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[167] At the beginning of the algorithm the edges of the task graph are assigned a priority, which determines the order in which they are considered The main part of the algorithm iterates over all edges E and checks for each edge if its zeroing results in a schedule length that is maller than or equal to the schedule length of the present clustering If yes, the zeroing is accepted: that is, the clusters of the incident nodes of the edge are merged This procedure is repeated until all edges have been considered Algorithm 17 outlines a generic version of the above described algorithm Algorithm 17 Single Edge Clustering Algorithm (G = (V, E, w, c)) Create initial clustering C0 : allocate each node n V to a distinct cluster C C, |C| = |V| i 0 Eunex E Eunex : set of unexamined edges, Eunex E there is at least one unexamined edge while Eunex = do i i+1 Let eij be the edge of Eunex with highest priority if proc(ni ) = proc(nj ) then incident nodes are in same cluster nothing to do Ci Ci 1 else Create new clustering Ci : merge clusters proc(ni ) and proc(nj ) into one cluster Schedule Ci using heuristic merging increases current schedule length if sl(Ci ) > sl(Ci 1 ) then Ci Ci 1 reject new clustering Ci end if end if Eunex Eunex {eij } Mark edge eij as examined end while Observe the if statement that checks whether the incident nodes ni and nj of the currently considered edge are already in the same cluster (proc(ni ) = proc(nj )) Even though all nodes are initially allocated to a distinct cluster, this situation can in fact occur due to the zeroing of previous edges in the list To illustrate this, regard Figure 56, where a three-node task graph is clustered by zeroing one edge at a time The edges are considered in the order eab , eac , ebc Figure 56(a) shows the initial clustering, Figure 56(b) the clustering after the zeroing of eab , and Figure 56(c) after the zeroing of eac The zeroing of eac merges all three nodes a, b, c into one cluster, which implicitly zeros edge ebc as its communication is now also local Therefore, the correct clustering after the zeroing of eac is the one shown in Figure 56(d) A key characteristic of this approach to clustering is that there is no clear implicit schedule This is always a problem, irrespective of the order in which the edges are considered Independent nodes might be allocated to the same cluster Consequently, Algorithm 17 contains a statement for the determination of the schedule of each new clustering Ci In essence, this is scheduling with a given processor allocation as discussed in Section 52, where the processor allocation is given by the clustering Ci of the nodes As a consequence, the determination of the schedule reduces to the.

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Type of Graph Problem in Java Draw ANSI/AIM Code 39 n Java Type of Graph Problem.negative-cost cycle A cycle whose cost is less than zero and makes most, if not all, paths undefined because we can loop around the cycle arbitrarily many times and obtain an arbitrarily small weighted path length (p 5 16) path A sequence of vertices connected by edges (p 490) path length The number of edges on a path (p 490) positive-cost cycle In a longest-path problem, the equivalent of a negative-cost cycle in a shortest-path problem (p 524) simple path A path in which all vertices are distinct, except that the first and last vertices can be the same (p 490) single-source algorithms Algorithms that compute the shortest paths from some starting point to all vertices in a graph (p 496) slack time The amount of time that an activity can be delayed without delaying overall completion (p 525) topological sort A process that orders vertices in a directed acyclic graph such that if there is a path from u to v, then v appears after u in the ordering A graph that has a cycle cannot have a topological order (p 5 17) unweighted path length The number of edges on a path (p 503) weighted path length The sum f the edge costs on a path (p 509). Code 3 Of 9 Creator In .NET Using Barcode creation for .Related: QR Code Generating Java , Codabar Printing ASP.NET , Codabar Printing .NET WinForms

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