Some graph models associate activities with the nodes of the graph and others associate activities with the edges. It is generally assumed that the completion times for individual tasks are statistically indepe
Throughout this section, we assume that (X, m) is a multiplicative metric space and G = (V, E) is a directed graph such that V = X, {(x, x): x E V } E and G has no parallel edges. CARISTI MAPPING IN MULTIPLICATIVE METRIC SPACES We denote by [.sup.[lambda]]G the multigra...
Each process in the queue can be considered as a consumer of a sequence of data items for the process preceding it in the queue and as a producer of data for the process following it in the queue. The queue does not need to be a linear chain; it can be a directed graph. The most...
The log N edges connected to each vertex of the hypercube are now separately connected to log N vertices in the chain, one per vertex. The total number of nodes in cube-connected cycles is N log N and the number of links is 1.5 N log N. The number of disjoint paths between any two...
Due to this advantage, the problem size is reduced by analyzing the changes made on the graph instead of analyzing the whole graph again. This algorithm can handle up to 100 million updates per second in social networks with 30 million edges, providing a speedup from 4 times to 3700 times ...
The adjacency graph format starts with a sequence of offsets one for each vertex, followed by a sequence of directed edges ordered by their source vertex. The offset for a vertex i refers to the location of the start of a contiguous block of out edges for vertex i in the sequence of ed...
We present fast algorithms for approximate shortest paths in the massively parallel computation (MPC) model. We provide randomized algorithms that takerounds in the near-linear memory MPC model. Our results are for unweighted undirected graphs withnvertices andmedges. Our first contribution is a-appr...
Pluripotent stem cells have remarkable self-renewal capacity: the ability to proliferate indefinitely while maintaining the pluripotent identity essential for their ability to differentiate into almost any cell type in the body. To investigate the interp
if (item.Value.Count == 0) { thisIterationIds.Add(item.Key); // Remove all outbound edges List<int> depIds; if (dependenciesFromTo.TryGetValue(item.Key, out depIds)) { foreach (var depId in depIds) { dependenciesToFrom[depId].Remove(item.Key); } } } } // If nothing was ...
Each node µ of T has an associated planar st-graph (possibly with multiple edges), called the skeleton of µ and denoted by skeleton(µ). Also it is associated with an edge of the skeleton of the parent ν of µ, called the virtual edge of µ in skeleton(ν). Tree T is ...