We give two self-stabilizing algorithms for tree networks. The first computes an index, called guide pair, for each process P in O(h) rounds using O(δP log n) space per process, where h is the height of the tree, δP the degree of P , and n the number of processes in the network. Guide pairs have numerous applications, including ordered traversal or navigation in the tree. Our second algorithm, ...

We prove that rational data of bounded input length are uniformly distributed (in the classical sense of H. Weyl, in [42]) with respect to the probability distribution of condition numbers of Numerical Analysis. We deal both with condition numbers of Linear Algebra and with condition numbers for systems of multivariate polynomial equations. For instance, we prove that for a randomly chosen n×n ...

We develop nearly-linear time algorithms for approximately solving sparse symmetric diagonally-dominant linear systems. In particular, we present a linear-system solver that, given an n-by-n symmetric diagonally-dominant matrix A with m non-zero entries and an n-vector b, produces a vector x̃ satisfying ‖x̃ − x‖ ≤ ǫ, where x is the solution to Ax = b, in time m log m+O (m log(1/ǫ)) + n2 √ log n l...

We present a generalization of the Viterbi algorithm for identifying the path with minimal (resp. maximal) weight in a n-tape weighted finite-state machine (n-WFSM), that accepts a given n-tuple of input strings 〈s1, . . . sn〉. It also allows us to compile the best transduction of a given input n-tuple by a weighted (n+m)-WFSM (transducer) with n input and m output tapes. Our algorithm has a wo...

In a paper that considered arithmetic precision as a limited resource in the design and analysis of algorithms, Liotta, Preparata and Tamassia defined an “implicit Voronoi diagram” supporting logarithmictime proximity queries using predicates of twice the precision of the input and query coordinates. They reported, however, that computing this diagram uses five times the input precision. We def...

First, a process of building of the neural network for events forecasting is presented, that is the selection of networks’ architecture and parameters. Next, the effect of adding data calibrated by nonlinear input function to input data calibrated linearly is described. The nonlinear input function hyperbolic tangent was accepted. Hyperbolic tangent sigmoid transfer function and log sigmoid tra...

We describe efficient PRAM algorithms for constructing unbalanced quadtrees, balanced quadtrees, and quadtree-based finite element meshes. Our algorithms take time O(logn) for point set input and O(logn log k) time for planar straight-line graphs, using O(n+k/ logn) processors, where n measures input size and k output size.