Tight Bounds for Graph Problems in Insertion Streams

Despite the large amount of work on solving graph problems in the data stream model, there do not exist tight space bounds for almost any of them, even in a stream with only edge insertions. For example, for testing connectivity, the upper bound is O(n log n) bits, while the lower bound is only Ω(n) bits. We remedy this situation by providing the first tight Ω(n log n) space lower bounds for randomized algorithms which succeed with constant probability in a stream of edge insertions for a number of graph problems. Our lower bounds apply to testing bipartiteness, connectivity, cycle-freeness, whether a graph is Eulerian, planarity, H-minor freeness, finding a minimum spanning tree of a connected graph, and testing if the diameter of a sparse graph is constant. We also give the first Ω(nk log n) space lower bounds for deterministic algorithms for k-edge connectivity and k-vertex connectivity; these are optimal in light of known deterministic upper bounds (for k-vertex connectiv...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Xiaoming Sun, David P. Woodruff
• Keywords: Algorithms, APPROX 2015