Matrix analysis
On the communication complexity of graph properties
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Communication complexity
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Reductions in streaming algorithms, with an application to counting triangles in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Graph distances in the streaming model: the value of space
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On graph problems in a semi-streaming model
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Matroid intersection, pointer chasing, and Young's seminormal representation of Sn
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On determinism versus non-determinism and related problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Complexity classes in communication complexity theory
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
The streaming complexity of cycle counting, sorting by reversals, and other problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Cycle-Counting is the following communication complexity problem: Alice and Bob each holds a permutation of size n with the promise there will be either a cycles or b cycles in their product. They want to distinguish between these two cases by communicating a few bits. We show that the quantum/nondeterministic communication complexity is roughly Ω((n - b)/(b - a)) when a ≡ b (mod 2). It is proved by reduction from a variant of the inner product problem over —m. It constructs a bridge for various problems, including In-Same-Cycle [10], One-Cycle [14], and Bipartiteness on constant degree graph [9]. We also give space lower bounds in the streaming model for the Connectivity, Bipartiteness and Girth problems [7]. The inner product variant we used has a quantum lower bound of Ω(nlogp(m)), where p(m) is the smallest prime factor of m. It implies that our lower bounds for Cycle-Counting and related problems still hold for quantum protocols, which was not known before this work.