A Privacy Conscious Bluetooth Infrastructure for Location Aware Computing

We present a low cost and easily deployed infrastructure for location aware computing that is built using standard Bluetooth® technologies and personal computers. Mobile devices are able to determine their location to room-level granularity with existing bluetooth technology, and to even greater resolution with the use of the recently adopted bluetooth 1.2 specification, all while maintaining complete anonymity. Various techniques for improving the speed and resolution of the system are described, along with their tradeoffs in privacy. The system is trivial to implement on a large scale – our network covering 5,000 square meters was deployed by a single student over the course of a few days at a cost of less than US$1,000.

Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems

We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the correlation between these measures and IPM iteration counts (solved using the software SDPT3) when the measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.896), and is a very good predictor of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations.