In this paper we present efficient deterministic and randomized algorithms for selection on any interconnection network when the number of input keys (n) is ≥ the number of processors (p). Our deterministic algorithm runs on any network in time O(np log log p + T s p logn), where T s p is the time needed for sorting p keys using p processors (assuming that broadcast and prefix computations take...

Given a description of a probabilistic automaton (one-head probabilistic nite automaton or probabilistic Turing machine) and an input string x of length n, we ask how much space does a deterministic Turing machine need in order to decide the acceptance of the input string by that automaton? The question is interesting even in the case of one-head one-way probabilistic nite automata (PFA). We ca...

We develop nearly-linear time algorithms for approximately solving sparse symmetric diagonally-dominant linear systems. In particular, for every β > 0 we present a linearsystem solver that, given an n-by-n symmetric diagonally-dominant matrix A with m nonzero entries and an n-vector b, produces a vector x̃ within relative distance ǫ of the solution to Ax = b in time m ( log + log(1/ǫ) ) +min(m,n...

We convert constructive solid geometry input to explicit representations of polygons, polyhedra, or more generally d-dimensional polyhedra, in time O(n), improving a previous O(n log n) bound. We then show that any Boolean formula can be preprocessed in time O(n log n/ log logn) so that the value of the formula can be maintained, as variables are changed one by one, in time O(log n/ log logn) p...

We present a randomized algorithm for reconstructing directed rooted trees of n nodes and node degree at most d, by asking at most O(dn log n) path queries. Each path query takes as input an origin node and a target node, and answers whether there is a directed path from the origin to the target. Our algorithm is only a factor of O(d log n) from the informationtheoretic lower bound of Ω(n log n...

Examining scaling patterns of networks can help understand how structural features relate to the behavior of the networks. Input–output networks consist of industries as nodes and inter-industrial exchanges of products as links. Previous studies consider limitedmeasures for node strengths and link weights, and also ignore the impact of dataset choice. We consider a comprehensive set of indicato...

We develop a method for performing boolean convolutions efficiently in word RAM model of computation, having a word size of w = Ω(log n) bits, where n is the input size. The technique is applied to approximate string matching under Hamming distance. The obtained algorithms are the fastest known. In particular, we reduce the complexity of the Amir et al. [1] algorithm for k-mismatches from O(n √...

A space-efficient linear-time approximation algorithm for the grammar-based compression problem, which requests for a given string to find a smallest context-free grammar deriving the string, is presented. The algorithm consumes only O(g∗ log g∗) space and achieves the worstcase approximation ratio O(log g∗ log n), with the size n of an input and the optimum grammar size g∗. Experimental result...

In a sequence of recent results (PODC 2015 and PODC 2016), the running time of the fastest algorithm for the minimum spanning tree (MST) problem in the Congested Clique model was first improved to O(log log logn) from O(log logn) (Hegeman et al., PODC 2015) and then to O(log∗ n) (Ghaffari and Parter, PODC 2016). All of these algorithms use Θ(n2) messages independent of the number of edges in th...

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 within relative distance ǫ of the solution to Ax = b in time m ( log n+ log(nκf (A)/ǫ) ) +min ( m,n log ...