38715917
Perfect Matchings of Generalized Polyomino Graphs
30935891
K-coverable polyhex graphs
32766485
Accelerating convergence in the Fermat-Weber location problem
This paper presents a simple procedure for accelerating convergence in a generalized Fermat-Weber problem with l"p distances. The main idea is to multiply the predetermined step size of the Weiszfeld algorithm by a factor which is a function of the parameter p. The form of this function is derived from the local convergence properties of the iterative sequence. Computational results are obtained which demonstrate that the total number of iterations to meet a given stopping criterion will be reduced substantially by the new step size, with the most dramatic results being observed for values of p close to 1.
412842
Location problems with costs being sums of powers of euclidean distances
The Cooper problem of minimizing the sum of weighted powers of the Euclidean distances is further studied. The practical significance of this problem is that instead of the Weber problem where the weighted sum of the Euclidean distances is minimized, here economies and diseconomies of scale are allowed for, which results in a problem of minimizing the sum of weighted powers of the Euclidean distances. The original Cooper solution has been a modification of the Weiszfeld method for the Weber problem; it can be shown to be a steepest descent method with a step size determined by an expression depending on the weights and distances, which is not optimal in any sense. In the present work, the matter of the best step size to be taken is investigated. It is shown that multiplying the step size given by Cooper by 2n where n is the power of the Euclidean distances, improves the iterative process substantially. For the cases with n≥l considered by Cooper, namely 1≤n≤3, the number of steps needed to reach a certain termination criterion is reduced. For higher values of n, the original Cooper step size is usually too large and there is no convergence. With the present amended method, the problem can be solved, using an appropriate normalization, even for powers of 100 and more. A semi-intuitive proof for this step size is given as well as numerical examples of solutions with n = 1,10 and 100. The method can easily be extended to location problems in three (and more) dimensions.
3158206
Live updating operating systems using virtualization
Many critical IT infrastructures require non-disruptive operations. However, the operating systems thereon are far from perfect that patches and upgrades are frequently applied, in order to close vulnerabilities, add new features and enhance performance. To mitigate the loss of availability, such operating systems need to provide features such as live update through which patches and upgrades can be applied without having to stop and reboot the operating system. Unfortunately, most current live updating approaches cannot be easily applied to existing operating systems: some are tightly bound to specific design approaches (e.g. object-oriented); others can only be used under particular circumstances (e.g. quiescence states).In this paper, we propose using virtualization to provide the live update capability. The proposed approach allows a broad range of patches and upgrades to be applied at any time without the requirement of a quiescence state. Moreover, such approach shares good portability for its OS-transparency and is suitable for inclusion in general virtualization systems. We present a working prototype, LUCOS, which supports live update capability on Linux running on Xen virtual machine monitor. To demonstrate the applicability of our approach, we use real-life kernel patches from Linux kernel 2.6.10 to Linux kernel 2.6.11, and apply some of those kernel patches on the fly. Performance measurements show that our implementation incurs negligible performance overhead: a less than 1% performance degradation compared to a Xen-Linux. The time to apply a patch is also very minimal.
6760399
On fixed input distributions for noncoherent communication over high-SNR Rayleigh-fading channels
It is well known that independent and identically distributed Gaussian inputs, scaled appropriately based on the signal-to-noise ratio (SNR), achieve capacity on the additive white Gaussian noise (AWGN) channel at all values of SNR. In this correspondence, we consider the question of whether such good input distributions exist for frequency-nonselective Rayleigh-fading channels, assuming that neither the transmitter nor the receiver has a priori knowledge of the fading coefficients. In this noncoherent regime, for a Gauss-Markov model of the fading channel, we obtain explicit mutual information bounds for the Gaussian input distribution. The fact that Gaussian input generates bounded mutual information motivates the search for better choices of fixed input distributions for high-rate transmission over rapidly varying channels. Necessary and sufficient conditions are derived for characterizing such distributions for the worst case scenario of memoryless fading, using the criterion that the mutual information is unbounded as the SNR gets large. Examples of both discrete and continuous distributions that satisfy these conditions are given. A family of fixed input distributions with mutual information growth rate of O((loglogSNR)/sup 1-u/), u>0 are constructed. It is also proved that there does not exist a single fixed-input distribution that achieves the optimal mutual information growth rate of loglogSNR.
9829795
Poisson Generators on Mesh-Connected Computers with Multiple Broadcasting