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Problem Suppose the problem involves an operation on a recursive data structure (such as a list, tree, or graph) that appears to require sequential processing How can operations on these data structures be performed in parallel Context Some problems with recursive data structures naturally use the divide and conquer strategy described in the Divide and Conquer pattern with its inherent potential for concurrency Other operations on these data structures, however, seem to have little if any potential for concurrency because it appears that the only way to solve the problem is to sequentially move through the data structure, computing a result at one element before moving on to the next Sometimes, however, it is possible to reshape the operations in a way that a program can operate concurrently on all elements of the data structure An example from [J92] illustrates the situation: Suppose we have a forest of rooted directed trees (defined by specifying, for each node, its immediate ancestor, with a root node's ancestor being itself) and want to compute, for each node in the forest, the root of the tree containing that node To do this in a sequential program, we would probably trace depth first through each tree from its root to its leaf nodes; as we visit each node, we have the needed information about the corresponding root Total running time of such a program for a forest of N nodes would be O(N) There is some potential for concurrency (operating on subtrees concurrently), but there is no obvious way to operate on all elements concurrently, because it appears that we cannot find the root for a particular node without knowing its parent's root However, a rethinking of the problem exposes additional concurrency: We first define for each node a "successor", which initially will be its parent and ultimately will be the root of the tree to which the node belongs We then calculate for each node its "successor's successor" or nodes one "hop" from F the root, this calculation does not change the value of its successor (because a root's parent is itself) For nodes at least two "hops" away from a root, this calculation makes the node's successor its parent's parent We repeat this calculation until it converges (that is, the values produced by one step are the same as those produced by the preceding step), at which point every node's successor is the desired value Fig 421 shows an example requiring three steps to converge At each step we can operate on all N nodes in the tree concurrently, and the algorithm converges in at most log N steps.

access to the specified remote address and port The designation is a misnomer, as UDP doesn't actually create a "connection" between one machine and another However, if this method is used, it causes exceptions to be thrown if an attempt is made to send packets to, or read packets from, any other host and port than those specified void disconnect() disconnects the DatagramSocket and removes any restrictions imposed on it by an earlier connect operation InetAddress getInetAddress() returns the remote address to which the socket is connected, or null if no such connection exists int getPort() returns the remote port to which the socket is connected, or 1 if no such connection exists InetAddress getLocalAddress() returns the local address to which the socket is bound int getLocalPort() returns the local port to which the socket is bound int getReceiveBufferSize() throws javanetSocketException returns the maximum buffer size used for incoming UDP packets int getSendBufferSize() throws javanetSocketException returns the maximum buffer size used for outgoing UDP packets int getSoTimeout() throws javanetSocketException returns the value of the timeout socket option This value is used to determine the number of milliseconds a read operation will block before throwing a javaioInterruptedIOException By default, this value will be zero, indicating that blocking I/O will be used void receive(DatagramPacket packet) throws javaioIOException reads a UDP packet and stores the contents in the specified packet The address and port

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Figure 421 Finding roots in a forest Solid lines represent the original parent-child relationships among nodes; dashed lines point from nodes to their successors

fields of the packet will be overwritten with the sender address and port fields, and the length field of the packet will contain the length of the original packet, which can be less than the size of the packet's byte-array If a timeout value hasn't been specified by using DatagramSocketsetSoTimeout(int duration), this method will block indefinitely If a timeout value has been specified, a javaioInterruptedIOException will be thrown if the time is exceeded void send(DatagramPacket packet) throws javaioIOException sends a UDP packet, represented by the specified packet parameter void setReceiveBufferSize(int length) throws javanet SocketException sets the maximum buffer size used for incoming UDP packets Whether the specified length will be adhered to is dependent on the operating system void setSendBufferSize(int length) throws javanetSocketException sets the maximum buffer size used for outgoing UDP packets Whether the specified length will be adhered to is dependent on the operating system void setSoTimeout(int duration) throws javanetSocket Exception sets the value of the timeout socket option This value is the number of milliseconds a read operation will block before throwing a javaioInterruptedIOException

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