Task graphs are rooted digraphs used in computer science as a representation of the paths that might be traversed in a program during its execution. Some implementations utilize concurrent programming; the core concept is the encapsulation of concurrent threads of execution, such that the encompassing kernel, user threads, or processes; with control flow constructs that have clear entry and exit […]

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• Symmetric directed graphs are directed graphs where all edges are bi-directional. This means, for every arrow that belongs to the digraph, the corresponding inverse arrow also belongs to it.  • Simple directed graphs are directed graphs that have no loops, arrows that directly connect vertices to themselves, and no multiple arrows with same source and target nodes. As already introduced, in case of […]

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Understanding Processor Performance: Power Efficiency Matters When designing computer systems, processor performance isn’t just about raw speed. For many systems, efficiency is king. System designers, especially those creating large-scale computer systems like Google, prioritize CPUs that deliver the most processing power while consuming the least amount of energy. This is because, over time, the cost […]

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In formal terms, a directed graph is an ordered pair G = (V, A) where • V is a set whose elements are called vertices, nodes, or points; • A is a set of ordered pairs of vertices, called arrows, directed edges (sometimes simply edges with the corresponding set named E  instead of A), directed arcs, or directed lines.  It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called edges, […]

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Reachability and DAG Reduction Example: The reachability relationship in any directed acyclic graph can be formalized as a partial order ≤ on the vertices of the DAG. In this partial order, two vertices u and v are ordered as u ≤ v exactly when there exists a directed path from u to v in the DAG; that is, when v is reachable from u.  However, different DAGs may give rise to the same reachability relation and the same partial order.  For example, the […]

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