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].
9510976
An interior point potential reduction algorithm for the linear complementarity problem
AbstractThe linear complementarity problem (LCP) can be viewed as the problem of minimizingxTy subject toy=Mx+q andx, y⩾0. We are interested in finding a point withxTy  0. The algorithm proceeds by iteratively reducing the potential function
$$f(x,y) = \rho \ln x^T y - \Sigma \ln x_j y_j ,$$
 where, for example,ρ=2n. The direction of movement in the original space can be viewed as follows. First, apply alinear scaling transformation to make the coordinates of the current point all equal to 1. Take a gradient step in the transformed space using the gradient of the transformed potential function, where the step size is either predetermined by the algorithm or decided by line search to minimize the value of the potential. Finally, map the point back to the original space.A bound on the worst-case performance of the algorithm depends on the parameterλ*=λ*(M, ε), which is defined as the minimum of the smallest eigenvalue of a matrix of the form
$$(I + Y^{ - 1} MX)(I + M^T Y^{ - 2} MX)^{ - 1} (I + XM^T Y^{ - 1} )$$
 whereX andY vary over the nonnegative diagonal matrices such thateTXYe ⩾ε andXjjYjj⩽n2. IfM is a P-matrix,λ* is positive and the algorithm solves the problem in polynomial time in terms of the input size, |log ε|, and 1/λ*. It is also shown that whenM is positive semi-definite, the choice ofρ = 2n+
$$\sqrt {2n} $$
 yields a polynomial-time algorithm. This covers the convex quadratic minimization problem.
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.
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.
12762926
Theory of semidefinite programming for Sensor Network Localization
AbstractWe analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore, we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient criterion for checking whether a given instance of the localization problem has a unique realization in
$$\mathcal{R}^2$$ using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will identify all strongly localizable sub-networks in the input network.
2615907
Stochastic Combinatorial Optimization with Controllable Risk Aversion Level
Due to their wide applicability and versatile modeling power, stochastic programming problems have received a lot of attention in many communities. In particular, there has been substantial recent interest in 2–stage stochastic combinatorial optimization problems. Two objectives have been considered in recent work: one sought to minimize the expected cost, and the other sought to minimize the worst–case cost. These two objectives represent two extremes in handling risk — the first trusts the average, and the second is obsessed with the worst case. In this paper, we interpolate between these two extremes by introducing an one–parameter family of functionals. These functionals arise naturally from a change of the underlying probability measure and incorporate an intuitive notion of risk. Although such a family has been used in the mathematical finance [11] and stochastic programming [13] literature before, its use in the context of approximation algorithms seems new. We show that under standard assumptions, our risk–adjusted objective can be efficiently treated by the Sample Average Approximation (SAA) method [9]. In particular, our result generalizes a recent sampling theorem by Charikar et al. [2], and it shows that it is possible to incorporate some degree of robustness even when the underlying probability distribution can only be accessed in a black–box fashion. We also show that when combined with known techniques (e.g. [4,14]), our result yields new approximation algorithms for many 2–stage stochastic combinatorial optimization problems under the risk–adjusted setting.
17341139
Context-aware browsing of large component repositories
The paper proposes a novel approach to locating software components from a large component repository: context-aware browsing. Without any explicit input from software developers, this approach automatically locates and presents a list of software components that could possibly be used in the current development situation. This automation of the component location process not only greatly reduces the search space of components so that software developers can easily browse and choose the desired components, but also enables software developers to use components whose existence they do not even anticipate. A software agent that supports context-aware browsing has been developed and evaluated.
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.
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.
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.