Abstract
We present three semi-streaming algorithms for Maximum Bipartite Matching with one and two passes. Our one-pass semi-streaming algorithm is deterministic and returns a matching of size at least 1/2 + 0.005 times the optimal matching size in expectation, assuming that edges arrive one by one in (uniform) random order. Our first two-pass algorithm is randomized and returns a matching of size at least 1/2 + 0.019 times the optimal matching size in expectation (over its internal random coin flips) for any arrival order. These two algorithms apply the simple Greedy matching algorithm several times on carefully chosen subgraphs as a subroutine. Furthermore, we present a two-pass deterministic algorithm for any arrival order returning a matching of size at least 1/2 + 0.019 times the optimal matching size. This algorithm is built on ideas from the computation of semi-matchings.
Supported by the French ANR Defis program under contract ANR-08-EMER-012 (QRAC project). Christian Konrad is supported by a Fondation CFM-JP Aguilar grant. Claire Mathieu is supported by NSF grant CCF-0964037.
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Konrad, C., Magniez, F., Mathieu, C. (2012). Maximum Matching in Semi-streaming with Few Passes. In: Gupta, A., Jansen, K., Rolim, J., Servedio, R. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2012 2012. Lecture Notes in Computer Science, vol 7408. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32512-0_20
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DOI: https://doi.org/10.1007/978-3-642-32512-0_20
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