eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2016-03-14
13:1
13:18
10.4230/LIPIcs.ICDT.2016.13
article
Streaming Partitioning of Sequences and Trees
Konrad, Christian
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+epsilon)-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/epsilon) * p * log(nm)) and for partitioning trees is O((1/epsilon) * 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 Omega(n) space, and computing a (1+epsilon)-approximation in one pass requires Omega((1/epsilon) * log(n)) space, rendering our algorithm tight for instances with p,m in O(1).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol048-icdt2016/LIPIcs.ICDT.2016.13/LIPIcs.ICDT.2016.13.pdf
Streaming Algorithms
XML Documents
Data Partitioning
Communication Complexity