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Algorithm Engineering pp 352–378Cite as

Engineering a Bipartite Matching Algorithm in the Semi-Streaming Model

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9220))

Abstract

We describe the Algorithm Engineering process for designing a pass-efficient semi-streaming algorithm for the bipartite maximum matching problem, using the augmenting paths technique. This algorithm was first published by the author at SEA 2011. This text not only discusses the algorithm, but also describes how Algorithm Engineering helped to invent and refine it.

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Notes

  1. 1.

    This can also be achieved by orienting the edges

    $$\begin{aligned} {\varvec{E}} :=\left\{ (a,b) \in A \times B; \{a,b\} \in E \setminus M\right\} \cup \left\{ (b,a) \in B \times A; \{a,b\} \in M \right\} \end{aligned}$$

    and then using normal BFS in this directed bipartite graph \((A,B,{\varvec{E}})\).

  2. 2.

    By \({\text {poly}}x\) we denote a polynomial in x, another way to write \(\mathcal {O}\left( {\text {poly}}x\right) \) is \(x^{\mathcal {O}\left( 1\right) }\).

  3. 3.

    The “semi” attribute was chosen since the term “streaming model” is generally associated with logarithmic space. The semi-streaming model is considered “between” logarithmic and quadratic space, the latter being equivalent to the RAM model since a graph can be stored in \(\mathcal {O}\left( n^2\right) \) bits of space.

  4. 4.

    The statement (i) can also be formulated as the algorithm with threshold 0 being a \((\lambda _1,\lambda _2,0)\) DAP approximation algorithm.

  5. 5.

    Recall that so far we have always used \(\lambda _1=\lambda _2\). A distinction between the two parameters will be made shortly.

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Acknowledgments

I thank Peter Munstermann for helpful discussions. Financial support through DFG Priority Program “Algorithm Engineering” (Grants Sr7/12-2, Sr7/12-3, and KL 2078/1-1) is also gratefully acknowledged.

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Authors and Affiliations

  1. Department of Computer Science, Kiel University, Christian-Albrechts-Platz 4, 24118, Kiel, Germany

    Lasse Kliemann

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  1. Lasse Kliemann
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Correspondence to Lasse Kliemann .

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Editors and Affiliations

  1. Kiel University , Kiel, Germany

    Lasse Kliemann

  2. Karlsruhe Institute of Technology , Karlsruhe, Germany

    Peter Sanders

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Kliemann, L. (2016). Engineering a Bipartite Matching Algorithm in the Semi-Streaming Model. In: Kliemann, L., Sanders, P. (eds) Algorithm Engineering. Lecture Notes in Computer Science(), vol 9220. Springer, Cham. https://doi.org/10.1007/978-3-319-49487-6_11

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  • DOI: https://doi.org/10.1007/978-3-319-49487-6_11

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