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the node ni V, Vcur to be scheduled next on processor procS (ni ) = P, it holds / that tdr,Sinsert,cur (ni , P) tdr,Send,cur (ni , P) tdr,S (ni , P), with the above argumentation With the end technique, ni is scheduled at the end of the last node already scheduled on P But this cannot be later than in S, because the nodes on P in Send,cur are the same nodes that are executed before ni on P in S, due to the schedule order of the nodes, and, according to the assumption, no node starts later than in S With the insertion technique, ni is scheduled in the worst case (ie, there is no idle period between two nodes already scheduled on P complying with Eq (61)) also at the end of the last node already scheduled on P Thus, ts,Sinsert,cur (ni , P) ts,Send,cur (ni , P) ts,S (ni , P) for node ni By induction this is true for all nodes of the schedule, in particular, the last node, which proves the theorem Theorem 51 of Section 51 establishes that an optimal schedule is de ned by the processor allocation and the nodes execution order List scheduling with the end technique can construct an optimal schedule from these inputs While this result is included in Theorem 61, it also establishes that the insertion technique might improve a given nonoptimal schedule Rescheduling a given schedule with list scheduling and the insertion technique, using the processor allocation and the node order of the original schedule, might improve the schedule length In particular, schedules produced with the end technique might be improved What rst sounds like a contradiction to Theorem 51, after all it states that the end technique is optimal given a processor allocation and the nodes execution order, becomes clear when one realizes that rescheduling with the insertion technique can only reduce the length of a schedule by reordering the nodes Inserting a node in an earlier slot changes the node order on the corresponding processor Complexity Regarding the complexity of list scheduling with the insertion technique, the second part of the corresponding Algorithm 9 is examined Determining the data ready time remains O(PE) for all nodes on all processors (see Section 51) What changes is the time complexity of the start time calculation In the worst case, it must be checked for every consecutive node pair on a processor, if the time period between them is large enough to accommodate the node to be scheduled At the time a node is scheduled, there are at most O(V) nodes scheduled on all processors So if the start time is determined for every processor as in the typical case of start time minimization this amortizes to O(max(V, P)), which is of course O(V), because it is meaningless to schedule on more processors than the task graph has nodes The start time is calculated for every node; thus, the nal complexity of the second part of simple list scheduling with start time minimization is O(V2 + PE) For comparison, with the end technique it is O(P(V + E)) (see Section 51) The insertion technique is employed n various scheduling heuristics, for example, ISH (insertion scheduling heuristic) by Kruatrachue [105], (E)CPFD ((economical) critical path fast duplication) by Ahmad and Kwok [4], BSA (bubble scheduling and allocation) by Kwok and Ahmad [114], and MD (mobility directed) by Wu and Gajski [207].

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Vector and Bitmap Graphics Just as display devices have two general methods of operation, graphics file formats can be divided into two general classes, vector and bitmap2 Vector graphics formats use a series of drawing commands to represent an image A Windows metafile is a commonly used vector graphics format Figure 13 contains a simple vector image created using commands to draw two arcs and a rectangle Vector graphics formats are not limited to output devices, such as plotters, that create images through drawing commands Computer monitors and laser printers usually have software that converts vector commands into pixels There are two main drawbacks with vector graphics First, they are not suitable for reproducing photographs or paintings A painting such as Whistlers Mother would require tens of thousands of drawing commands simply determining which commands to use to represent the painting would be a monumental task Second, complex images take a long time to display On most display systems, each vector object has to be converted to a pixel image All of the image formats covered in this book are bitmap image formats Such formats represent images as 2-dimensional arrays where each array element represents a color to be displayed at a specific location When displayed on a computer screen, each element is generally mapped to a single screen pixel If pixels are close enough on the display device, it becomes difficult for the human eye to detect the array structure that composes the image The greatest advantage of bitmap images is their quality As the amount of disk space and memory has increased along with the speed of processors, the use of bitmap images has expanded as well One of the most visible examples of this is in the computer game industry Currently even games that require high performance, such as flight simulators and shoot-em-ups, use bitmap graphics Contrast the graphics in games like Quake and Doom to the vector graphics of Tank or even the Death Star graphics in the original Star Wars movie A major drawback with bitmap images is the amount of data required to hold them The size of an image in bytes (not counting overhead) is width height bits per pixel + 7 8 Thus, an 800 x 600 image with 24 bits per pixel requires 1,440,000 ytes of memory to display or disk space to store As the amount of memory on computers has grown, so has the number and size of images that can be displayed at the.

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Code 2d Barcode In VS .NET Using Barcode maker for VS .NET Control to generate, create QR .The algorithm concentrates on the next node of the dynamic sequence nDS , even if it is only partially free The free nodes that are scheduled until nDS becomes free are not allowed to have a negative effect on the scheduling of nDS Hence, DSC implements a list scheduling with a lookahead technique The node riority is the sum of the allocated bottom level and allocated top level of the scheduled task graph, tl(n, Ci 1 ) + bl(n, Ci 1 ) in Gscheduled Note that the bottom level of a node does not change during list scheduling (Section 513), that is, (bl(n, Ci 1 ) in Gscheduled ) = (bl(n) in G) To reduce complexity, the top level is estimated in a form that does not change the behavior of the algorithm, but does not require a complete traversal of the task graph.Related: Print EAN-8 .NET , Printing UPC-E .NET , ISBN Printing .NET

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A fundamental part of any graphics software is the coordinate system used to specify the location of objects drawn on a drawing surface The desktop NET Framework supports seven distinct drawing coordinate systems in the GraphicsUnit enumeration Among the supported coordinate systems are Pixel, Inch, and Millimeter While the NET Compact Framework supports this same enumeration, it has only one member: Pixel This means that when you draw on a device screen, you are limited to using pixel coordinates One xception involves fonts, whose height is always specified in Point units This brings up another difference between the desktop NET Framework and the NET Compact Framework: available coordinate transformations The desktop provides a rich set of coordinate transformations scrolling, scaling, and rotating through the Matrix class and the 3 3 geometric transform provided in the SystemDrawingDrawing2D namespace The NET Compact Framework, by contrast, supports no coordinate mapping That means that, on handheld devices, application software that wants to scale, scroll, or rotate must handle the arithmetic itself because neither the NET Compact Framework nor the underlying operating system provides any coordinate transformation helpers What the NET Compact Framework provides, as far as coordinates go, is actually the same thing that the underlying Windows CE system provides: pixels, more pixels, and only pixels While it might be lean, the set of drawing services provided in the NET Compact Framework is surprisingly complete That is, almost anything you can draw with the desktop NET Framework can be drawn with the NET Compact Framework The key difference between the two implementations is that the desktop provides a far wider array of tools and helpers for drawing Programmers of the desktop NET Framework are likely to have little trouble getting comfortable in the NET Compact Framework, once they get used to the fact that there are far fewer features But those same programmers are likely to be a bit frustrated when porting desktop NET Framework code to the NET Compact Framework world and are likely to have to rewrite and retrofit quite a few of their applications drawing elements.

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