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In the previous sections, we discussed the DDBE Platform Requirements for any environment and any distributed processing environment. In this section, we will brie y discuss the remaining DDBE Platform Requirements some of which we will discuss again in s 15 19. The remaining DDBE Platform Requirements consider requirements that are especially important for distributed processing environments with distributed data. Once again, the Platform Requirements discussed in this section are not irrelevant to other environments, but they are also somewhat less important when there is no data in the environment. In Section 14.4.1 we consider the Architectural Security Requirements treating security as a DDBE architectural issue. Then, in Section 14.4.2, we will discuss the Database Connectivity Requirements here we will consider how the COSs in our environment connect to the local databases and other similar issues. Lastly, in Section 14.4.3, we will consider the Transaction Management Requirements these requirements focus on things like the level of distributed transaction support supplied by the DDBE Platform.

On the other hand, the derivative of the error-location polynomial is equal to (X ) = By replacing X with the root value jh , ( jh ) = So from the above equations, ejh = W ( jh ) ( jh )

The corollary follows from the prior proof by noting that in a graph of thickness , there is at least one node of degree not exceeding 6 1 [25]. The analysis in [14] establishes: Theorem 5 For q-inductive graphs, progressive_min_deg_last has an approximation ratio of 2q 1. Several classes of graphs, including graphs of bounded genus, are q-inductive. See [12] for additional information on q-inductive graphs. In regard to running times, it is shown in [24]: Theorem 6 For planar graphs, progressive_min_deg_last has a running time of O(n ). For arbitrary graphs of thickness , progressive_min_deg_last has a running time of O(n ). 16.4.3 A Better Ratio for Unit Disk Graphs Among the methods cited above, several are 13-approximate when applied to unit disk graphs. These ratios follow from a general result of [18] on the performance of greedy algorithms. The best approximation ratio relative to unit disk graphs belongs to the following algorithm (of the traditional greedy variety): Algorithm Continuous_color(G): Let u be an arbitrary node of G; L a list of the nodes of G sorted in increasing order of Euclidean distance to u; while L 0 do / Let v be the first node of L; Greedily color v and remove v from L; Theorem 7 For unit disk graphs, Continuous_color has an approximation ratio of seven.

hide5ws( hide5ws( hide5ws( hide5ws( // last 5 WS str_ptr+15 str_ptr+20 str_ptr+25 str_ptr+30 ); ); ); );

resource representations The primary Web protocol is HTTP (Hypertext Transfer Protocol) [4] XML is an open standard data representation language that enjoys widespread adoption across IT vendors and computing platforms XML is popular because of its openness, simplicity, expressiveness, extensibility, and readability XML de nes a simple syntax to structure and collect data into documents Application designers use XML to de ne a markup vocabulary appropriate to their application and industry (Standards bodies such as Oasis help de ne uniform industry vocabularies, allowing application-level interoperability) Application grammar and the baseline XML syntax are used to structure the data through the technique of data markup Hence, XML documents are application customized to be both humanreadable and machine-processible.

Since any XML document must conform to the syntax rules de ned by the XML speci cation [5], developers can choose from a host of available, general-purpose XML tools, including codecs, programming libraries, database libraries, and user interface tools SOAP is the core Web services messaging technology2 The SOAP speci cation addresses XML messaging between processing nodes supporting a distributed application SOAP details how an XML message is structured, how the XML data are encoded (data typing), how a SOAP node must behave according to a speci c processing model, and details on binding the XML message to an Internet protocol, namely, the Hypertext Transfer Protocol (HTTP) SOAP de nes how the message infrastructure may be extended using message headers and how intermediaries must behave when SOAP messages are passed through them.