ملخص
We generalize and unify techniques from several papers to obtain relatively simple and general technique for designing approximation algorithms for finding min-cost k-node connected spanning subgraphs. For the general instance of the problem, the previously best known algorithm has approximation ratio 2k. For k ≤ 5, algorithms with approximation ratio [(k+1)/2] are known. For metric costs Khuller and Raghavachari gave a (2 + 2(k−1)/n)-approximation algorithm. We obtain the following results. (i) An I(k−k0)-approximation algorithm for the problem of making a k0-connected graph k-connected by adding a minimum cost edge set, where I(k) = 2+ (eqution found). (ii) A (2 + k−1/n)-approximation algorithm for metric costs. (iv) A [(k + 1)/2]-approximation algorithm for k = 6, 7. (v) A fast [(k + 1)/2]-approximation algorithm for k = 4. The multiroot problem generalizes the min-cost k-connected subgraph problem. In the multiroot problem, requirements ku for every node u are given, and the aim is to find a minimum-cost subgraph that contains max{ku, kv} internally disjoint paths between every pair of nodes u, v. For the general instance of the problem, the best known algorithm has approximation ratio 2k, where k = maxku. For metric costs there is a 3-approximation algorithm. We consider the case of metric costs, and, using our techniques, improve for k ≤ 7 the approximation guarantee from 3 to 2 + [(k−1)/2]/k < 2.5.
اللغة الأصلية | الإنجليزيّة |
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عنوان منشور المضيف | Approximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings |
المحررون | Klaus Jansen, Samir Khuller |
ناشر | Springer Verlag |
الصفحات | 194-205 |
عدد الصفحات | 12 |
رقم المعيار الدولي للكتب (الإلكتروني) | 9783540679967 |
المعرِّفات الرقمية للأشياء | |
حالة النشر | نُشِر - 2000 |
الحدث | 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 - Saarbrucken, ألمانيا المدة: ٥ سبتمبر ٢٠٠٠ → ٨ سبتمبر ٢٠٠٠ |
سلسلة المنشورات
الاسم | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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مستوى الصوت | 1913 |
رقم المعيار الدولي للدوريات (المطبوع) | 0302-9743 |
رقم المعيار الدولي للدوريات (الإلكتروني) | 1611-3349 |
!!Conference
!!Conference | 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 |
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الدولة/الإقليم | ألمانيا |
المدينة | Saarbrucken |
المدة | ٥/٠٩/٠٠ → ٨/٠٩/٠٠ |
ملاحظة ببليوغرافية
Publisher Copyright:© Springer-Verlag Berlin Heidelberg 2000.