In this paper we present a simple linear-time algorithm constructing a context-free grammar of size O(g log(N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this string. The algorithm works for arbitrary size alphabets, but the running time is linear assuming that the alphabet Σ of the input string can be identified with number...

In this paper we devise an optimal deterministic algorithm for routing -relations on-line on an -input/output multibutterfly. The algorithm, which is obtained by generalizing the circuit-switching techniques of [3], routes any -relation with messages of bits, in log steps in the bit model, and in log log communication steps in the word model. Unlike other recently developed algorithms, our algo...

We examine the space requirement for the classic linesegment intersection problem. Using so-called implicit data structures, we show how to make the standard sweep-line algorithm run in O((n+ k) log n) time with only O(log n) extra space, where n is the number of line segments and k is the number of intersections. If division is allowed and input can be destroyed, the algorithm can run in O((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 within relative distance ǫ of the solution to Ax = b in time m ( log n+ log(nκf (A)/ǫ) ) +min ( m,n log ...

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(nκ(A)/ǫ) ) +min...

In this paper, we give streaming algorithms for some problems which are known to be in deterministic log-space, when the number of passes made on the input is unbounded. If the input data is massive, the conventional deterministic log-space algorithms may not run efficiently. We study the complexity of the problems when the number of passes is bounded. The first problem we consider is the membe...