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52
A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems: A Summary
 Research ReportRJ7493 (70008), IBM Almaden Research Center
, 1990
"... This note summarizes a report with the same title, where a study was carried out regarding a unified approach, proposed by Kojima, Mizuno and Yoshise, for interior point algorithms for the linear complementarily problem with a positive semidefinite matrix. This approach is extended to nonsymmetri ..."
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Cited by 143 (8 self)
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This note summarizes a report with the same title, where a study was carried out regarding a unified approach, proposed by Kojima, Mizuno and Yoshise, for interior point algorithms for the linear complementarily problem with a positive semidefinite matrix. This approach is extended to nonsymmetric matrices with nonnegative principal minors.
An O(log k) approximate mincut maxflow theorem and approximation algorithm
 SIAM J. Comput
, 1998
"... Abstract. It is shown that the minimum cut ratio is within a factor of O(log k) of the maximum concurrent flow for kcommodity flow instances with arbitrary capacities and demands. This improves upon the previously bestknown bound of O(log 2 k) and is existentially tight, up to a constant factor. A ..."
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Cited by 126 (6 self)
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Abstract. It is shown that the minimum cut ratio is within a factor of O(log k) of the maximum concurrent flow for kcommodity flow instances with arbitrary capacities and demands. This improves upon the previously bestknown bound of O(log 2 k) and is existentially tight, up to a constant factor. An algorithm for finding a cut with ratio within a factor of O(log k) of the maximum concurrent flow, and thus of the optimal mincut ratio, is presented.
Energyefficient target coverage in wireless sensor networks
 in IEEE Infocom
, 2005
"... Abstract — A critical aspect of applications with wireless sensor networks is network lifetime. Powerconstrained wireless sensor networks are usable as long as they can communicate sensed data to a processing node. Sensing and communications consume energy, therefore judicious power management and ..."
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Cited by 83 (2 self)
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Abstract — A critical aspect of applications with wireless sensor networks is network lifetime. Powerconstrained wireless sensor networks are usable as long as they can communicate sensed data to a processing node. Sensing and communications consume energy, therefore judicious power management and sensor scheduling can effectively extend network lifetime. To cover a set of targets with known locations when ground access in the remote area is prohibited, one solution is to deploy the sensors remotely, from an aircraft. The lack of precise sensor placement is compensated by a large sensor population deployed in the drop zone, that would improve the probability of target coverage. The data collected from the sensors is sent to a central node (e.g. cluster head) for processing. In this paper we propose an efficient method to extend the sensor network life time by organizing the sensors into a maximal number of set covers that are activated successively. Only the sensors from the current active set are responsible for monitoring all targets and for transmitting the collected data, while all other nodes are in a lowenergy sleep mode. By allowing sensors to participate in multiple sets, our problem formulation increases the network lifetime compared with related work [2], that has the additional requirements of sensor sets being disjoint and operating equal time intervals. In this paper we model the solution as the maximum set covers problem and design two heuristics that efficiently compute the sets, using linear programming and a greedy approach. Simulation results are presented to verify our approaches.
SelfScaled Cones and InteriorPoint Methods in Nonlinear Programming
 Working Paper, CORE, Catholic University of Louvain, LouvainlaNeuve
, 1994
"... : This paper provides a theoretical foundation for efficient interiorpoint algorithms for nonlinear programming problems expressed in conic form, when the cone and its associated barrier are selfscaled. For such problems we devise longstep and symmetric primaldual methods. Because of the special ..."
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Cited by 28 (2 self)
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: This paper provides a theoretical foundation for efficient interiorpoint algorithms for nonlinear programming problems expressed in conic form, when the cone and its associated barrier are selfscaled. For such problems we devise longstep and symmetric primaldual methods. Because of the special properties of these cones and barriers, our algorithms can take steps that go typically a large fraction of the way to the boundary of the feasible region, rather than being confined to a ball of unit radius in the local norm defined by the Hessian of the barrier. Key words: Nonlinear Programming, conical form, interior point algorithms, selfconcordant barrier, selfscaled cone, selfscaled barrier, pathfollowing algorithms, potentialreduction algorithms. AMS 1980 subject classification. Primary: 90C05, 90C25, 65Y20. CORE, Catholic University of Louvain, LouvainlaNeuve, Belgium. Email: nesterov@core.ucl.ac.be. Part of this work was done while the author was visiting the Cornell C...
The Many Facets of Linear Programming
, 2000
"... . We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex, ellipsoid, interiorpoint, and other methods. Key words. linear programming  history  simplex method  ellipsoid method  interiorpoint methods 1. Introduction A ..."
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Cited by 26 (1 self)
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. We examine the history of linear programming from computational, geometric, and complexity points of view, looking at simplex, ellipsoid, interiorpoint, and other methods. Key words. linear programming  history  simplex method  ellipsoid method  interiorpoint methods 1. Introduction At the last Mathematical Programming Symposium in Lausanne, we celebrated the 50th anniversary of the simplex method. Here, we are at or close to several other anniversaries relating to linear programming: the sixtieth of Kantorovich's 1939 paper on "Mathematical Methods in the Organization and Planning of Production" (and the fortieth of its appearance in the Western literature) [55]; the fiftieth of the historic 0th Mathematical Programming Symposium that took place in Chicago in 1949 on Activity Analysis of Production and Allocation [64]; the fortyfifth of Frisch's suggestion of the logarithmic barrier function for linear programming [37]; the twentyfifth of the awarding of the 1975 Nobe...
On connected multiple point coverage in wireless sensor networks
 Journal of Wireless Information Networks
, 2006
"... Abstract — We consider a wireless sensor network consisting of a set of sensors deployed randomly. A point in the monitored area is covered if it is within the sensing range of a sensor. In some applications, when the network is sufficiently dense, area coverage can be approximated by guaranteeing ..."
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Cited by 24 (0 self)
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Abstract — We consider a wireless sensor network consisting of a set of sensors deployed randomly. A point in the monitored area is covered if it is within the sensing range of a sensor. In some applications, when the network is sufficiently dense, area coverage can be approximated by guaranteeing point coverage. In this case, all the points of wireless devices could be used to represent the whole area, and the working sensors are supposed to cover all the sensors. Many applications related to security and reliability require guaranteed kcoverage of the area at all times. In this paper, we formalize the k(Connected) Coverage Set (kCCS/kCS) problems, develop a linear programming algorithm, and design two nonglobal solutions for them. Some theoretical analysis is also provided followed by simulation results. Index Terms — Coverage problem, linear programming, localized algorithms, reliability, wireless sensor networks.
InfeasibleInteriorPoint PrimalDual PotentialReduction Algorithms For Linear Programming
 SIAM Journal on Optimization
, 1995
"... . In this paper, we propose primaldual potentialreduction algorithms which can start from an infeasible interior point. We first describe two such algorithms and show that both are polynomialtime bounded. One of the algorithms decreases the TanabeToddYe primaldual potential function by a const ..."
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Cited by 20 (4 self)
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. In this paper, we propose primaldual potentialreduction algorithms which can start from an infeasible interior point. We first describe two such algorithms and show that both are polynomialtime bounded. One of the algorithms decreases the TanabeToddYe primaldual potential function by a constant at each iteration under the condition that the duality gap decreases by at most the same ratio as the infeasibility. The other reduces a new potential function, which has one more term in the TanabeToddYe potential function, by a fixed constant at each iteration without any other conditions on the step size. Finally, we describe modifications of these methods (incorporating centering steps) which dramatically decrease their computational complexity. Our algorithms also extend to the case of monotone linear complementarity problems. Key words. Polynomial Time, Linear Programming, PrimalDual, InfeasibleInteriorPoint Algorithm, Potential Function. AMS subject classifications. 90C05, ...
Solving Sparse Semidefinite Programs Using the Dual Scaling Algorithm with an Iterative Solver
, 2000
"... Recently, the dualscaling interiorpoint algorithm has been used to solve largescale semidefinite programs arisen from discrete optimization, since it better exploits the sparsity structure of the problems than several other interiorpoint methods, while retain the same polynomial time complexity. ..."
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Cited by 17 (0 self)
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Recently, the dualscaling interiorpoint algorithm has been used to solve largescale semidefinite programs arisen from discrete optimization, since it better exploits the sparsity structure of the problems than several other interiorpoint methods, while retain the same polynomial time complexity. However, solving a linear system of a fully dense Gram matrix in each iteration of the algorithm becomes the timebottleneck of computational eciency. To overcome this diculty, we have tested using an iterative method, the conjugate gradient method with a simple preconditioner, to solve the linear system for a prescribed accuracy. In this report, we report computational results of solving semidenite programs with dimension up to 20,000, which show that the iterative method could save computation time upto 25 times of using the directed Cholesky factorization solver. Key words. Semidenite program, dualscaling algorithm, conjugate gradient method, precondition. This work is partially ...
Design and Performance of Parallel and Distributed Approximation Algorithms for Maxcut
, 1995
"... We develop and experiment with a new parallel algorithm to approximate the maximum weight cut in a weighted undirected graph. Our implementation starts with the recent (serial) algorithm of Goemans and Williamson for this problem. We consider several different versions of this algorithm, varying the ..."
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Cited by 17 (0 self)
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We develop and experiment with a new parallel algorithm to approximate the maximum weight cut in a weighted undirected graph. Our implementation starts with the recent (serial) algorithm of Goemans and Williamson for this problem. We consider several different versions of this algorithm, varying the interiorpoint part of the algorithm in order to optimize the parallel efficiency of our method. Our work aims for an efficient, practical formulation of the algorithm with closeto optimal parallelization. We analyze our parallel algorithm in the LogP model and predict linear speedup for a wide range of the parameters. We have implemented the algorithm using the message passing interface (MPI) and run it on several parallel machines. In particular, we present performance measurements on the IBM SP2, the Connection Machine CM5, and a cluster of workstations. We observe that the measured speedups are predicted well by our analysis in the LogP model. Finally, we test our implementation on s...