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… (More)
We study the complexity of the following problems in the streaming model. Membership testing for DLIN. We show that every language in DLIN can be recognised by a randomized one-pass O(log n) space algorithm with inverse polynomial one-sided error, and by a deterministic p-pass O(n/p) space algorithm. We show that these algorithms are optimal. Membership… (More)
We provide proofs of the following theorems by considering the entropy of random walks. Theorem 1.(Alon, Hoory and Linial) Let G be an undirected simple graph with n vertices, girth g, minimum degree at least 2 and average degree ¯ d.
A Fibonacci-rowed matrix is defined to be a matrix in which each row consists of consecutive Fibonacci numbers in increasing order. Laderman  presented a noncommutative algorithm for multiplying two 3 x 3 matrices using 23 multiplications. It still needs 18 multiplications if Laderman 1 s algorithm is applied to the product of two 3 x 3 Fibonacci-rowed… (More)