
Breaking the Quadratic Barrier for Matroid Intersection
The matroid intersection problem is a fundamental problem that has been ...
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On the Recoverable Traveling Salesman Problem
In this paper we consider the Recoverable Traveling Salesman Problem (TS...
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Faster Matroid Intersection
In this paper we consider the classic matroid intersection problem: give...
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Breaking Quadratic Time for Small Vertex Connectivity and an Approximation Scheme
Vertex connectivity a classic extensivelystudied problem. Given an inte...
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An Approximation Algorithm for Optimal Subarchitecture Extraction
We consider the problem of finding the set of architectural parameters f...
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Roos' Matrix Permanent Approximation Bounds for Data Association Probabilities
Matrix permanent plays a key role in data association probability calcul...
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Computing The Packedness of Curves
A polygonal curve P with n vertices is cpacked, if the sum of the lengt...
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Breaking O(nr) for Matroid Intersection
We present algorithms that break the Õ(nr)independencequery bound for the Matroid Intersection problem for the full range of r; where n is the size of the ground set and r≤ n is the size of the largest common independent set. The Õ(nr) bound was due to the efficient implementations [CLSSW FOCS'19; Nguyen 2019] of the classic algorithm of Cunningham [SICOMP'86]. It was recently broken for large r (r=ω(√(n))), first by the Õ(n^1.5/ϵ^1.5)query (1ϵ)approximation algorithm of CLSSW [FOCS'19], and subsequently by the Õ(n^6/5r^3/5)query exact algorithm of BvdBMN [STOC'21]. No algorithm, even an approximation one, was known to break the Õ(nr) bound for the full range of r. We present an Õ(n√(r)/ϵ)query (1ϵ)approximation algorithm and an Õ(nr^3/4)query exact algorithm. Our algorithms improve the Õ(nr) bound and also the bounds by CLSSW and BvdBMN for the full range of r.
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