Abstract
We study the problem of finding a maximum matching in a graph given by an input stream listing its edges in some arbitrary order, where the quantity to be maximized is given by a monotone submodular function on subsets of edges. This problem, which we call maximum submodular-function matching (MSM), is a natural generalization of maximum weight matching (MWM). We give two incomparable algorithms for this problem with space usage falling in the semi-streaming range—they store only O(n) edges, using O(nlogn) working memory—that achieve approximation ratios of 7.75 in a single pass and (3 + ε) in O(ε − 3) passes respectively. The operations of these algorithms mimic those of known MWM algorithms. We identify a general framework that allows this kind of adaptation to a broader setting of constrained submodular maximization.
Note. A full version of this extended abstract [1] can be found online at the following URL: http://arxiv.org/abs/1309.2038 .
Supported in part by NSF grant CCF-1217375.
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References
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Chakrabarti, A., Kale, S. (2014). Submodular Maximization Meets Streaming: Matchings, Matroids, and More. In: Lee, J., Vygen, J. (eds) Integer Programming and Combinatorial Optimization. IPCO 2014. Lecture Notes in Computer Science, vol 8494. Springer, Cham. https://doi.org/10.1007/978-3-319-07557-0_18
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