|
Cardinal Optimization Inc. |
The market for real-time location-based services is quickly expanding and is estimated to reach $1.26 billion in 2011. Many localization applications require accuracy and coverage that are greater than simple triangulation or trilateration approaches can deliver. Even GPS-based localization is insufficiently accurate in some applications; and of course, it is ineffective in obstructed environments or ultra-low-power deployments. An alternative approach is to utilize distances not just to nearby base stations or anchors but also to nearby peers to improve localization accuracy. Yet even for small peer to peer networks, determining nodes' locations accurately and efficiently has been a difficult computational problem. A suite of high-performance algorithms has been developed at Stanford University to estimate node positions for wireless sensor networks. These algorithms are also applicable to WiFi networks, cell phone networks, RFID networks, and public safety networks. The algorithms are capable of estimating node positions in static, dynamic, and distributed networks of arbitrary size. These algorithms help achieve the speed necessary for large real-time network applications without sacrificing accuracy in the estimated locations.
Advantages:
Region partition and routing software finds numerous real industrial applications. It utilizes two phases of optimization algorithms. The first phase partitions the interested area into sub-regions according to specific objectives; the second phase applies optimization techniques to find optimal route for each region with given criteria and constraints. A software demo is given [here].
The PageRank eigenvector problem involves a square system Ax = b in which x is naturally nonnegative and somewhat sparse (depending on b). We seek an approximate x that is nonnegative and extremely sparse. We experiment with an active-set optimization method designed for the dual of the BPDN (Basis Persuit Denoising) problem, and find that it tends to extract the important elements of x in a greedy fashion.
The method explores using Basis Persuit Denoising to find Sparse solutions for Nonnegative Matrix Factorization. It is in particularly useful for large clustering applications.