稀疏证明图分解
Sparsity-certifying Graph Decompositions
摘要：
我们描述了一个新的算法，$(k,\ell)$ -卵石游戏的颜色，并使用它获得了家庭的$(k,\ell)$ -稀疏图的一个特征和算法的解决方案，家庭的问题有关的树分解的图。稀疏图的特殊例子出现在刚性理论中，近年来受到越来越多的关注。特别地，我们的有色卵石推广和加强了Lee和Streinu的结果，并给出了树荫度的Tutte-Nash-Williams刻画的一个新证明。我们还提出了一个新的分解，证明稀疏的基础上的$(k,\ell)$卵石游戏的颜色。我们的工作还揭示了卵石游戏算法和以前的稀疏图算法的Gabow，Gabow和Westermann和Hendrickson之间的连接。
英文摘要：
We describe a new algorithm, the $(k,\ell)$-pebble game with colors, and use it obtain a characterization of the family of $(k,\ell)$-sparse graphs and algorithmic solutions to a family of problems concerning tree decompositions of graphs. Special instances of sparse graphs appear in rigidity theory and have received increased attention in recent years. In particular, our colored pebbles generalize and strengthen the previous results of Lee and Streinu and give a new proof of the Tutte-Nash-Williams characterization of arboricity. We also present a new decomposition that certifies sparsity based on the $(k,\ell)$-pebble game with colors. Our work also exposes connections between pebble game algorithms and previous sparse graph algorithms by Gabow, Gabow and Westermann and Hendrickson.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
