We show the existence of a polynomial-size extended formulation for the base polytope of a (k, ℓ) -sparsity matroid. For an undirected graph G= (V, E) , the size of the formulation is O(| V| · | E|) when k≥ ℓ and O(| V| 2| E|) when k≤ ℓ. To this end, we employ the technique developed by Faenza et al. recently that uses a randomized communication protocol.
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