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382 MS-FAP MS-FAP is the most studied FCA problem For this problem, analytic techniques have been provided by many researchers and lower bounds have been tested extensively on the Philadelphia distances Heuristic methods also have been developed but they seem to be less accurate in providing optimal solutions in all cases; more difficult benchmark instances are necessary to distinguish among the heuristics The first heuristics were proposed in the 1970s and 1980s [5, 50, 59] Box [5] proposed a simple iterative technique based on a ranking of the channel requirements of various cells in descending order of assignment difficulty This is a measure of how hard it is to find a compatible frequency to satisfy a given channel requirement The order is changed when a denial occurs, and channels are assigned to each cell based on the assignment difficulty during each iteration.

Three color transmission standards exist:

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Zoellner and Beall [59] proposed a technique examining cochannel interference that assigns channels using a frequency-exhaustive or requirement-exhaustive strategy Moreover, Siravajan et al [50] developed a collection of techniques based on the previous approaches and examined their performance on 13 Philadelphia instances Hurley et al [25] described a software system called FASoft that operates as a planning tool for frequency assignment and proposed possible heuristics like tabu search, simulated annealing, and genetic algorithms based on Philadelphia instances Valenzuela et al [56] applied also a GA and tested their model on eight Philadelphia instances In three cases, the optimal solution was found In the framework of the CALMA project, all heuristics performed equally and found the optimal solution An application of the tabu search is discussed in Tiourine et al [54].

Remark The uniform distribution is a stationary distribution of P if and only if the probability transition matrix is doubly stochastic (see Problem 4.1). 4. The conditional entropy H (Xn |X1 ) increases with n for a stationary Markov process. If the Markov process is stationary, H (Xn ) is constant. So the entropy is nonincreasing. However, we will prove that H (Xn |X1 ) increases with n. Thus, the conditional uncertainty of the future increases. We give two alternative proofs of this result. First, we use the properties of entropy, H (Xn |X1 ) H (Xn |X1 , X2 ) (conditioning reduces entropy) (4.50) = H (Xn |X2 ) (by Markovity) = H (Xn 1 |X1 ) (by stationarity). (4.51) (4.52)

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Kim and Kim [29] proposed an efficient two-phase optimization procedure for the MSFAP based on the notion of frequency reuse patterns Their heuristic was tested on randomly generated instances Finally, Wang and Rushforth [57], described several channel assignment algorithms based on local search techniques Experiments showed that in.

Positioning could also be useful for the end of day reports of our nurse. She has to send her conclusions and the results of some analyses of her patients to the hospital or to the doctor. This transmission could also be achieved more ef ciently using positioning; when driving back home and passing in front of the hospital, a secured transmission link is established that allows the downloading of her reports. Similarly, when passing in the vicinity of some doctors of ces, she can automatically send the corresponding reports. Moreover, if she passes close to someone who is a member of the hospital administration that is in charge of receiving the reports, such a transfer can be carried out. Of course, this requires secured transmission and veri cations in order to avoid loss of reports or multiple transmissions.