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ALGORITHM 4. Calculate the Set of Maximal Independent Sets M Require: is a n n matrix where n = number of nodes. [i][j] = 1 if i can hear node j. Else [i][j] = 0. Require: N is an array of all the nodes. {// L denotes the number of iterations we attempt to compute unique independent sets.} {// M is the set if all MICS} Initialize M to empty set for i = 1 to L do Randomize the ordering of N S = {N[1]} {// S denotes a maximal independent set being computed} for i = 2 to N.size() do src N[i] for j = 1 to S.size() do if [src][S[j]] == 1 then Break the for loop i end if end for Add src to to independent set S end for {// At this point, S will be one of the maximal independent sets} if S is not present in M then Add the maximal independent set S to M end if end for return M

The semantics are uniform Each test is guaranteed to be implemented in the same manner The function can be reused rather than rewritten for other applications

There is, however, one serious drawback to making min() a function: calling the function is slower than directly evaluating the conditional operator The two arguments must be copied, machine registers must be saved, and the program must branch to a new location The handwritten conditional operator is simply faster Inline functions provide a solution A function specified as inline is expanded "in line" at each point in the program in which it is invoked For example,

int minVal2 = min( i, j );

int minVal2 = i < j i : j;

remainder(n 1..0)

The computation of maximal independent sets plays an important role in the analysis of CSMA protocols [31, 57 59], as well as routing protocols [49]. The problem is NP-hard, and approximation techniques are often used for practical purposes. A simple way of approximating the maximal independent sets of nodes that can concurrently transmit under the Protocol Model of interference is given in Algorithm 4. The model is validated by observing the interactions in a simulated environment. The results show that the model captures a vast majority of the interactions. Two or more links initiating at the same instant of time without the knowledge of each other accounts for a miniature fraction of the packet losses, which is not captured by the model in reference 31. In the IEEE 802.11 [19] MAC protocol, a packet loss is observed when the sender does not receive a CTS for the RTS (which is called as RTS timeout), or if the ACK packet is not received for the DATA (an ACK timeout). In Figure 7.6a, the formulation is validated against simulation results to see if the model captures such losses. It was seen that less than 3% of the packet losses occurred between different MICS and thus were not captured by the model. Accordingly, truly concurrent transmissions are rare, and most collisions occur due to the failure of the MAC protocol to prevent interfering sources from concurrent transmissions. This result supports the use of the

The run-time overhead of making min() a function is thus removed min() is declared inline by specifying the inline keyword before the function's return type in the function declaration or definition:

inline int min( int v1, int v2 ) { /* */ }

Note, however, that the inline specification is only a recommendation to the compiler The compiler may choose to ignore this recommendation, because the function declared inline is not a good candidate for expansion at the point of call A recursive function, such as rgcd(), for example, cannot be completely expanded at the point of call (although its first invocation can) A 1,200-line function is also likely not to be expanded at the point of call In general, the inline mechanism is meant to optimize small, straightline, frequently called functions It is of primary importance in the support of information hiding in the design of abstract data types, such as the IntArray class introduced in Section 23 with its size() inline member function An inline function definition must be visible for the compiler to be able to inline a function at the point of the call Unlike a non-inline function, an inline function must be defined in every text file in which the inline function is called Of course, the definitions of the inline function that appear in the different files that compose a program must be the same For a program made of two files computeC and drawC, a programmer must not define the inline function min() to mean one thing in computeC and something else in drawC If the two definitions are not the same, the program has undefined behavior: it is uncertain which of the many different definitions the compiler will use as the definition to call for non-inlined function calls, and the program may not

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The iostream library supports in-memory operations on string objects The ostringstream class inserts characters into a string The istringstream class reads characters from a string object, and the stringstream class can be used to support both reading and writing To use a string stream, the associated header file must be included:

4 2.5 x 10

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