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their own routing algorithms Hence, their produced schedules can only be accurate and ef cient if the target parallel system can be directed to use the computed routes However, that is rarely the case in a generic parallel system, especially at the application level (Culler and Singh [48]) Fortunately, using the target system s own routing algorithm does not imply that for every target system a different routing algorithm must be implemented in scheduling Most parallel computers employ minimal routing, which means they choose the shortest possible path, in terms of number of edges, through the network for every communication An example is dimension ordered routing in a multidimensional mesh (Culler and Singh [48], Kumar et al [108]) A message is rst routed along one dimension, then along the second dimension, and so on until it reaches its destination Given the graph based representation of the network, nding a shortest path can be accomplished with a BFS (breadth rst search Algorithm 1) Thus, the BFS can be used as a generic routing algorithm in the topology graph, which serves, at least, as a good approximation in many cases Shortest Path in Topology Graph with BFS Although BFS is an algorithm for directed and undirected graphs, it can readily be applied to the topology graph The only graph concept used in BFS is that of adjacency (in the for loop, Algorithm 1) As this is already de ned for directed and undirected edges (Section 31), it only remains to de ne adjacency for hyperedges De nition 74 (Adjacency Hyperedge) Let V be a nite set of vertices and H a nite set of hyperedges A vertex u V, u H, H H is adjacent to all vertices v H-u and all vertices v H-u are adjacent to u The set H H:u H H-u of all vertices adjacent to u V is denoted by adj(u) Now in the topology graph, the total set of all vertices adjacent to a given vertex u is the union of the two adjacent sets induced by the directed edges and the hyperedges So with this de nition of vertex adjacency, the BFS can be applied to the topology graph without any modi cation and returns a shortest path in terms of number of edges Complexity As routing depends on the algorithm of the target parallel system, there is no general time complexity expression that is valid for all networks On that account, the routing complexity shall be denoted generically by O(routing) The algorithm for routing in regular networks is usually linear in the number of network vertices or even of constant time For example, in a fully connected network it is obviously O(1), as it is in a network with one central switch (Figure 77(b)) In a topology graph for a mesh network of any dimension (Section 221), it is at most linear in the number of processors O(P) Whenever it is possible to calculate the routes for a given system once and then to store them; for example, in a table, O(routing) is just the complexity of the length of the route For example, in a ring network the length of a route (ie, the number of links) is O(P); hence, O(routing) O(P).



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1. P. Abry. Ondelettes et Turbulences Mutiresolutions, Algorithmes de Decompositions, Invariance d'Echelle et Signaux de Pression. Diderot, Editeur des Sciences et des Arts, Paris, 1997. 2. P. Abry, P. Goncalves, and P. Flandrin. Wavelet-based spectral analysis of 1=f processes. In Proc. IEEE ICASSP'93, pp. III.237 III.240, Minneapolis, MN, 1993. 3. P. Abry, P. Goncalves, and P. Flandrin. Wavelets, spectrum estimation and 1=f processes. In A. Antoniadis and G. Oppenheim, eds., Wavelets and Statistics, Lectures Note in Statistics, 103, pp. 15 30. Springer-Verlag, New York, 1995.





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18 Jan 2014 ... Hi there,. I have been working on a small app recently which reads an image and converts it into text using optical character recognition .

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4 P Abry and P Flandrin, Point processes, long-range dependence and wavelets In A Aldroubi and M Unser, eds Wavelets in Medicine and Biology, pp 413 438 CRC Press, Boca Raton, FL, 1996 5 P Abry and D Veitch Wavelet analysis of long-range dependent traf c IEEE Trans Inf Theory, 44(1):2 15, 1998 6 P Abry, D Veitch, and P Flandrin Long-range dependence: revisiting aggregation with wavelets J Time Series Anal, 19(3):253 266, 1998 7 P Abry and F Sellan The wavelet based synthesis for fractional Brownian motion proposed by F Sellan and Y Meyer: remarks and implementation Appl Comput Harmonic Anal, 3: 377 383, 1996 8 P Abry, L Delbeke, and P Flandrin Wavelet-based estimator for the self-similarity parameter of a-stable processes In ICASSP-99, Phoenix, USA, 1999 9 P Abry, M S Taqqu, D Veitch, and P Flandrin.

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On the automatic selection of scaling range in the semi-parametric estimation of scaling exponents In preparation 10 P Abry, P Flandrin, M S Taqqu, and D Veitch Unpublished note 11 A Aldroubi and M Unser Sampling procedure in function spaces and asymptotic equivalence with Shannon's sampling theory Numer Funct Anal Optim, 15:1 21, 1994 12 J Andren, M Hilding, and D Veitch Understanding end-to-end Internet traf c dynamics In Proc Globecom '98, Sydney, pp 1118 1122, 1998 13 W Allan Statistics of atomic frequency standards Proc IEEE, 54:221 230, 1966 14 A Arneodo, J F Muzy, and S G Roux Experimental analysis of self-similar random cascade processes: application to fully developed turbulence J Phys II France, 7:363 370, 1997 15 A Arneodo, E Bacry, and J F Muzy Random cascades on wavelet dyadic trees J Math Phys, 39(8):4142 4164, August 1998 16 E Bacry, J F.

The BFS used to re ect minimal routing, has linear complexity for directed and undirected graphs, O(V + E) (Section 312) With the above de nition of adjacency with hyperedges, this result extends directly to the topology graph Hence, in the topology graph BFS s complexity is O(N + L) To obtain this complexity it is important that every hyperedge is considered only once and not one time for every incident vertex A nal word regarding the number of network vertices In a dynamic network, switches can outnumber the processors Yet, in practice the number of switches is at most O(P2 ) hence O(N) O(P2 ) because a higher number of switches would make such a network more expensive than a fully connected network Other Aspects Other aspects of routing, such as ow control, deadlock handling, and buffer sizes (Culler and Singh [48]), are not relevant for edge scheduling Also, packet dropping due to congestion, for example, in TCP/IP based networks, is not re ected, once more, because the separation into packets is unregarded In any case, the effect of packet dropping should be signi cantly reduced when a program is executed according to a contention aware schedule The contention is already taken care of by the scheduling algorithm and should not arise often during execution

class PlayingField extends Canvas implements Runnable, CommandListener{ private Command goCommand = new Command("Go", Command.SCREEN, 1); private Command backCommand = new Command("Back", Command.BACK, 1); protected static final int PUCK_SIZE = 30; protected static final int Y_POS = 40; protected static final int LOOP_COUNT = 500; protected static final int BLACK = 0x00000000; protected static final int RED = 0x00C12100; protected static final int BLUE = 0x000000FF; protected static final int GREEN = 0x00008800; protected static final int WHITE = 0x00FFFFFF; protected static final int GREY = 0x00808080; int colourBackground = BLUE; protected int xPos = 0; protected int xPosOld = 0; protected int xDelta = 1; protected int xMax; int paintCount = 0;

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