Query Lower Bounds for Matroid Intersection
نویسندگان
چکیده
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(nr) independence queries suffice. Unfortunately, very little is known about lower bounds for this problem. This paper describes three lower bounds which, to our knowledge, are the best known: 2n− 2 queries are needed for rank 1 matroids, n queries are needed for rank n− 1 matroids, and (log2 3)n − o(n) queries are needed for matroids of rank n/2. The first two results are elementary, and the last uses methods from communication complexity and group representation theory.
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