There is a natural relationship between lower bounds in the multi-pass stream model and lower bounds in multi-round communication. However, this connection is less understood than the connection between single-pass streams and one-way communication. In this paper, we consider data-stream problems for which reductions from natural multi-round communication problems do not yield tight bounds or d...

The paper presents a load balancing method for some CGM (Coarse-Grained Multicomputer) algorithms. This method can be applied on different dynamic programming problems such as: Longest Increasing Subsequence, Longest Common Subsequence, Longest Repeated Suffix Ending at each point in a word and Detection of Repetitions. We present also experimental results showing that our method is efficient.

Let Ln be the length of a longest increasing subsequence in a random permutation of {1, ..., n}. It is known that the expected value of Ln is asymptotically equal to 2 √ n as n gets large. This note derives upper bound on the probability that Ln − 2 √ n exceeds certain quantities. In particular, we prove that Ln − 2 √ n has order at most n1/6 with high probability. Our main result is an isoperi...

Standard tableaux. A Young tableau (also known as a standard tableau) is an arrangement of distinct integers in an array of left justiied rows, such that the entries of each row are in increasing order from left to right and the entries of each column are in increasing order from bottom to top 2. For instance, here is an array of size 15: 11 4 8 12 14 3 6 7 13 1 2 5 9 10 15 : In general a table...

The weak Bruhat order on Sn is the partial order ≺ so that σ ≺ τ whenever the set of inversions of σ is a subset of the set of inversions of τ . We investigate the time complexity of computing the size of intervals with respect to ≺. Using relationships between two-dimensional posets and the weak Bruhat order, we show that the size of the interval [σ1, σ2] can be computed in polynomial time whe...

Complementing the results claiming that the maximal length L n of an increasing subsequence in a random permutation of f1; 2; : : : ; ng is highly concentrated, we show that L n is not concentrated in a short interval: sup l P(l L n l + n 1=16 log ?3=8 n) ! 0 as n ! 1.

Let S = s1, s2, . . . , sn be an integer sequence. The longest increasing subsequence problem is to find an increasing subsequence of S with the longest length. By regarding S as a weight sequence of the vertices in a path, we can redefine the longest increasing subsequence problem on graphs as follows. Let G = (V,E) be a graph in which every vertex v ∈ V has a weight w(v). A longest increasing...