44474419
On the complexity of approximating a KKT point of quadratic programming
We present a potential reduction algorithm to approximate a Karush—Kuhn—Tucker (KKT) point of general quadratic programming (QP). We show that the algorithm is a fully polynomial-time approximation scheme, and its running-time dependency on accuracy ε ∈ (0, 1) is O((l/ε) log(l/ε) log(log(l/ε))), compared to the previously best-known result O((l/ε)2). Furthermore, the limit of the KKT point satisfies the second-order necessary optimality condition of being a local minimizer. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
9107374
Market equilibria for homothetic, quasi-concave utilities and economies of scale in production
Eisenberg and Gale (1959) gave a convex program for computing market equilibrium for Fisher's model for linear utility functions, and Eisenberg (1961) generalized this to concave homogeneous functions of degree one. We further generalize to:1. Homothetic, quasi-concave utilities. This also helps extend Eisenberg's result to concave homogeneous functions of arbitrary degree.2. We introduce the notion of a trading cone which enables us to compute market equilibrium in the presence of economies of scale in production provided differential pricing is allowed. Applications to network pricing are provided.
6954893
How Partial Knowledge Helps to Solve Linear Programs
We present results on how partial knowledge helps to solve linear programs. In particular, if a linear system,Ax=bandx?0, has an interior feasible point, then we show that finding a feasible point to this system can be done inO(n2.5c(A)) iterations by the layered interior-point method, and each iteration solves a least-squares problem, wherenis the dimension of vectorxandc(A) is the condition number of matrixAdefined by Vavasis and Ye. This complexity bound is reduced by a factornfrom that when this property does not exists. We also present a result for solving the problem using a little strong knowledge.
37608022
Improved Combinatorial Approximation Algorithms for the k-Level Facility Location Problem
In this paper we present improved combinatorial approximation algorithms for the k-level facility location problem. First, by modifying the path reduction developed in [2], we obtain a combinatorial algorithm with a performance factor of 3.27 for any k ≥ 2, thus improving the previous bound of 4.56. Then we develop another combinatorial algorithm that has a better performance guarantee and uses the first algorithm as a subroutine. The latter algorithm can be recursively implemented and achieves a guarantee factor h(k), where h(k) is strictly less than 3.27 for any k and tends to 3.27 as k goes to ∞. The values of h(k) can be easily computed with an arbitrary accuracy: h(2) ≅ 2.4211, h(3) ≅ 2.8446, h(4) ≅ 3.0565, h(5) ≅ 3.1678 and so on. Thus, for the cases of k = 2 and k = 3the second combinatorial algorithm ensures an approximation factor significantly better than 3, which is currently the best approximation ratio for the k-level problem provided by the non-combinatorial algorithm due to Aardal, Chudak, and Shmoys [1].
206798229
On affine scaling algorithms for nonconvex quadratic programming
We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a “hard” problem, we show that the problem with an ellipsoidal constraint is “easy”. When the “hard” QP is solved by successively solving the “easy” QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.
5857931
On Solving Coverage Problems in a Wireless Sensor Network Using Voronoi Diagrams
Owing to numerous potential applications, wireless sensor networks have been the focus of a lot of research efforts lately. In this note we study one fundamental issue in such networks, namely the coverage problem, in which we would like to determine whether a region of interest is sufficiently covered by a given set of sensors. This problem is motivated by monitoring applications in sensor networks, as well as robustness concerns and protocol requirements. We show that the coverage problem and some of its variants can be treated in a unified manner using suitable generalizations of the Voronoi diagram. As a result, we are able to give algorithms that have better runtimes than those proposed in previous works (see, e.g., [5, 6]). Our approach also yields efficient algorithms for coverage problems where the sensing region of a sensor is an ellipse or an L p –ball, where p≥1.
12123304
Integrating active information delivery and reuse repository systems
Although software reuse can improve both the quality and productivity of software development, it will not do so until software developers stop believing that it is not worth their effort to find a component matching their current problem. In addition, if the developers do not anticipate the existence of a given component, they will not even make an effort to find it in the first place.
Even the most sophisticated and powerful reuse repositories will not be effective if developers don't anticipate a certain component exists, or don't deem it worthwhile to seek for it. We argue that this crucial barrier to reuse is overcome by integrating active information delivery, which presents information without explicit queries from the user, and reuse repository systems. A prototype system, CodeBroker, illustrates this integration and raises several issues related to software reuse.
17936055
An Empirical User Study of an Active Reuse Repository System
This paper reports an empirical user study of an active reuse repository system. Instead of waiting passively for software developers to initiate the component location process with a well-defined reuse query, active reuse repository systems infer reuse queries from syntactic and semantic cues present in partially constructed programs in development environments, and proactively deliver components that match the inferred reuse queries. The reported empirical user study of an implemented active reuse repository system called CodeBroker shows that active repository systems promote reuse by motivating and enabling software developers to reuse components whose existence is not anticipated, and reducing the cost of reuse through the automation of the component location process.
6298363
Supporting reuse by delivering task-relevant and personalized information
Technical, cognitive, and social factors inhibit the widespread success of systematic software reuse. Our research is primarily concerned with the cognitive and social challenges faced by software developers: how to motivate them to reuse and how to reduce the difficulty of locating components from a large reuse repository. Our research has explored a new interaction style between software developers and reuse repository systems enabled by information delivery mechanisms. Instead of passively waiting for software developers to explore the reuse repository with explicit queries, information delivery autonomously locates and presents components by using the developers' partially written programs as implicit queries.We have designed, implemented, and evaluated a system called CodeBroker, which illustrates different techniques to address the essential challenges in information delivery: to make the delivered information relevant to the task-at-hand and personalized to the background knowledge of an individual developer. Empirical evaluations of CodeBroker show that information delivery is effective in promoting reuse.
18302519
Dynamic community: a new conceptual framework for supporting knowledge collaboration in software development
Software development is a knowledge intensive activity and software developers are knowledge workers. Knowledge needed for software development is often distributed among different developers. Supporting efficient knowledge collaboration and transfer is thus essential for software development organizations to remain competitive. This paper proposes a new theory /sub y/namic community to support knowledge collaboration and discusses its application in software development. Dynamic community integrates the traditional knowledge management approach in which knowledge is formalized and accumulated in knowledge repositories, and the community-based knowledge collaboration approach in which knowledge is transferred through informal community participation and human contacts. The dynamic community theory takes into full consideration individual knowledge workers' ever-changing needs for new knowledge as well as the role of social relationship of knowledge workers in effective knowledge collaboration. This paper introduces the dynamic community theory, a general system architecture of sociotechnical environments in support of dynamic community, and its application in software development.
1476378
Toward an understanding of the motivation of open source software developers
An Open Source Software (OSS) project is unlikely to be successful unless there is an accompanied community that provides the platform for developers and users to collaborate. Members of such communities are volunteers whose motivation to participate and contribute is of essential importance to the success of OSS projects. In this paper, we aim to create an understanding of what motivates people to participate in OSS communities. We theorize that learning is one of the motivational forces. Our theory is grounded in the learning theory of Legitimate Peripheral Participation, and is supported by analyzing the social structure of OSS communities and the co-evolution between OSS systems and communities. We also discuss practical implications of our theory for creating and maintaining sustainable OSS communities as well as for software engineering research and education.