We consider the unweighted bipartite maximum matching problem in the one-pass turnstile streaming model where the input stream consists of edge insertions and deletions. In the insertion-only model, a one-pass 2-approximation streaming algorithm can be easily obtained with space O(n logn), where n denotes the number of vertices of the input graph. We show that no such result is possible if edge deletions are allowed, even if space O(n3/2 − δ) is granted, for every δ > 0. Specifically, for every 0 ≤ ε ≤ 1, we show that in the one-pass turnstile streaming model, in order to compute a O(n ε )-approximation, space Ω(n3/2 − 4ε) is required for constant error randomized algorithms, and, up to logarithmic factors, space O~(n2−2ϵ) is sufficient.
Our lower bound result is proved in the simultaneous message model of communication and may be of independent interest.
|Title of host publication||Algorithms - ESA 2015|
|Subtitle of host publication||23rd Annual European Symposium, Patras, Greece, September 14-16, 2015, Proceedings|
|Publisher||Springer Berlin Heidelberg|
|Number of pages||13|
|Publication status||Published - 12 Nov 2015|
|Name||Lecture Notes in Computer Science|
- Input Graph
- Maximum Match
- Vertex Group
- Bipartite Match
- Edge Insertion