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.
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.
13094296
Improved complexity results on solving real-number linear feasibility problems
We present complexity results on solving real-number standard linear programs LP(A,b,c), where the constraint matrix the right-hand-side vector and the objective coefficient vector are real. In particular, we present a two-layered interior-point method and show that LP(A,b,0), i.e., the linear feasibility problem Ax = b and x ≥ 0, can be solved in in O(n2.5c(A)) interior-point method iterations. Here 0 is the vector of all zeros and c(A) is the condition measure of matrix A defined in [25]. This complexity iteration bound is reduced by a factor n from that for general LP(A, b, c) in [25]. We also prove that the iteration bound will be further reduced to O(n1.5c(A)) for LP(A, 0, 0), i.e., for the homogeneous linear feasibility problem. These results are surprising since the classical view has been that linear feasibility would be as hard as linear programming.
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.
13990458
Approximation Algorithms for Metric Facility Location Problems
In this paper we present a 1.52-approximation algorithm for the metric uncapacitated facility location problem, and a 2-approximation algorithm for the metric capacitated facility location problem with soft capacities. Both these algorithms improve the best previously known approximation factor for the corresponding problem, and our soft-capacitated facility location algorithm achieves the integrality gap of the standard linear programming relaxation of the problem. Furthermore, we will show, using a result of Thorup, that our algorithms can be implemented in quasi-linear time.
359291
A 2-Approximation Algorithm for the Soft-Capacitated Facility Location Problem
This paper is divided into two parts. In the first part of this paper, we present a 2-approximation algorithm for the soft-capacitated facility location problem. This achieves the integrality gap of the natural LP relaxation of the problem. The algorithm is based on an improved analysis of an algorithm for the linear facility location problem, and a bifactor approximate-reduction from this problem to the soft-capacitated facility location problem. We will define and use the concept of bifactor approximate reductions to improve the approximation factor of several other variants of the facility location problem. In the second part of the paper, we present an alternative analysis of the authors’ 1.52-approximation algorithm for the uncapacitated facility location problem, using a single factor-revealing LP. This answers an open question of [16]Furthermore, this analysis, combined with a recent result of Thorup [21] shows that our algorithm can be implemented in quasi-linear time, achieving the best known approximation factor in the best possible running time.
10972009
On Approximating Complex Quadratic Optimization Problems via Semidefinite Programming Relaxations
In this paper we study semidefinite programming (SDP) models for a class of discrete and continuous quadratic optimization problems in the complex Hermitian form. These problems capture a class of well–known combinatorial optimization problems, as well as problems in control theory. For instance, they include Max–3–Cut where the Laplacian matrix is positive semidefinite (in particular, some of the edge weights can be negative). We present a generic algorithm and a unified analysis of the SDP relaxations which allow us to obtain good approximation guarantees for our models. Specifically, we give an $(k sin(\frac{\pi}{k}))^{2}/(4\pi)$ –approximation algorithm for the discrete problem where the decision variables are k–ary and the objective matrix is positive semidefinite. To the best of our knowledge, this is the first known approximation result for this family of problems. For the continuous problem where the objective matrix is positive semidefinite, we obtain the well–known π/4 result due to [2], and independently, [12]. However, our techniques simplify their analyses and provide a unified framework for treating these problems. In addition, we show for the first time that the integrality gap of the SDP relaxation is precisely π/4. We also show that the unified analysis can be used to obtain an O(1/log n)–approximation algorithm for the continuous problem in which the objective matrix is not positive semidefinite.