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and convey the location/tracking information periodically or on-demand to data sinks. Each type of node has its own battery power (and hence transmission radius), computational capacity, and memory. Credible research was conducted in the literature only for the unit-graph model, while other models are sporadically mentioned, without many results. One example is fuzzy unit graph, used in [22] to improve routing with guaranteed delivery [23]. In this model, there exist two transmission radii, r and R. Two nodes always communicate if their distance is r, never communicate of their distance if !R, and may or may not communicate otherwise. The unit-graph model is ideal in the sense that the probability of receiving a packet between two nodes does not, in reality, suddenly change from 1 to 0 when nodes move from distance R 2 1 to R 1 for a very small 1. There exist few articles that consider a more realistic physical layer, but the rst one to formalize the communication model is ref. [24]. They applied the log normal shadow fading model to represent a realistic physical layer to derive the probability p(x) for receiving a packet successfully as a function of distance x between two nodes, as shown in Figure 10.2. The transmission radius R is de ned in ref. [23] as the distance at which p(R) 0.5. Then p(x) is approximated reasonably accurately by P(x) 1 2 (x/R)nb/2 for x , R, and ((2R 2 x)/R)nb/2 otherwise, where b is the power attenuation factor (between 2 and 6), and n depends on packet length L (e.g., n 2 for L 120). Two nodes are considered neighbors if the distance x between them is such that p(x) ! w, where w is a threshold parameter (for example, when w 0.05, then x % 1.4R).

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The term R(Y j / X j ) determines the probability that at time instant j, the symbol Y j is the output of the channel if the symbol X j was input to that channel. This will happen with a transition probability P(y j /x j ) that the input symbol x j converts into the output symbol y j . A decoder for this Markov process has to estimate the MAP probability of states and outputs n of the discrete hidden Markov source by observing the output sequence Y1 = {Y1 , Y2 , . . . , Yn }. This means that it should calculate the probabilities

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The approximation ratio of P_Greedy is min( , n1/2) [26, 22] on arbitrary graphs, and 13 on unit disk graphs [18] Aside from P_Greedy, a variety of centralized approximation algorithms have been proposed for broadcast scheduling These algorithms can be placed into three general categories, using a classification adapted from [11]: 1 Traditional algorithms that preorder the nodes according to a specified criterion, and then color the nodes in a greedy fashion according to that ordering A representative of such methods is Static_min_deg_last [11] In this method, the nodes are placed into descending order according to their degrees The nodes are then greedily colored according to that ordering The running time is O(n min(n, 2)) on arbitrary graphs and O(n log n + n ) on unit disk graphs The algorithm is -approximate on arbitrary graphs, and 13-approximate on unit disk graphs [18] 2.

A common MythTV problem when running within the de facto standard MythTV desktop environment, KDE, is that when you exit playback of a movie, your remote quits working. That s because KDE shifts focus to the Kicker (the panel at the bottom of the screen) for some reason, rather than to the MythTV window, so your remote control is now trying to work on the Kicker, and does nothing. One possible fix is to change to a different window manager, but that s a fair amount of work for such a trivial issue. The easy fix is to change KDE s window focus behavior, so that you make focus follow the mouse. This is a bit goofy for people who are trying to use the system as a normal computer, but it works well if you dump the cursor in the middle of the screen, because when MythVideo (MPlayer or xine) exits, focus will return to MythTV, and your remote keeps working. You can change window focus behavior by opening Control Center (off the menu button at the bottom left of the Kicker), navigating to Desktop Window Behavior, changing the focus policy to Focus Follows Mouse, and clicking Apply (see Figure 15-7).

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