Improved bounds for matroid partition and intersection algorithms
SIAM Journal on Computing
Communication complexity
Combinatorial optimization
Some bounds on multiparty communication complexity of pointer jumping
Computational Complexity
The communication complexity of pointer chasing
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Lower Bounds for Multi-Player Pointer Jumping
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Submodular function minimization
Mathematical Programming: Series A and B
A Faster Strongly Polynomial Time Algorithm for Submodular Function Minimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
The streaming complexity of cycle counting, sorting by reversals, and other problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The relationship between inner product and counting cycles
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
| Hi-index | 0.00 |
We consider the number of queries needed to solve the matroid intersection problem, a question raised by Welsh (1976). Given two matroids of rank r on n elements, it is known that O(nr1.5) independence queries suffice. However, no non-trivial lower bounds are known for this problem. We make the first progress on this question. We describe a family of instances of rank r = n/2 based on a pointer chasing problem, and prove that (log2 3) n-o (n) queries are necessary to solve these instances. This gives a constant factor improvement over the trivial lower bound of n for matroids of this rank. Our proof uses methods from communication complexity and group representation theory. We analyze the communication matrix by viewing it as an operator in the group algebra of the symmetric group and explicitly computing its spectrum.