Approximating node connectivity problems via set covers

Guy Kortsarz, Zeev Nutov

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

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 الأصليةالإنجليزيّة
عنوان منشور المضيفApproximation Algorithms for Combinatorial Optimization - 3rd International Workshop, APPROX 2000, Proceedings
المحررونKlaus Jansen, Samir Khuller
ناشرSpringer Verlag
الصفحات194-205
عدد الصفحات12
رقم المعيار الدولي للكتب (الإلكتروني)9783540679967
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - 2000
الحدث3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000 - Saarbrucken, ألمانيا
المدة: ٥ سبتمبر ٢٠٠٠٨ سبتمبر ٢٠٠٠

سلسلة المنشورات

الاسمLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
مستوى الصوت1913
رقم المعيار الدولي للدوريات (المطبوع)0302-9743
رقم المعيار الدولي للدوريات (الإلكتروني)1611-3349

!!Conference

!!Conference3rd International Workshop on Approximation Algorithms for Combinatorial Optimization, APPROX 2000
الدولة/الإقليمألمانيا
المدينةSaarbrucken
المدة٥/٠٩/٠٠٨/٠٩/٠٠

ملاحظة ببليوغرافية

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

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