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Though 50% is a tight bound, in practice, this greedy peeling procedure yields about 80% of the optimal density on real-world graphs. [3] In 2020, Boob et al. gave an iterative peeling algorithm that aims to get closer to the optimal subgraph by repeated the peeling procedure multiple times. [3]
The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.
The graph of any cubic function is similar to such a curve. The graph of a cubic function is a cubic curve, though many cubic curves are not graphs of functions. Although cubic functions depend on four parameters, their graph can have only very few shapes. In fact, the graph of a cubic function is always similar to the graph of a function of ...
The clique problem arises in the following real-world setting. Consider a social network, where the graph's vertices represent people, and the graph's edges represent mutual acquaintance. Then a clique represents a subset of people who all know each other, and algorithms for finding cliques can be used to discover these groups of mutual friends.
A real-valued discrete random variable can equivalently be defined as a random variable whose cumulative distribution function increases only by jump discontinuities—that is, its cdf increases only where it "jumps" to a higher value, and is constant in intervals without jumps. The points where jumps occur are precisely the values which the ...
Models provide clarity and precision, enabling the translation of theoretical concepts into quantifiable predictions that can be tested against real-world data. [ 156 ] At the start of the 20th century, there was a development to express historical movements in formulas.
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This algorithm performs well on real-world graphs, [3] but does not have theoretical guarantee on the parallelism (consider if a graph has no edges, the algorithm requires O(n) levels of recursions). Blelloch et al. [8] in 2016 shows that if the reachability queries are applied in a random order, the cost bound of O(n log n) still holds ...