Streaming Partitioning of Sequences and Trees

We study streaming algorithms for partitioning integer sequences and trees. In the case of trees, we suppose that the input tree is provided by a stream consisting of a depth-first-traversal of the input tree. This captures the problem of partitioning XML streams, among other problems. We show that both problems admit deterministic (1+ )-approximation streaming algorithms, where a single pass is sufficient for integer sequences and two passes are required for trees. The space complexity for partitioning integer sequences is O( 1 p log(nm)) and for partitioning trees is O( 1 p 2 log(nm)), where n is the length of the input stream, m is the maximal weight of an element in the stream, and p is the number of partitions to be created. Furthermore, for the problem of partitioning integer sequences, we show that computing an optimal solution in one pass requires Ω(n) space, and computing a (1 + )-approximation in one pass requires Ω( 1 logn) space, rendering our algorithm tight for instances with p,m ∈ O(1). 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems