LINEAR PROGRAM Research Papers - Academia.edu (original) (raw)
This paper deals with approximating feedback sets in directed graphs. We consider two related problems: the weighted feedback vertex set (FVS) problem, and the weighted feedback edge set (FES) problem. In the {FVS} (resp. FES) problem,... more
This paper deals with approximating feedback sets in directed graphs. We consider two related problems: the weighted feedback vertex set (FVS) problem, and the weighted feedback edge set (FES) problem. In the {FVS} (resp. FES) problem, one is given a directed graph with weights (each of which is at least one) on the vertices (resp. edges), and is asked to find a subset of vertices (resp. edges) with minimum total weight that intersects every directed cycle in the graph. These problems are among the classical NP-hard problems and have many applications. We also consider a generalization of these problems: subset-fvs and subset-fes, in which the feedback set has to intersect only a subset of the directed cycles in the graph. This subset consists of all the cycles that go through a distinguished input subset of vertices and edges, denoted by X . This generalization is also NP-hard even when |X|=2 . We present approximation algorithms for the subset-fvs and subset-fes problems. The first algorithm we present achieves an approximation factor of O(log 2 |X|) . The second algorithm achieves an approximation factor of O(min{log τ * log log τ * , log n log log n)} , where τ * is the value of the optimum fractional solution of the problem at hand, and n is the number of vertices in the graph. We also define a multicut problem in a special type of directed networks which we call circular networks, and show that the subset-fes and subset-fvs problems are equivalent to this multicut problem. Another contribution of our paper is a combinatorial algorithm that computes a (1+ɛ) approximation to the fractional optimal feedback vertex set. Computing the approximate solution is much simpler and more efficient than general linear programming methods. All of our algorithms use this approximate solution.
The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations. Under this scenario, average and probabilistic... more
The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations. Under this scenario, average and probabilistic Quality of Service (QoS) measures are introduced to evaluate the performance of any control strategy, while a solution of the stochastic optimal power control is obtained through
Policy makers and other stakeholders concerned with regional rural development increasingly face the need for instruments that can improve transparency in the policy debate and that enhance understanding of opportunities for and... more
Policy makers and other stakeholders concerned with regional rural development increasingly face the need for instruments that can improve transparency in the policy debate and that enhance understanding of opportunities for and limitations to development. To this end, a methodology called SOLUS (Sustainable Options for Land Use) was developed by an interdisciplinary team of scientists over a 10-year period in the Atlantic Zone of Costa Rica. The main tools of SOLUS include a linear programming (LP) model, two expert systems that define technical coefficients for a large number of production activities, and a geographic information system (GIS). A five-step procedure was developed for GIS to spatially reference biophysical and economic parameters, to create input for the expert systems and the LP model, to store and spatially reference model output data, and to create maps of both model input and output data. SOLUS can be used to evaluate the potential effects of alternative policies and incentive structures on the performance of the agricultural sector. A number of practical applications demonstrate SOLUS's capability to quantify trade-offs between economic objectives (income, employment) and environmental sustainability (soil nutrient balances, pesticide use, greenhouse gas emissions). GIS-created maps visualize the spatial aspects of such trade-offs and indicate hotspots where local goals may conflict with regional goals.
Based on the MPS standard for linear programs, data conventions for the description of multistage stochastic linear programs were described by Birge et al. [3]. This paper proposes extensions to the so-called SMPS standard, in order to... more
Based on the MPS standard for linear programs, data conventions for the description of multistage stochastic linear programs were described by Birge et al. [3]. This paper proposes extensions to the so-called SMPS standard, in order to address known shortcomings and to extend the range of problems that can be expressed within the standard.
This paper shows that managerial questions are not answered satisfactorily with the mathematical interpretation of sensitivity analysis when the solution of a linear programing model is degenerate. Most of the commercially available... more
This paper shows that managerial questions are not answered satisfactorily with the mathematical interpretation of sensitivity analysis when the solution of a linear programing model is degenerate. Most of the commercially available software packages provide sensitivity results about the optimality of a basis and not about the optimality of the values of the decision variables. The misunderstanding of the shadow price and the validity range information provided by a simplex based computer program may lead to wrong decision with considerable financial losses and strategic consequences. The paper classifies the most important types of sensitivity information, graphically illustrates degeneracy, and demonstrates its effect on sensitivity analysis. A production planning example is provided to show the possibility of faulty production management decisions when sensitivity results are not understood correctly. Finally the recommendations for the users of linear programing models and for software developers are provided.
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,... more
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 k-coverage of the area at all times. In this paper, we formalize the k-(Connected) Coverage Set (k-CCS/k-CS) problems, develop a linear programming algorithm, and design two non-global solutions for them. Some theoretical analysis is also provided followed by simulation results.