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Showing papers on "Approximation algorithm published in 2014"


Proceedings ArticleDOI
23 Jun 2014
TL;DR: Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.
Abstract: As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function. However, this greatly restricts its capability and flexibility in dealing with many practical problems (e.g., denoising), where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, where the singular values are assigned different weights. The solutions of the WNNM problem are analyzed under different weighting conditions. We then apply the proposed WNNM algorithm to image denoising by exploiting the image nonlocal self-similarity. Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.

1,876 citations


Journal ArticleDOI
TL;DR: It is shown that the optimal nearest neighbor algorithm and its parameters depend on the data set characteristics and an automated configuration procedure for finding the best algorithm to search a particular data set is described.
Abstract: For many computer vision and machine learning problems, large training sets are key for good performance. However, the most computationally expensive part of many computer vision and machine learning algorithms consists of finding nearest neighbor matches to high dimensional vectors that represent the training data. We propose new algorithms for approximate nearest neighbor matching and evaluate and compare them with previous algorithms. For matching high dimensional features, we find two algorithms to be the most efficient: the randomized k-d forest and a new algorithm proposed in this paper, the priority search k-means tree. We also propose a new algorithm for matching binary features by searching multiple hierarchical clustering trees and show it outperforms methods typically used in the literature. We show that the optimal nearest neighbor algorithm and its parameters depend on the data set characteristics and describe an automated configuration procedure for finding the best algorithm to search a particular data set. In order to scale to very large data sets that would otherwise not fit in the memory of a single machine, we propose a distributed nearest neighbor matching framework that can be used with any of the algorithms described in the paper. All this research has been released as an open source library called fast library for approximate nearest neighbors (FLANN), which has been incorporated into OpenCV and is now one of the most popular libraries for nearest neighbor matching.

1,339 citations


Journal ArticleDOI
13 May 2014
TL;DR: The techniques developed in this area are now finding applications in other areas including data structures for dynamic graphs, approximation algorithms, and distributed and parallel computation.
Abstract: Over the last decade, there has been considerable interest in designing algorithms for processing massive graphs in the data stream model. The original motivation was two-fold: a) in many applications, the dynamic graphs that arise are too large to be stored in the main memory of a single machine and b) considering graph problems yields new insights into the complexity of stream computation. However, the techniques developed in this area are now finding applications in other areas including data structures for dynamic graphs, approximation algorithms, and distributed and parallel computation. We survey the state-of-the-art results; identify general techniques; and highlight some simple algorithms that illustrate basic ideas.

405 citations


Journal ArticleDOI
TL;DR: Simulation results show that ADCMCST could greatly reduce the topology formation time, and achieve good approximation results; when the compression ratio is less than 70 %, the network lifetime of ADC MCST will be larger than that of energy driven tree construction.
Abstract: In this paper we propose an approximation algorithm, which is called ADCMCST (algorithm with the minimum number of child nodes when the depth is restricted), to construct a tree network for homogeneous wireless sensor network, so as to reduce and balance the payload of each node, and consequently prolong the network lifetime. When the monitoring node obtains the neighbor graph, ADCMCST tries to find a tree topology with a minimum number of child nodes, and then broadcast the topology to every node, and finally a tree network is constructed. Simulation results show that ADCMCST could greatly reduce the topology formation time, and achieve good approximation results; when the compression ratio is less than 70 %, the network lifetime of ADCMCST will be larger than that of energy driven tree construction.

348 citations


Journal ArticleDOI
TL;DR: In this article, a joint routing and caching problem aiming to maximize the fraction of content requests served locally by the deployed SBSs is formulated and a novel reduction to a variant of the facility location problem, which allows to exploit the rich literature of it, to establish algorithms with approximation guarantees for the problem.
Abstract: Small cells constitute a promising solution for managing the mobile data growth that has overwhelmed network operators Local caching of popular content items at the small cell base stations (SBSs) has been proposed to decrease the costly transmissions from the macrocell base stations without requiring high capacity backhaul links for connecting the SBSs with the core network However, the caching policy design is a challenging problem especially if one considers realistic parameters such as the bandwidth capacity constraints of the SBSs that can be reached in congested urban areas We consider such a scenario and formulate the joint routing and caching problem aiming to maximize the fraction of content requests served locally by the deployed SBSs This is an NP-hard problem and, hence, we cannot obtain an optimal solution Thus, we present a novel reduction to a variant of the facility location problem, which allows us to exploit the rich literature of it, to establish algorithms with approximation guarantees for our problem Although the reduction does not ensure tight enough bounds in general, extensive numerical results reveal a near-optimal performance that is even up to 38% better compared to conventional caching schemes using realistic system settings

275 citations


Journal ArticleDOI
TL;DR: This work introduces incremental mechanisms for three representative information entropies and develops a group incremental rough feature selection algorithm based on information entropy that aims to find the new feature subset in a much shorter time when multiple objects are added to a decision table.
Abstract: Many real data increase dynamically in size. This phenomenon occurs in several fields including economics, population studies, and medical research. As an effective and efficient mechanism to deal with such data, incremental technique has been proposed in the literature and attracted much attention, which stimulates the result in this paper. When a group of objects are added to a decision table, we first introduce incremental mechanisms for three representative information entropies and then develop a group incremental rough feature selection algorithm based on information entropy. When multiple objects are added to a decision table, the algorithm aims to find the new feature subset in a much shorter time. Experiments have been carried out on eight UCI data sets and the experimental results show that the algorithm is effective and efficient.

264 citations


Proceedings ArticleDOI
18 Oct 2014
TL;DR: It is proved that sufficient progress would imply a breakthrough on one of five major open problems in the theory of algorithms, including dynamic versions of bipartite perfect matching, bipartites maximum weight matching, single source reachability, single sources shortest paths, strong connectivity, subgraph connectivity, diameter approximation and some nongraph problems.
Abstract: We consider several well-studied problems in dynamic algorithms and prove that sufficient progress on any of them would imply a breakthrough on one of five major open problems in the theory of algorithms: 1) Is the 3SUM problem on n numbers in O(n2 -- aepsi;) time for some aepsi; > 0? 2) Can one determine the satisfiability of a CNF formula on n variables and poly n clauses in O((2 -- aepsi;)npolyn) time for some aepsi; > 0? 3) Is the All Pairs Shortest Paths problem for graphs on n vertices in O(n3 -- aepsi;) time for some aepsi; > 0? 4) Is there a linear time algorithm that detects whether a given graph contains a triangle? 5) Is there an O(n3 -- aepsi;) time combinatorial algorithm for n × n Boolean matrix multiplication? The problems we consider include dynamic versions of bipartite perfect matching, bipartite maximum weight matching, single source reachability, single source shortest paths, strong connectivity, subgraph connectivity, diameter approximation and some nongraph problems such as Pagh's problem defined in a recent paper by pa#x0103;traa#x015F;cu [STOC 2010].

249 citations


Proceedings ArticleDOI
08 Jul 2014
TL;DR: A pricing mechanism based on bargaining theory is designed, in which the price of each task is determined by the performing cost and market demand (i.e., the number of mobile users who intend to perform the task).
Abstract: Crowdsensing offers an efficient approach to meet the demand in large scale sensing applications In crowdsensing, it is of great interest to find the optimal task allocation, which is challenging since sensing tasks with different requirements of quality of sensing are typically associated with specific locations and mobile users are constrained by time budgets We show that the allocation problem is NP hard We then focus on approximation algorithms, and devise an efficient local ratio based algorithm (LRBA) Our analysis shows that the approximation ratio of the aggregate rewards obtained by the optimal allocation to those by LRBA is 5 This reveals that LRBA is efficient, since a lower (but not tight) bound on the approximation ratio is 4 We also discuss about how to decide the fair prices of sensing tasks to provide incentives since mobile users tend to decline the tasks with low incentives We design a pricing mechanism based on bargaining theory, in which the price of each task is determined by the performing cost and market demand (ie, the number of mobile users who intend to perform the task) Extensive simulation results are provided to demonstrate the advantages of our proposed scheme

249 citations


Journal ArticleDOI
TL;DR: In this paper, the problem of maximizing a nonnegative submodular set function over a ground set subject to a variety of packing-type constraints including (multiple) matroid constraints, knapsack constraints, and their intersections was studied.
Abstract: We consider the problem of maximizing a nonnegative submodular set function $f:2^N \rightarrow {\mathbb R}_+$ over a ground set $N$ subject to a variety of packing-type constraints including (multiple) matroid constraints, knapsack constraints, and their intersections. In this paper we develop a general framework that allows us to derive a number of new results, in particular, when $f$ may be a nonmonotone function. Our algorithms are based on (approximately) maximizing the multilinear extension $F$ of $f$ over a polytope $P$ that represents the constraints, and then effectively rounding the fractional solution. Although this approach has been used quite successfully, it has been limited in some important ways. We overcome these limitations as follows. First, we give constant factor approximation algorithms to maximize $F$ over a downward-closed polytope $P$ described by an efficient separation oracle. Previously this was known only for monotone functions. For nonmonotone functions, a constant factor was ...

237 citations


Journal ArticleDOI
TL;DR: In this article, a single UAV routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot is considered, and an approximation algorithm for the problem is developed.
Abstract: We consider a single Unmanned Aerial Vehicle (UAV) routing problem where there are multiple depots and the vehicle is allowed to refuel at any depot. The objective of the problem is to find a path for the UAV such that each target is visited at least once by the vehicle, the fuel constraint is never violated along the path for the UAV, and the total fuel required by the UAV is a minimum. We develop an approximation algorithm for the problem, and propose fast construction and improvement heuristics to solve the same. Computational results show that solutions whose costs are on an average within 1.4% of the optimum can be obtained relatively fast for the problem involving five depots and 25 targets.

217 citations


Journal ArticleDOI
TL;DR: In this paper, the authors use graphical methods to study defending mechanisms against false-data injection attacks on power system state estimation and propose both exact and reduced-complexity approximation algorithms.
Abstract: The normal operation of power system relies on accurate state estimation that faithfully reflects the physical aspects of the electrical power grids. However, recent research shows that carefully synthesized false-data injection attacks can bypass the security system and introduce arbitrary errors to state estimates. In this paper, we use graphical methods to study defending mechanisms against false-data injection attacks on power system state estimation. By securing carefully selected meter measurements, no false data injection attack can be launched to compromise any set of state variables. We characterize the optimal protection problem, which protects the state variables with minimum number of measurements, as a variant Steiner tree problem in a graph. Based on the graphical characterization, we propose both exact and reduced-complexity approximation algorithms. In particular, we show that the proposed tree-pruning based approximation algorithm significantly reduces computational complexity, while yielding negligible performance degradation compared with the optimal algorithms. The advantageous performance of the proposed defending mechanisms is verified in IEEE standard power system testcases.

Journal ArticleDOI
TL;DR: In this article, the authors proposed FrameSense, a greedy algorithm for the selection of optimal sensor locations, where the core cost function is the frame potential, a scalar property of matrices that measures the orthogonality of its rows.
Abstract: A classic problem is the estimation of a set of parameters from measurements collected by only a few sensors. The number of sensors is often limited by physical or economical constraints and their placement is of fundamental importance to obtain accurate estimates. Unfortunately, the selection of the optimal sensor locations is intrinsically combinatorial and the available approximation algorithms are not guaranteed to generate good solutions in all cases of interest. We propose FrameSense, a greedy algorithm for the selection of optimal sensor locations. The core cost function of the algorithm is the frame potential, a scalar property of matrices that measures the orthogonality of its rows. Notably, FrameSense is the first algorithm that is near-optimal in terms of mean square error, meaning that its solution is always guaranteed to be close to the optimal one. Moreover, we show with an extensive set of numerical experiments that FrameSense achieves state-of-the-art performance while having the lowest computational cost, when compared to other greedy methods.

Proceedings ArticleDOI
18 Oct 2014
TL;DR: It is shown that the Fréchet distance cannot be computed in strongly subquadratic time, i.e., in time O(n2-δ) for any delta > 0.001-approximation, which means that finding faster algorithms is as hard as finding faster CNF-SAT algorithms, and the existence of a strongly subaquadratic algorithm can be considered unlikely.
Abstract: The Frechet distance is a well-studied and very popular measure of similarity of two curves. Many variants and extensions have been studied since Alt and Godau introduced this measure to computational geometry in 1991. Their original algorithm to compute the Frechet distance of two polygonal curves with n vertices has a runtime of O(n^2 log n). More than 20 years later, the state of the art algorithms for most variants still take time more than O(n2 / log n), but no matching lower bounds are known, not even under reasonable complexity theoretic assumptions. To obtain a conditional lower bound, in this paper we assume the Strong Exponential Time Hypothesis or, more precisely, that there is no O*((2-adelta;)N) algorithm for CNF-SAT for any delta > 0. Under this assumption we show that the Frechet distance cannot be computed in strongly subquadratic time, i.e., in time O(n2-adelta;) for any delta > 0. This means that finding faster algorithms for the Frechet distance is as hard as finding faster CNF-SAT algorithms, and the existence of a strongly subquadratic algorithm can be considered unlikely. Our result holds for both the continuous and the discrete Frechet distance. We extend the main result in various directions. Based on the same assumption we (1) show non-existence of a strongly subquadratic 1.001-approximation, (2) present tight lower bounds in case the numbers of vertices of the two curves are imbalanced, and (3) examine realistic input assumptions (c-packed curves).

Posted Content
TL;DR: In this paper, the Gauss-Seidel (GS) method was used to iteratively realize the MMSE algorithm without the complicated matrix inversion, and a diagonal-approximate initial solution to the GS method was proposed to accelerate the convergence rate and reduce the complexity.
Abstract: For uplink large-scale MIMO systems, minimum mean square error (MMSE) algorithm is near-optimal but involves matrix inversion with high complexity. In this paper, we propose to exploit the Gauss-Seidel (GS) method to iteratively realize the MMSE algorithm without the complicated matrix inversion. To further accelerate the convergence rate and reduce the complexity, we propose a diagonal-approximate initial solution to the GS method, which is much closer to the final solution than the traditional zero-vector initial solution. We also propose a approximated method to compute log-likelihood ratios (LLRs) for soft channel decoding with a negligible performance loss. The analysis shows that the proposed GS-based algorithm can reduce the computational complexity from O(K^3) to O(K^2), where K is the number of users. Simulation results verify that the proposed algorithm outperforms the recently proposed Neumann series approximation algorithm, and achieves the near-optimal performance of the classical MMSE algorithm with a small number of iterations.

Journal ArticleDOI
TL;DR: In this paper, the authors obtained a polynomial-time algorithm with approximation ratio of 7.5 for the minimum T-tour problem with approximation guarantee of 4.3.
Abstract: We prove new results for approximating the graph-TSP and some related problems. We obtain polynomial-time algorithms with improved approximation guarantees. For the graph-TSP itself, we improve the approximation ratio to 7=5. For a generalization, the minimum T-tour problem, we obtain the first nontrivial approximation algorithm, with ratio 3=2. This contains the s-t-path graph-TSP as a special case. Our approximation guarantee for finding a smallest 2-edge-connected spanning subgraph is 4=3. The key new ingredient of all our algorithms is a special kind of ear-decomposition optimized using forest representations of hypergraphs. The same methods also provide the lower bounds (arising from LP relaxations) that we use to deduce the approximation ratios.

Proceedings ArticleDOI
16 Jun 2014
TL;DR: This work represents the first online combinatorial auction designed in the cloud computing paradigm, which is general and expressive enough to both optimize system efficiency across the temporal domain instead of at an isolated time point, and model dynamic provisioning of heterogeneous Virtual Machine (VM) types in practice.
Abstract: Auction mechanisms have recently attracted substantial attention as an efficient approach to pricing and resource allocation in cloud computing. This work, to the authors' knowledge, represents the first online combinatorial auction designed in the cloud computing paradigm, which is general and expressive enough to both (a) optimize system efficiency across the temporal domain instead of at an isolated time point, and (b) model dynamic provisioning of heterogeneous Virtual Machine (VM) types in practice. The final result is an online auction framework that is truthful, computationally efficient, and guarantees a competitive ratio ~ e+ 1 over e-1 ~ 3.30 in social welfare in typical scenarios. The framework consists of three main steps: (1) a tailored primal-dual algorithm that decomposes the long-term optimization into a series of independent one-shot optimization problems, with an additive loss of 1 over e-1 in competitive ratio, (2) a randomized auction sub-framework that applies primal-dual optimization for translating a centralized co-operative social welfare approximation algorithm into an auction mechanism, retaining a similar approximation ratio while adding truthfulness, and (3) a primal-dual update plus dual fitting algorithm for approximating the one-shot optimization with a ratio λ close to e. The efficacy of the online auction framework is validated through theoretical analysis and trace-driven simulation studies. We are also in the hope that the framework, as well as its three independent modules, can be instructive in auction design for other related problems.

Journal ArticleDOI
TL;DR: This paper reconstructs the interference-plus-noise covariance matrix in a sparse way, instead of searching for an optimal diagonal loading factor for the sample covariance Matrix, to demonstrate that the performance of the proposed adaptive beamformer is almost always equal to the optimal value.

Journal ArticleDOI
TL;DR: The experimental analysis showed that the proposed GA with a new multi-parent crossover converges quickly to the optimal solution and thus exhibits a superior performance in comparison to other algorithms that also solved those problems.

Proceedings ArticleDOI
08 Jul 2014
TL;DR: This paper forms this problem as an (NP-hard) optimization problem and presents approximation algorithms for it and shows that practical use of these algorithms result in a significant reduction in forwarding table size, while having a small effect on the global objective.
Abstract: Software Defined Networks (SDNs) are becoming the leading technology behind many traffic engineering solutions, both for backbone and data-center networks, since it allows a central controller to globally plan the path of the flows according to the operator’s objective. Nevertheless, networking devices’ forwarding table is a limited and expensive resource (e.g., TCAM-based switches) which should thus be considered upon configuring the network. In this paper, we concentrate on satisfying global network objectives, such as maximum flow, in environments where the size of the forwarding table in network devices is limited. We formulate this problem as an (NP-hard) optimization problem and present approximation algorithms for it. We show through extensive simulations that practical use of our algorithms (both in Data Center and backbone scenarios) result in a significant reduction (factor 3) in forwarding table size, while having a small effect on the global objective (maximum flow).

Proceedings ArticleDOI
31 May 2014
TL;DR: The time complexity of approximating weighted (undirected) shortest paths on distributed networks with a O (log n) bandwidth restriction on edges is studied to find a sublinear-time algorithm with almost optimal solution.
Abstract: A distributed network is modeled by a graph having n nodes (processors) and diameter D. We study the time complexity of approximating weighted (undirected) shortest paths on distributed networks with a O (log n) bandwidth restriction on edges (the standard synchronous CONGEST model). The question whether approximation algorithms help speed up the shortest paths and distance computation (more precisely distance computation) was raised since at least 2004 by Elkin (SIGACT News 2004). The unweighted case of this problem is well-understood while its weighted counterpart is fundamental problem in the area of distributed approximation algorithms and remains widely open. We present new algorithms for computing both single-source shortest paths (SSSP) and all-pairs shortest paths (APSP) in the weighted case. Our main result is an algorithm for SSSP. Previous results are the classic O(n)-time Bellman-Ford algorithm and an O(n1/2+1/2k + D)-time (8k⌈log(k + 1)⌉ --1)-approximation algorithm, for any integer k ≥ 1, which follows from the result of Lenzen and Patt-Shamir (STOC 2013). (Note that Lenzen and Patt-Shamir in fact solve a harder problem, and we use O(·) to hide the O(poly log n) term.) We present an O (n1/2D1/4 + D)-time (1 + o(1))-approximation algorithm for SSSP. This algorithm is sublinear-time as long as D is sublinear, thus yielding a sublinear-time algorithm with almost optimal solution. When D is small, our running time matches the lower bound of Ω(n1/2 + D) by Das Sarma et al. (SICOMP 2012), which holds even when D=Θ(log n), up to a poly log n factor. As a by-product of our technique, we obtain a simple O (n)-time (1+ o(1))-approximation algorithm for APSP, improving the previous O(n)-time O(1)-approximation algorithm following from the results of Lenzen and Patt-Shamir. We also prove a matching lower bound. Our techniques also yield an O(n1/2) time algorithm on fully-connected networks, which guarantees an exact solution for SSSP and a (2+ o(1))-approximate solution for APSP. All our algorithms rely on two new simple tools: light-weight algorithm for bounded-hop SSSP and shortest-path diameter reduction via shortcuts. These tools might be of an independent interest and useful in designing other distributed algorithms.

Journal ArticleDOI
TL;DR: In this article, it was shown that the Douglas-Rachford splitting algorithm converges strongly to the projection of the starting point onto the intersection of two convex sets, and if the sum of the two subspaces is closed, then the convergence is linear with the rate being the cosine of the Friedrichs angle between the subspace.

Journal ArticleDOI
TL;DR: In this article, the authors showed that constraint satisfaction problems with bounded fractional hypertree width can be solved in polynomial time (provided that the tree decomposition is given in the input).
Abstract: Many important combinatorial problems can be modeled as constraint satisfaction problems. Hence, identifying polynomial-time solvable classes of constraint satisfaction problems has received a lot of attention. In this article, we are interested in structural properties that can make the problem tractable. So far, the largest structural class that is known to be polynomial-time solvable is the class of bounded hypertree width instances introduced by Gottlob et al. [2002]. Here we identify a new class of polynomial-time solvable instances: those having bounded fractional edge cover number. Combining hypertree width and fractional edge cover number, we then introduce the notion of fractional hypertree width. We prove that constraint satisfaction problems with bounded fractional hypertree width can be solved in polynomial time (provided that the tree decomposition is given in the input). Together with a recent approximation algorithm for finding such decompositions [Marx 2010], it follows that bounded fractional hypertree width is now the most generally known structural property that guarantees polynomial-time solvability.

Proceedings ArticleDOI
05 Jan 2014
TL;DR: Two algorithms are deterministic, and thus the first deterministic (2 -- e)-approximation algorithm for the diameter that takes subquadratic time in sparse graphs is presented.
Abstract: The diameter is a fundamental graph parameter and its computation is necessary in many applications. The fastest known way to compute the diameter exactly is to solve the All-Pairs Shortest Paths (APSP) problem.In the absence of fast algorithms, attempts were made to seek fast algorithms that approximate the diameter. In a seminal result Aingworth, Chekuri, Indyk and Motwani [SODA'96 and SICOMP'99] designed an algorithm that computes in O (n2 + m√n) time an estimate D for the diameter D in directed graphs with nonnegative edge weights, such that [EQUATION], where M is the maximum edge weight in the graph. In recent work, Roditty and Vassilevska W. [STOC 13] gave a Las Vegas algorithm that has the same approximation guarantee but improves the (expected) runtime to O (m√n). Roditty and Vassilevska W. also showed that unless the Strong Exponential Time Hypothesis fails, no O (n2-e) time algorithm for sparse unweighted undirected graphs can achieve an approximation ratio better than 3/2. Thus their algorithm is essentially tight for sparse unweighted graphs. For weighted graphs however, the approximation guarantee can be meaningless, as M can be arbitrarily large.In this paper we exhibit two algorithms that achieve a genuine 3/2-approximation for the diameter, one running in O (m3/2) time, and one running in O (mn2/3). time. Furthermore, our algorithms are deterministic, and thus we present the first deterministic (2 -- e)-approximation algorithm for the diameter that takes subquadratic time in sparse graphs.In addition, we address the question of obtaining an additive c-approximation for the diameter, i.e. an estimate D such that D -- c ≤ D ≤ D. An extremely simple O (mn1-e) time algorithm achieves an additive ne-approximation; no better results are known. We show that for any e > 0, getting an additive ne-approximation algorithm for the diameter running in O (n2-e) time for any δ > 2e would falsify the Strong Exponential Time Hypothesis. Thus the simple algorithm is probably essentially tight for sparse graphs, and moreover, obtaining a subquadratic time additive c-approximation for any constant c is unlikely.Finally, we consider the problem of computing the eccentricities of all vertices in an undirected graph, i.e. the largest distance from each vertex. Roditty and Vassilevska W. [STOC 13] show that in O (m√n) time, one can compute for each v e V in an undirected graph, an estimate e(v) for the eccentricity e (v) such that max{R, 2/3 · e(v)} ≤ e (v) ≤ min {D, 3/2 · e(v)} where R = minv e (v) is the radius of the graph. Here we improve the approximation guarantee by showing that a variant of the same algorithm can achieve estimates e' (v) with 3/5 · e (v) ≤ e' (v) ≤ e (v).

Proceedings ArticleDOI
24 Aug 2014
TL;DR: The problem of mining activity networks to identify interesting events, such as a big concert or a demonstration in a city, or a trending keyword in a user community in a social network is considered, using graph-theoretic formulations.
Abstract: With the fast growth of smart devices and social networks, a lot of computing systems collect data that record different types of activities. An important computational challenge is to analyze these data, extract patterns, and understand activity trends. We consider the problem of mining activity networks to identify interesting events, such as a big concert or a demonstration in a city, or a trending keyword in a user community in a social network.We define an event to be a subset of nodes in the network that are close to each other and have high activity levels. We formalize the problem of event detection using two graph-theoretic formulations. The first one captures the compactness of an event using the sum of distances among all pairs of the event nodes. We show that this formulation can be mapped to the maxcut problem, and thus, it can be solved by applying standard semidefinite programming techniques. The second formulation captures compactness using a minimum-distance tree. This formulation leads to the prize-collecting Steiner-tree problem, which we solve by adapting existing approximation algorithms. For the two problems we introduce, we also propose efficient and effective greedy approaches and we prove performance guarantees for one of them. We experiment with the proposed algorithms on real datasets from a public bicycling system and a geolocation-enabled social network dataset collected from twitter. The results show that our methods are able to detect meaningful events.

Proceedings ArticleDOI
01 Jan 2014
TL;DR: In this paper, the authors focus on the optimized placement of VMs to minimize the cost, the combination of N-cost and PM-cost, and prove it to be NP-hard.
Abstract: As tenants take networked virtual machines (VMs) as their requirements, effective placement of VMs is needed to reduce the network cost in cloud data centers. The cost is one of the major concerns for the cloud providers. In addition to the cost caused by network traffics (N-cost), the cost caused by the utilization of physical machines (PM-cost) is also non-negligible. In this paper, we focus on the optimized placement of VMs to minimize the cost, the combination of N-cost and PM-cost. We define N-cost by various functions, according to different communication models. We formulate the placement problem, and prove it to be NP-hard. We investigate the problem from two aspects. Firstly, we put a special emphasis on minimizing the N- cost with fixed PM-cost. For the case that tenants request the same amount of VMs, we present optimal algorithms under various definitions of N-cost. For the case that tenants require different numbers of VMs, we propose an approximation algorithm. Also, a greedy algorithm is implemented as the baseline to evaluate the performance. Secondly, we study the general case of the VM placement problem, in which both N-cost and PM-cost are taken into account. We present an effective binary-search- based algorithm to determine how many PMs should be used, which makes a tradeoff between PM-cost and N-cost. For all of the algorithms, we conduct theoretical analysis and extensive simulations to evaluate their performance and efficiency.

Journal ArticleDOI
TL;DR: A novel 8-point DCT approximation that requires only 14 addition operations and no multiplications is introduced and is compared to state-of-the-art DCT approximations in terms of both algorithm complexity and peak signal-to-noise ratio.
Abstract: Video processing systems such as HEVC requiring low energy consumption needed for the multimedia market has lead to extensive development in fast algorithms for the efficient approximation of 2-D DCT transforms The DCT is employed in a multitude of compression standards due to its remarkable energy compaction properties Multiplier-free approximate DCT transforms have been proposed that offer superior compression performance at very low circuit complexity Such approximations can be realized in digital VLSI hardware using additions and subtractions only, leading to significant reductions in chip area and power consumption compared to conventional DCTs and integer transforms In this paper, we introduce a novel 8-point DCT approximation that requires only 14 addition operations and no multiplications The proposed transform possesses low computational complexity and is compared to state-of-the-art DCT approximations in terms of both algorithm complexity and peak signal-to-noise ratio The proposed DCT approximation is a candidate for reconfigurable video standards such as HEVC The proposed transform and several other DCT approximations are mapped to systolic-array digital architectures and physically realized as digital prototype circuits using FPGA technology and mapped to 45 nm CMOS technology

Journal ArticleDOI
Haipeng Dai1, Xiaobing Wu1, Guihai Chen1, Lijie Xu1, Shan Lin1 
TL;DR: This paper investigates the minimum MCs problem (MinMCP) for two-dimensional (2D) wireless rechargeable sensor networks (WRSNs) and proposes approximation algorithms for this problem and proves that MinMCP is NP-hard.

Journal ArticleDOI
TL;DR: A new prediction band is given by combining the idea of ‘conformal prediction’ with non‐parametric conditional density estimation and the proposed estimator, called COPS, always has a finite sample guarantee.
Abstract: Summary We study distribution-free, non-parametric prediction bands with a focus on their finite sample behaviour. First we investigate and develop different notions of finite sample coverage guarantees. Then we give a new prediction band by combining the idea of ‘conformal prediction’ with non-parametric conditional density estimation. The proposed estimator, called COPS (conformal optimized prediction set), always has a finite sample guarantee. Under regularity conditions the estimator converges to an oracle band at a minimax optimal rate. A fast approximation algorithm and a data-driven method for selecting the bandwidth are developed. The method is illustrated in simulated and real data examples.

Journal ArticleDOI
TL;DR: This work proposes and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex problems and combines these methods with dual decomposition and constraint tightening and applies this framework to linear model predictive control obtaining a suboptimal and feasible control scheme.
Abstract: We propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex problems. The complicating constraints are moved into the cost using the Lagrange multipliers. The dual problem is solved by inexact first-order methods based on approximate gradients for which we prove sublinear rate of convergence. In particular, we provide a complete rate analysis and estimates on the primal feasibility violation and primal and dual suboptimality of the generated approximate primal and dual solutions. Moreover, we solve approximately the inner problems with a linearly convergent parallel coordinate descent algorithm. Our analysis relies on the Lipschitz property of the dual function and inexact dual gradients. Further, we combine these methods with dual decomposition and constraint tightening and apply this framework to linear model predictive control obtaining a suboptimal and feasible control scheme.

Journal ArticleDOI
TL;DR: The experimental results indicate that the proposed methods improve multi-label classification accuracy and stability compared to the RAKEL algorithm and to other state-of-the-art algorithms.
Abstract: Ensemble methods have been shown to be an effective tool for solving multi-label classification tasks. In the RAndom k-labELsets (RAKEL) algorithm, each member of the ensemble is associated with a small randomly-selected subset of k labels. Then, a single label classifier is trained according to each combination of elements in the subset. In this paper we adopt a similar approach, however, instead of randomly choosing subsets, we select the minimum required subsets of k labels that cover all labels and meet additional constraints such as coverage of inter-label correlations. Construction of the cover is achieved by formulating the subset selection as a minimum set covering problem (SCP) and solving it by using approximation algorithms. Every cover needs only to be prepared once by offline algorithms. Once prepared, a cover may be applied to the classification of any given multi-label dataset whose properties conform with those of the cover. The contribution of this paper is two-fold. First, we introduce SCP as a general framework for constructing label covers while allowing the user to incorporate cover construction constraints. We demonstrate the effectiveness of this framework by proposing two construction constraints whose enforcement produces covers that improve the prediction performance of random selection by achieving better coverage of labels and inter-label correlations. Second, we provide theoretical bounds that quantify the probabilities of random selection to produce covers that meet the proposed construction criteria. The experimental results indicate that the proposed methods improve multi-label classification accuracy and stability compared to the RAKEL algorithm and to other state-of-the-art algorithms.