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Seidel's Algorithm
Seidel's algorithm is an algorithm designed by Raimund Seidel in 1992 for the all-pairs-shortest-path problem for undirected, unweighted, connected graphs. It solves the problem in O(V^\omega \log V) expected time for a graph with V vertices, where \omega 2 and O(V^2 \log^2 V) for \omega = 2. Computing the shortest-paths lengths The Python code below assumes the input graph is given as a n\times n 0-1 adjacency matrix In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simp ... A with zeros on the diagonal. It defines the function APD which returns a matrix with entries D_ such that D_ is the length of the shortest path between the vertices i and j. The matrix class used can be any matrix class implementation supporting the multiplication, exponentiation, and indexing operators (for examp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raimund Seidel
Raimund G. Seidel is a German and Austrian theoretical computer scientist and an expert in computational geometry. Seidel was born in Graz, Austria, and studied with Hermann Maurer at the Graz University of Technology. He received his M. Sc. in 1981 from University of British Columbia under David G. Kirkpatrick. He received his Ph.D. in 1987 from Cornell University under the supervision of John Gilbert. After teaching at the University of California, Berkeley, he moved in 1994 to Saarland University. In 1997 he and Christoph M. Hoffmann were program chairs for the Symposium on Computational Geometry. In 2014, he took over as Scientific Director of the Leibniz Center for Informatics (LZI) from Reinhard Wilhelm. Seidel invented backwards analysis of randomized algorithms and used it to analyze a simple linear programming algorithm that runs in linear time for problems of bounded dimension. With his student Cecilia R. Aragon in 1989 he devised the treap data structure, . and he is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |