldırım, A. E.
Given a set A of m points in n-dimensional space with corresponding positive weights, the weighted Euclidean one-center problem, which is a generalization of the minimum enclosing ball problem, involves the computation of a point c A n that minimizes the maximum weighted Euclidean distance from c A to each point in A In this paper, given ε > 0, we propose and analyze an algorithm that computes a (1 + ε)-approximate solution to the weighted Euclidean one-center problem. Our algorithm explicitly constructs a small subset X ⊆ A, called an ε-core set of A, for which the optimal solution of the corresponding weighted Euclidean one-center problem is a close approximation to that of A. In addition, we establish that \X\ depends only on ε and on the ratio of the smallest and largest weights, but is independent of the number of points m and the dimension n. This result subsumes and generalizes the previously known core set results for the minimum enclosing ball problem. Our algorithm computes a (1 + ε)-approximate solution to the weighted Euclidean one-center problem for A in O(mn\X\) arithmetic operations. Our computational results indicate that the size of the ε-core set computed by the algorithm is, in general, significantly smaller than the theoretical worst-case estimate, which contributes to the efficiency of the algorithm, especially for large-scale instances. We shed some light on the possible reasons for this discrepancy between the theoretical estimate and the practical performance.
Open Access
An approximation algorithm for computing the visibility region of a point on a terrain and visibility testing
(IEEE, 2014-01) Alipour, S.; Ghodsi, M.; Güdükbay, Uğur; Golkari, M.
Given a terrain and a query point p on or above it, we want to count the number of triangles of terrain that are visible from p. We present an approximation algorithm to solve this problem. We implement the algorithm and then we run it on the real data sets. The experimental results show that our approximation solution is very close to the real solution and compare to the other similar works, the running time of our algorithm is better than their algorithm. The analysis of time complexity of algorithm is also presented. Also, we consider visibility testing problem, where the goal is to test whether p and a given triangle of train are visible or not. We propose an algorithm for this problem and show that the average running time of this algorithm will be the same as running time of the case where we want to test the visibility between two query point p and q.
Open Access
Çok kullanıcılı çok antenli sistemlerde iş birlikli iletim
(IEEE, 2008-04) Yazarel, Y. K.; Aktaş, Defne
Bu çalışmada işbirlikli, çok kullanıcılı, ve çok antenli bir haberleşme sisteminde telsiz erişim terminallerinin en iyi veri iletimi tekniğine ortaklaşa karar vermeleri problemini inceliyoruz. Burada pek çok çalışmadan farklı olarak kullanıcıların bireysel başarım hedefleri ve anten başına iletim gücü kısıtlamaları olduğu durumu ele alıyoruz. Önceki bir çalışmamızda bu kısıtlamalar altında en iyi sonucu bulan döngülü bir algoritma sunmuştuk. Ancak bu algoritma merkezi bir yapıda olduğu için tam anlamıyla dağıtılmış şekilde gerçeklenememektedir. Bununla birlikte basit yaklaşıklıklar kullanarak en iyiye yakın bir başarım sağlayan ve kısıtlı ve yerel veri iletimi ile gerçeklenebilecek etkin bir algoritma öneriyoruz.
Open Access
Computing minimum-volume enclosing axis-aligned ellipsoids
(Springer, 2008) Kumar, P.; Yıldırım, E. A.
Given a set of points S = {x1 ,..., xm}⊂ ℝn and ε>0, we propose and analyze an algorithm for the problem of computing a (1+ε)-approximation to the minimum-volume axis-aligned ellipsoid enclosing S. We establish that our algorithm is polynomial for fixed ε. In addition, the algorithm returns a small core set X ⊆ S, whose size is independent of the number of points m, with the property that the minimum-volume axis-aligned ellipsoid enclosing X is a good approximation of the minimum-volume axis-aligned ellipsoid enclosing S. Our computational results indicate that the algorithm exhibits significantly better performance than the theoretical worst-case complexity estimate.
Open Access
Effective preconditioners for large integral-equation problems
(IET, 2007-11) Malas, Tahir; Ergül, Özgür; Gürel, Levent
We consider effective preconditioning schemes for the iterative solution of integral-equation methods. For parallel implementations, the sparse approximate inverse or the iterative solution of the near-field system enables fast convergence up to certain problem sizes. However, for very large problems, the near-field matrix itself becomes too crude approximation to the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximation strategy to the multilevel fast multipole algorithm (MLFMA) to be used as a preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve targets with tens of millions of unknowns in a few hours.
Open Access
Heat transfer through dipolar coupling: Sympathetic cooling without contact
(American Physical Society, 2016) Renklioglu, B.; Tanatar, Bilal; Oktel, M. Ö.
We consider two parallel layers of dipolar ultracold Fermi gases at different temperatures and calculate the heat transfer between them. The effective interactions describing screening and correlation effects between the dipoles in a single layer are modeled within the Euler-Lagrange Fermi-hypernetted-chain approximation. The random-phase approximation is used for the interactions across the layers. We investigate the amount of transferred power between the layers as a function of the temperature difference. Energy transfer arises due to the long-range dipole-dipole interactions. A simple thermal model is established to investigate the feasibility of using the contactless sympathetic cooling of the ultracold polar atoms and molecules. Our calculations indicate that dipolar heat transfer is effective for typical polar molecule experiments and may be utilized as a cooling process.
Open Access
Identification and elimination of interior points for the minimum enclosing ball problem
(Society for Industrial and Applied Mathematics, 2008) Ahıpaşaoǧlu, S. D.; Yıldırım, E. A.
Given A := {a1,...,am} C ℝn, we consider the problem of reducing the input set for the computation of the minimum enclosing ball of A. In this note, given an approximate solution to the minimum enclosing ball problem, we propose a simple procedure to identify and eliminate points in.A that are guaranteed to lie in the interior of the minimum-radius ball enclosing A. Our computational results reveal that incorporating this procedure into two recent algorithms proposed by Yildirim lead to significant speed-ups in running times especially for randomly generated largescale problems. We also illustrate that the extra overhead due to the elimination procedure remains at an acceptable level for spherical or almost spherical input sets.
Open Access
Joint mixability of some integer matrices
(Elsevier B.V., 2016) Bellini, F.; Karaşan, O. E.; Pınar, M. Ç.
We study the problem of permuting each column of a given matrix to achieve minimum maximal row sum or maximum minimal row sum, a problem of interest in probability theory and quantitative finance where quantiles of a random variable expressed as the sum of several random variables with unknown dependence structure are estimated. If the minimum maximal row sum is equal to the maximum minimal row sum the matrix has been termed jointly mixable (see e.g. Haus (2015), Wang and Wang (2015), Wang et al. (2013)). We show that the lack of joint mixability (the joint mixability gap) is not significant, i.e., the gap between the minimum maximal row sum and the maximum minimal row sum is either zero or one for a class of integer matrices including binary and complete consecutive integers matrices. For integer matrices where all entries are drawn from a given set of discrete values, we show that the gap can be as large as the difference between the maximal and minimal elements of the discrete set. The aforementioned result also leads to a polynomial-time approximation algorithm for matrices with restricted domain. Computing the gap for a {0,1,2}-matrix is proved to be equivalent to finding column permutations minimizing the difference between the maximum and minimum row sums. A polynomial procedure for computing the optimum difference by solving the maximum flow problem on an appropriate graph is given. © 2016 Elsevier B.V. All rights reserved.
Open Access
A linearly convergent linear-time first-order algorithm for support vector classification with a core set result
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2011) Kumar, P.; Yıldırım, E. A.
We present a simple first-order approximation algorithm for the support vector classification problem. Given a pair of linearly separable data sets and. ε (0,1), the proposed algorithm computes a separating hyperplane whose margin is within a factor of (1-ε) of that of the maximum-margin separating hyperplane. We discuss how our algorithm can be extended to nonlinearly separable and inseparable data sets. The running time of our algorithm is linear in the number of data points and in 1/ε. In particular, the number of support vectors computed by the algorithm is bounded above by O(ζ/ε. for all sufficiently small ε >, where ζ is the square of the ratio of the distances between the farthest and closest pairs of points in the two data sets. Furthermore, we establish that our algorithm exhibits linear convergence. Our computational experiments, presented in the online supplement, reveal that the proposed algorithm performs quite well on standard data sets in comparison with other first-order algorithms. We adopt the real number model of computation in our analysis.
Open Access
Minimizing schedule length on identical parallel machines: an exact algorithm
(1991) Akyel, H. Cemal
The primary concern of this study is to investigate the combinatorial aspects of the single-stage identical parallel machine scheduling problem and to develop a computationally feasible branch and bound algorithm for its exact solution. Although there is a substantial amount of literature on this problem, most of the work in this area is on the development and performance analysis of approximation algorithms. The few optimizing algorithms proposed in the literature have major drawbacks from the computer implementation point of view. Even though the single-stage scheduling problem is known to be unary A/’P-hard, there is still a need to develop a computationally feasible optimizing algorithm that solves the problem in a reasonable time. Development of such an algorithm is necessary for solving the multi-stage parallel machine scheduling problems which are currently an almost untouched issue in the deterministic scheduling theory. In this study, a branch and bound algorithm for the single-stage identical parallel machine scheduling problem is proposed. Promising results were obtained in the empirical analysis of the performance of this algorithm. Furthermore, the procedure that is developed to determine tight bounds at a node of the enumeration tree, is an approximation algorithm that solves a special class of identical parallel machine scheduling problems of practical interest. This algorithm delivers a solution that is arbitrarily close to 4/3 times the optimum. To our knowledge this is the best result obtained for this problem so far.
Open Access
Minimum maximum-degree publish-subscribe overlay network design
(IEEE, 2011) Onus, Melih; Richa, A.W.
Designing an overlay network for publish/subscribe communication in a system where nodes may subscribe to many different topics of interest is of fundamental importance. For scalability and efficiency, it is important to keep the degree of the nodes in the publish/subscribe system low. It is only natural then to formalize the following problem: Given a collection of nodes and their topic subscriptions, connect the nodes into a graph that has least possible maximum degree in such a way that for each topic t, the graph induced by the nodes interested in t is connected. We present the first polynomial-time logarithmic approximation algorithm for this problem and prove an almost tight lower bound on the approximation ratio. Our experimental results show that our algorithm drastically improves the maximum degree of publish/subscribe overlay systems. We also propose a variation of the problem by enforcing that each topic-connected overlay network be of constant diameter while keeping the average degree low. We present three heuristics for this problem that guarantee that each topic-connected overlay network will be of diameter 2 and that aim at keeping the overall average node degree low. Our experimental results validate our algorithms, showing that our algorithms are able to achieve very low diameter without increasing the average degree by much. © 2011 IEEE.
Open Access
On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids
(Elsevier, 2007) Todd, M. J.; Yıldırım, E. A.
Given A {colon equals} { a1, ..., am } ⊂ Rd whose affine hull is Rd, we study the problems of computing an approximate rounding of the convex hull of A and an approximation to the minimum-volume enclosing ellipsoid of A. In the case of centrally symmetric sets, we first establish that Khachiyan's barycentric coordinate descent (BCD) method is exactly the polar of the deepest cut ellipsoid method using two-sided symmetric cuts. This observation gives further insight into the efficient implementation of the BCD method. We then propose a variant algorithm which computes an approximate rounding of the convex hull of A, and which can also be used to compute an approximation to the minimum-volume enclosing ellipsoid of A. Our algorithm is a modification of the algorithm of Kumar and Yi{dotless}ldi{dotless}ri{dotless}m, which combines Khachiyan's BCD method with a simple initialization scheme to achieve a slightly improved polynomial complexity result, and which returns a small "core set." We establish that our algorithm computes an approximate solution to the dual optimization formulation of the minimum-volume enclosing ellipsoid problem that satisfies a more complete set of approximate optimality conditions than either of the two previous algorithms. Furthermore, this added benefit is achieved without any increase in the improved asymptotic complexity bound of the algorithm of Kumar and Yi{dotless}ldi{dotless}ri{dotless}m or any increase in the bound on the size of the computed core set. In addition, the "dropping idea" used in our algorithm has the potential of computing smaller core sets in practice. We also discuss several possible variants of this dropping technique.
Open Access
On the minimum volume covering ellipsoid of ellipsoids
(Society for Industrial and Applied Mathematics, 2006) YIldırım, E. A.
Let S denote the convex hull of m full-dimensional ellipsoids in ℝn. Given ε > 0 and δ > 0, we study the problems of computing a (1 + ε)-approximation to the minimum volume covering ellipsoid of S and a (1 + δ)n-rounding of S. We extend the first-order algorithm of Kumar and Yildirim [J. Optim. Theory Appl., 126 (2005), pp. 1-21] that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in ℝn, which, in turn, is a modification of Khachiyan's algorithm [L. G. Khachiyan, Math. Oper. Res., 21 (1996), pp. 307-320]. Our algorithm can also compute a (1 + δ)n-rounding of 5. For fixed ε > 0 and δ > 0, we establish polynomial-time complexity results for the respective problems, each of which is linear in the number of ellipsoids m. In particular, our algorithm can approximate the minimum volume covering ellipsoid of S in asymptotically the same number of iterations as that required by the algorithm of Kumar and Yildirim to approximate the minimum volume covering ellipsoid of a set of m points. The main ingredient in our analysis is the extension of polynomial-time complexity of certain subroutines in the algorithm from a set of points to a set of ellipsoids. As a byproduct, our algorithm returns a finite "core" set χ ⊆ S with the property that the minimum volume covering ellipsoid of X provides a good approximation to the minimum volume covering ellipsoid of S. Furthermore, the size of the core set depends only on the dimension n and the approximation parameter ε, but not on the number of ellipsoids m. We also discuss the extent to which our algorithm can be used to compute an approximate minimum volume covering ellipsoid and an approximate n-rounding of the convex hull of other sets in ℝn. We adopt the real number model of computation in our analysis.
Open Access
Online Contextual Influence Maximization in social networks
(Institute of Electrical and Electronics Engineers Inc., 2017) Sarıtaç, Ömer; Karakurt, Altuğ; Tekin, Cem
In this paper, we propose the Online Contextual Influence Maximization Problem (OCIMP). In OCIMP, the learner faces a series of epochs in each of which a different influence campaign is run to promote a certain product in a given social network. In each epoch, the learner first distributes a limited number of free-samples of the product among a set of seed nodes in the social network. Then, the influence spread process takes place over the network, other users get influenced and purchase the product. The goal of the learner is to maximize the expected total number of influenced users over all epochs. We depart from the prior work in two aspects: (i) the learner does not know how the influence spreads over the network, i.e., it is unaware of the influence probabilities; (ii) influence probabilities depend on the context. We develop a learning algorithm for OCIMP, called Contextual Online INfluence maximization (COIN). COIN can use any approximation algorithm that solves the offline influence maximization problem as a subroutine to obtain the set of seed nodes in each epoch. When the influence probabilities are Hölder continuous functions of the context, we prove that COIN achieves sublinear regret with respect to an approximation oracle that knows the influence probabilities for all contexts. Moreover, our regret bound holds for any sequence of contexts. We also test the performance of COIN on several social networks, and show that it performs better than other methods. © 2016 IEEE.
Open Access
Online contextual influence maximization with costly observations
(IEEE, 2019-06) Sarıtaç, Anıl Ömer; Karakurt, Altuğ; Tekin, Cem
In the online contextual influence maximization problem with costly observations, the learner faces a series of epochs in each of which a different influence spread process takes place over a network. At the beginning of each epoch, the learner exogenously influences (activates) a set of seed nodes in the network. Then, the influence spread process takes place over the network, through which other nodes get influenced. The learner has the option to observe the spread of influence by paying an observation cost. The goal of the learner is to maximize its cumulative reward, which is defined as the expected total number of influenced nodes over all epochs minus the observation costs. We depart from the prior work in three aspects: 1) the learner does not know how the influence spreads over the network, i.e., it is unaware of the influence probabilities; 2) influence probabilities depend on the context; and 3) observing influence is costly. We consider two different influence observation settings: costly edge-level feedback, in which the learner freely observes the set of influenced nodes, but pays to observe the influence outcomes on the edges of the network; and costly node-level feedback, in which the learner pays to observe whether a node is influenced or not. Since the offline influence maximization problem itself is NP-hard, for these settings, we develop online learning algorithms that use an approximation algorithm as a subroutine to obtain the set of seed nodes in each epoch. When the influence probabilities are Hölder continuous functions of the context, we prove that these algorithms achieve sublinear regret (for any sequence of contexts) with respect to an approximation oracle that knows the influence probabilities for all contexts. Our numerical results on several networks illustrate that the proposed algorithms perform on par with the state-of-the-art methods even when the observations are cost free.
Open Access
Online solutions for scalable file server systems
(ACM, 2006) Tse, Savio S. H.
We propose three online algorithms for scalable file server systems. A scalable file server is expected to provide rather stable services while the numbers of users, tasks, and data volumes keep increasing. One of the purposes of parallel and distributed approaches is to achieve scalability. Sufficient hardware resources are essential for good services; however, a good coordination of them is also indispensable, as parallel and distributed resources need to complement the shortages of each other, and it falls on the shoulders of the algorithmic and architectural designs. In this paper, we address the load balancing problem in scalable file servers. The three online approximate algorithms proposed is for placing and deleting documents in a system of M distributed file servers located in a cluster in order to balance the loads and required storage spaces among all servers. In [7], we have proposed some algorithms without allowing re-allocation. In this paper, by paying the re-allocation cost, we have several improvements on some existing results. © 2006 ACM.
Open Access
Outer approximation algorithms for convex vector optimization problems
(Taylor and Francis Ltd., 2023-02-09) Keskin, İrem Nur; Ulus, Firdevs
In this study, we present a general framework of outer approximation algorithms to solve convex vector optimization problems, in which the Pascoletti-Serafini (PS) scalarization is solved iteratively. This scalarization finds the minimum ‘distance’ from a reference point, which is usually taken as a vertex of the current outer approximation, to the upper image through a given direction. We propose efficient methods to select the parameters (the reference point and direction vector) of the PS scalarization and analyse the effects of these on the overall performance of the algorithm. Different from the existing vertex selection rules from the literature, the proposed methods do not require solving additional single-objective optimization problems. Using some test problems, we conduct an extensive computational study where three different measures are set as the stopping criteria: the approximation error, the runtime, and the cardinality of the solution set. We observe that the proposed variants have satisfactory results, especially in terms of runtime compared to the existing variants from the literature. © 2023 Informa UK Limited, trading as Taylor & Francis Group.
Open Access
Parallel preconditioners for solutions of dense linear systems with tens of millions of unknowns
(2007-11) Malas, Tahir; Ergül, Özgür; Gürel, Levent
We propose novel parallel preconditioning schemes for the iterative solution of integral equation methods. In particular, we try to improve convergence rate of the ill-conditioned linear systems formulated by the electric-field integral equation, which is the only integral-equation formulation for targets having open surfaces. For moderate-size problems, iterative solution of the near-field system enables much faster convergence compared to the widely used sparse approximate inverse preconditioner. For larger systems, we propose an approximation strategy to the multilevel fast multipole algorithm (MLFMA) to be used as a preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve targets with tens of millions of unknowns, which are the largest problems ever reported in computational electromagnetics. ©2007 IEEE.
Open Access
Phase diagram and dynamics of Rydberg-dressed fermions in two dimensions
(American Physical Society, 2017) Khasseh, R.; Abedinpour, S. H.; Tanatar, Bilal
We investigate the ground-state properties and the collective modes of a two-dimensional two-component Rydberg-dressed Fermi liquid in the dipole-blockade regime. We find instability of the homogeneous system toward phase-separated and density ordered phases, using the Hartree-Fock and random-phase approximations, respectively. The spectral weight of collective density oscillations in the homogenous phase also signals the emergence of density-wave instability. We examine the effect of exchange hole on the density-wave instability and on the collective-mode dispersion using the Hubbard local-field factor.