A Fully-dynamic Approximation Algorithm for Maximum Weight b-Matchings in Graphs
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| Format: | Preprint |
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2024
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| _version_ | 1866913544602124288 |
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| author | Brandt-Tumescheit, Fabian Gerharz, Frieda Meyerhenke, Henning |
| author_facet | Brandt-Tumescheit, Fabian Gerharz, Frieda Meyerhenke, Henning |
| contents | Matching nodes in a graph G = (V, E) is a well-studied algorithmic problem with many applications. The b-matching problem is a generalizati on that allows to match a node with up to b neighbors. This allows more flexible connectivity patterns whenever vertices may have multiple associations. The algorithm b-suitor [Khan et al., SISC2016] is able to compute a (1/2)-approximation of a maximum weight b-matching in O(|E|) time. Since real-world graphs often change over time, fast dynamic methods for b-matching optimization are desirable. In this work, we propose Dyn-b-suitor, a dynamic algorithm for the weighted b-matching problem. As a non-trivial extension to the dynamic Suitor algorithm for 1-matchings [Angriman et al., JEA 2022], our approach computes (1/2)-approximate b-matchings by identifying and updating affected vertices without static recomputation. Our proposed algorithm is fully-dynamic, i. e., it supports both edge insertions and deletions, and we prove that it computes the same solution as its static counterpart.
In extensive experiments on real-world benchmark graphs and generated instances, our dynamic algorithm yields significant savings compared to the sequential b-suitor, e. g., for batch updates with $10^3$ edges with an average acceleration factor of $10^3$. When comparing our sequential dynamic algorithm with the parallel (static) b-suitor on a 128-core machine, our dynamic algorithm is still $59$x to $10^4$ faster. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_09965 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Fully-dynamic Approximation Algorithm for Maximum Weight b-Matchings in Graphs Brandt-Tumescheit, Fabian Gerharz, Frieda Meyerhenke, Henning Data Structures and Algorithms Social and Information Networks Matching nodes in a graph G = (V, E) is a well-studied algorithmic problem with many applications. The b-matching problem is a generalizati on that allows to match a node with up to b neighbors. This allows more flexible connectivity patterns whenever vertices may have multiple associations. The algorithm b-suitor [Khan et al., SISC2016] is able to compute a (1/2)-approximation of a maximum weight b-matching in O(|E|) time. Since real-world graphs often change over time, fast dynamic methods for b-matching optimization are desirable. In this work, we propose Dyn-b-suitor, a dynamic algorithm for the weighted b-matching problem. As a non-trivial extension to the dynamic Suitor algorithm for 1-matchings [Angriman et al., JEA 2022], our approach computes (1/2)-approximate b-matchings by identifying and updating affected vertices without static recomputation. Our proposed algorithm is fully-dynamic, i. e., it supports both edge insertions and deletions, and we prove that it computes the same solution as its static counterpart. In extensive experiments on real-world benchmark graphs and generated instances, our dynamic algorithm yields significant savings compared to the sequential b-suitor, e. g., for batch updates with $10^3$ edges with an average acceleration factor of $10^3$. When comparing our sequential dynamic algorithm with the parallel (static) b-suitor on a 128-core machine, our dynamic algorithm is still $59$x to $10^4$ faster. |
| title | A Fully-dynamic Approximation Algorithm for Maximum Weight b-Matchings in Graphs |
| topic | Data Structures and Algorithms Social and Information Networks |
| url | https://arxiv.org/abs/2410.09965 |