On the tree augmentation problem

نتاج البحث: فصل من :كتاب / تقرير / مؤتمرمنشور من مؤتمرمراجعة النظراء


In the Tree Augmentation problem we are given a tree T = (V, F) and a set E ⊆ V × V of edges with positive integer costs {ce : E ϵ E}. The goal is to augment T by a minimum cost edge set J ⊆ E such that T [ J is 2-edge-connected. We obtain the following results. Recently, Adjiashvili [SODA 17] introduced a novel LP for the problem and used it to break the 2-Approximation barrier for instances when the maximum cost M of an edge in E is bounded by a constant; his algorithm computes a 1.96418 + ϵ approximate solution in time n(M/-2)O(1) . Using a simpler LP, we achieve ratio 12/7 + ϵ in time 2O(M/-2). This also gives ratio better than 2 for logarithmic costs, and not only for constant costs. In addition, we will show that (for arbitrary costs) the problem admits ratio 3/2 for trees of diameter ≤ 7. One of the oldest open questions for the problem is whether for unit costs (when M = 1) the standard LP-relaxation, so called Cut-LP, has integrality gap less than 2. We resolve this open question by proving that for unit costs the integrality gap of the Cut-LP is at most 28/15 = 2 - 2/15. In addition, we will suggest another natural LP-relaxation that is much simpler than the ones in previous work, and prove that it has integrality gap at most 7/4.

اللغة الأصليةالإنجليزيّة
عنوان منشور المضيف25th European Symposium on Algorithms, ESA 2017
المحررونChristian Sohler, Christian Sohler, Kirk Pruhs
ناشرSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
رقم المعيار الدولي للكتب (الإلكتروني)9783959770491
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 1 سبتمبر 2017
الحدث25th European Symposium on Algorithms, ESA 2017 - Vienna, النمسا
المدة: ٤ سبتمبر ٢٠١٧٦ سبتمبر ٢٠١٧

سلسلة المنشورات

الاسمLeibniz International Proceedings in Informatics, LIPIcs
مستوى الصوت87
رقم المعيار الدولي للدوريات (المطبوع)1868-8969


!!Conference25th European Symposium on Algorithms, ESA 2017


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