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تسجيل مستخدم جديدتقسيمات شبكة تضمين البطء
Sparsity-certifying Graph Decompositions
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نحن نصف الخوارزمية الجديدة، لعبة الحصى $(k,ell)$ مع الألوان، واستخدامها للحصول على تشخيص لعائلة الشبكات $(k,ell)$ الناعمة والحلول الخوارزمية لعائلة مشاكل تتعلق بتقسيمات الأشجار للشبكات. الشبكات الناعمة الخاصة تظهر في نظرية الثبات ولقد تلقت اهتماما متزايدا في السنوات الأخيرة. بشكل خاص، تجاربنا الحصوى الملونة تعمق وتقوي النتائج السابقة للي وسترينو وتعطي دليلا جديدا على تشخيص توتي - ناش ويليامز للأربوريسيتي. كما نقدم تقسيما جديدا الذي يؤكد الناعمة على أساس لعبة الحصوى $(k,ell)$ مع الألوان. أيضا، عملنا يكشف الصلة بين خوارزميات لعبة الحصوى والخوارزميات السابقة لغابو وغابو ووسترمان وهندريكسون.
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.
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We describe a new algorithm, the $(k,\\ell)$-pebble game with colors, and use\nit obtain a characterization of the family of $(k,\\ell)$-sparse graphs and\nalgorithmic solutions to a family of problems concerning tree decompositions of\ngraphs. Spe
cial instances of sparse graphs appear in rigidity theory and have\nreceived increased attention in recent years. In particular, our colored\npebbles generalize and strengthen the previous results of Lee and Streinu and\ngive a new proof of the Tutte-Nash-Williams characterization of arboricity. We\nalso present a new decomposition that certifies sparsity based on the\n$(k,\\ell)$-pebble game with colors. Our work also exposes connections between\npebble game algorithms and previous sparse graph algorithms by Gabow, Gabow and\nWestermann and Hendrickson.\n
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