17282210
An approximation algorithm for scheduling two parallel machines with capacity constraints
We consider the problem of scheduling n independent jobs on two identical parallel machines, with a limit on the number of jobs that can be assigned to each single machine, so as to minimize the total weighted completion time of the jobs. We study a semidefinite programming-based approximation algorithm for solving this problem and prove that the algorithm has a worst case ratio at most 1.1626.
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.
10134807
A semidefinite programming approach to tensegrity theory and realizability of graphs
Recently, Connelly and Sloughter [14] have introduced the notion of d-realizability of graphs and have, among other things, given a complete characterization of the class of 3-realizable graphs. However, their work has left open the question of finding an algorithm for realizing those graphs. In this paper, we resolve that question by showing that the semidefinite programming (SDP) approach of [11, 32] can be used for realizing 3-realizable graphs. Specifically, we use SDP duality theory to show that given a graph G and a set of lengths on its edges, the optimal dual multipliers of a certain SDP give rise to a proper equilibrium stress for some realization of G. Using this result and the techniques in [14, 31], we then obtain a polynomial time algorithm for (approximately) realizing 3-realizable graphs. Our results also establish a little-explored connection between SDP and tensegrity theories and allow us to derive some interesting properties of tensegrity frameworks.
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.
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.
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.
1677204
Personalizing Delivered Information in a Software Reuse Environment
Browsing- and querying-oriented schemes have long served as the principal techniques for software developers to locate software components from a component repository for reuse. Unfortunately, the problem remains that software developers simply will not actively search for components when they are unaware that they need components or that relevant components even exist. Thus, to assist software developers in making full use of large component repositories, information access need to be complemented by information delivery. Effective delivery of components calls for the personalization of the components to the task being performed and the knowledge of the user performing it.We have designed, implemented, and evaluated the CodeBroker system to support personalized component delivery to increase the usefulness of a Java software reuse environment.
17120633
Promoting Reuse with Active Reuse Repository Systems
Software component-based reuse is difficult for software developers to adopt because first they must know what components exist in a reuse repository and then they must know how to retrieve them easily. This paper describes the concept and implementation of active reuse repository systems that address the above two issues. Active reuse repository systems employ active information delivery mechanisms to deliver potentially reusable components that are relevant to the current development task. They can help software developers reuse components they did not even know existed. They can also greatly reduce the cost of component location because software developers need neither to specify reuse queries explicitly, nor to switch working contexts back and forth between development environments and reuse repository systems.
1538182
Information delivery in support of learning reusable software components on demand
An inherent dilemma exists in the design of high-functionality applications (such as repositories of reusable software components). In order to be useful, high-functionality applications have to provide a large number of features, creating huge learning problems for users. We address this dilemma by developing intelligent interfaces that support learning on demand by enabling users to learn new features when they are needed during work. We support learning on demand with information delivery by identifying learning opportunities of which users might not be aware. The challenging issues in implementing information delivery are discussed and techniques to address them are illustrated with the CodeBroker system. CodeBroker supports Java programmers in learning reusable software components in the context of their normal development environments and practice by proactively delivering task-relevant and personalized information. Evaluations of the system have shown its effectiveness in supporting learning on demand.
8137126
An active and adaptive reuse repository system
Although software reuse repository systems have been an active research area for more than a decade, one important aspect has not been given enough attention: if software developers make no attempt to reuse, repository systems offer no help and reuse will not happen. Active information delivery, which presents information without being given explicit queries can motivate software developers to reuse. Critical challenges for active delivery systems are the contextualization of delivered information to the development task, and the adaptation of the information to each developer. This paper discusses how to address these challenges and demonstrates the feasibility of implementation through a prototype system.