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Kahn's algorithm for topological sorting builds the vertex ordering directly. It maintains a list of vertices that have no incoming edges from other vertices that have not already been included in the partially constructed topological ordering; initially this list consists of the vertices with no incoming edges at all.
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):
Kahn was assistant professor at the California Institute of Technology from 1995 to 1998 and was later a postdoc at the University of Toronto. After that, he worked for the investment firm Highbridge Capital Management as an analyst in financial mathematics. He was a postdoc and later assistant professor at the Stony Brook University.
The Dancing Links algorithm solving a polycube puzzle In computer science , dancing links ( DLX ) is a technique for adding and deleting a node from a circular doubly linked list . It is particularly useful for efficiently implementing backtracking algorithms, such as Knuth's Algorithm X for the exact cover problem . [ 1 ]
It is required to perform all tasks by assigning exactly one agent to each task in such a way that the maximum cost among the individual assignments is minimized. The term " bottleneck " is explained by a common type of application of the problem, where the cost is the duration of the task performed by an agent.
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.
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]
He was an invited speaker at the 1994 International Congress of Mathematicians in Zurich. [citation needed]In 2012, he was awarded the Fulkerson Prize (jointly with Anders Johansson and Van H. Vu) for determining the threshold of edge density above which a random graph can be covered by disjoint copies of a given smaller graph.