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To construct this matrix dynamically, as packets arrive to the receiver, i i i they are added to the decoding matrix row by row (a row is < (g0 , g1 , g2 , i i , xi , . . ., xi ) >). The ith information vector Xi is said to be inno. . ., gn 1 ), (x0 1 l 1 vative if it increases the rank of the matrix. If a packet is not innovative, it is reduced to a row of all 0s by Gaussian elimination and is ignored. While performing Gaussian elimination, as soon as the matrix contains a row of the form < ei ,X>, the node knows that the original packet M i is equal to X (remember that we have de ned ei in Section 4.4.1 as a vector that includes all 0s but one single 1 in the ith position). 4.4.3 Applications In reference 19, network coding was proposed to allow ef cient communication in extreme networks that is, in delay-tolerant networks or, more generally, intermittently connected networks. According to the forwarding scheme described, nodes do not simply forward packets they overhear but send out information that is coded over the

when the wind blows through her hair, it looks almost alive,

The other two occurrences of her contain no adjacent occurrence of hair they clearly do not match The solution to the query, then, is the second line of the text: (1) Were it not for the AndQuery operation, we would not need to maintain a location vector for each operation However, because any derived query type can be an operand of an AndQuery, each must calculate and maintain not just the set of unique lines, but the line and column location pair For example, consider either of the following two queries:

fiery && ( hair || bird || potato ) fiery && ( ! burr )

The possibility of a NotQuery being an operand to an AndQuery means that we must create not simply a vector containing an entry for each line number, but a vector holding a location pair for each line and column within the text (We'll look at this again when we walk through the NotQuery eval() function in Section 175) One necessary data member, therefore, is the location vector associated with the evaluation of each operation We have the choice of declaring it as a member of each derived class or of declaring it as a member of the abstract Query base class that each derived class inherits The space required to represent the member is the same for both approaches By placing it in the common Query base class, we localize its initialization and access support This is what we have chosen to do Whether we choose to represent the set of unique line numbers (we'll call it the line solution set) as a data member or calculate it onfile:///F|/WinDDK/resources/CPPPrimer/c++primerhtm (809 / 1065) [2001-3-29 11:32:13]

q(p) q(p 1)

content of several packets they have received Simulation results show that this algorithm achieves the reliability and robustness of ooding at a small fraction of the overhead Two interesting topics have been discussed, namely generations and redundancy The solution for generation recognition which has been proposed in reference 19 j is as follows Let X(i) be the jth information vector that originates at the ith source j node Si Then a function f (X(i) ) determines which generation the packet belongs to j j and = {X(i) |f (X(i) ) = } is the set of all the source vectors of a generation Namely, the generation membership is determined through hashing over the sender address and the packet identi er A new hash function is generated whenever the matrix becomes too big.

the-fly each time we need it is an implementation decision We have chosen to calculate it on demand, then tuck its address away for later access It, too, is declared as a member of the abstract Query base class To display the set of matching lines, we need both the line solution set and the actual text file in which the lines are stored However, whereas each operation requires its own location vector, only a single, shared instance of the text file is necessary Therefore, we define it as a static data member of Query (The implementation of the display() function depends only on these two members) Here, then, is a first iteration of our Query abstract base class representation, but without declaring any constructors, destructor, or copy assignment operator as yet (we get to these in Section 174 and Section 176 respectively):