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This algorithm can also be rewritten to use the Fast2Sum algorithm: [7] function KahanSum2(input) // Prepare the accumulator. var sum = 0.0 // A running compensation for lost low-order bits. var c = 0.0 // The array input has elements indexed for i = 1 to input.length do // c is zero the first time around.
An alternative algorithm for topological sorting is based on depth-first search.The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning of the topological sort or the node has no outgoing edges (i.e., a leaf node):
This algorithm may yield a non-optimal solution. For example, suppose there are two tasks and two agents with costs as follows: Alice: Task 1 = 1, Task 2 = 2. George: Task 1 = 5, Task 2 = 8. The greedy algorithm would assign Task 1 to Alice and Task 2 to George, for a total cost of 9; but the reverse assignment has a total cost of 7.
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
Robert Elliot Kahn (born December 23, 1938) is an American electrical engineer who, along with Vint Cerf, first proposed the Transmission Control Protocol (TCP) and the Internet Protocol (IP), the fundamental communication protocols at the heart of the Internet. In 2004, Kahn won the Turing Award with Vint Cerf for their work on TCP/IP. [1]
Kahn process networks were originally developed for modeling parallel programs, but have proven convenient for modeling embedded systems, high-performance computing systems, signal processing systems, stream processing systems, dataflow programming languages, and other computational tasks. KPNs were introduced by Gilles Kahn in 1974. [1]
The Kahn–Kalai conjecture, also known as the expectation threshold conjecture or more recently the Park-Pham Theorem, was a conjecture in the field of graph theory and statistical mechanics, proposed by Jeff Kahn and Gil Kalai in 2006. [1] [2] It was proven in a paper published in 2024. [3]
The following algorithm using that relaxation is an expected (1-1/e)-approximation: [10] Solve the linear program L and obtain a solution O; Set variable x to be true with probability y x where y x is the value given in O. This algorithm can also be derandomized using the method of conditional probabilities.