Online Matroid Intersection: Beating Half for Random Arrival

  • Guru Prashanth Guruganesh
  • Sahil SinglaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10328)


For two matroids \(\mathcal {M}_1\) and \(\mathcal {M}_2\) defined on the same ground set E, the online matroid intersection problem is to design an algorithm that constructs a large common independent set in an online fashion. The algorithm is presented with the ground set elements one-by-one in a uniformly random order. At each step, the algorithm must irrevocably decide whether to pick the element, while always maintaining a common independent set. While the natural greedy algorithm—pick an element whenever possible—is half competitive, nothing better was previously known; even for the special case of online bipartite matching in the edge arrival model. We present the first randomized online algorithm that has a \(\frac{1}{2} + \delta \) competitive ratio in expectation, where \(\delta >0\) is a constant. The expectation is over the random order and the coin tosses of the algorithm. As a corollary, we also obtain the first linear time algorithm that beats half competitiveness for offline matroid intersection.


Online algorithms Matroid intersection Randomized algorithms Competitive analysis Linear-time algorithms 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Computer Science DepartmentCarnegie Mellon UniversityPittsburghUSA

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