# Approximating minimum power edge-multi-covers

Nachshon Cohen, Zeev Nutov

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

## ملخص

Given a graph with edge costs, the power of a node is the maximum cost of an edge incident to it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider the following fundamental problem in wireless network design. Given a graph G = (V,E) with edge costs and degree bounds {r(v):v ∈ V}, the Minimum-Power Edge-Multi-Cover (MPEMC) problem is to find a minimum-power subgraph J of G such that the degree of every node v in J is at least r(v). Let k = max v ∈ V r(v). For k = Ω(logn), the previous best approximation ratio for MPEMC was O(logn), even for uniform costs [3]. Our main result improves this ratio to O(logk) for general costs, and to O(1) for uniform costs. This also implies ratios O(logk) for the Minimum-Power k -Outconnected Subgraph and O(log k log n/n-k) for the Minimum-Power k -Connected Subgraph problems; the latter is the currently best known ratio for the min-cost version of the problem. In addition, for small values of k, we improve the previously best ratio k + 1 to k + 1/2.

اللغة الأصلية الإنجليزيّة Computer Science - Theory and Applications - 7th International Computer Science Symposium in Russia, CSR 2012, Proceedings 64-75 12 https://doi.org/10.1007/978-3-642-30642-6_7 نُشِر - 2012 7th International Computer Science Symposium in Russia on Computer Science - Theory and Applications, CSR 2012 - Nizhny Novgorod, روسياالمدة: ٣ يوليو ٢٠١٢ → ٧ يوليو ٢٠١٢

### سلسلة المنشورات

الاسم Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 7353 LNCS 0302-9743 1611-3349

### !!Conference

!!Conference 7th International Computer Science Symposium in Russia on Computer Science - Theory and Applications, CSR 2012 روسيا Nizhny Novgorod ٣/٠٧/١٢ → ٧/٠٧/١٢

## بصمة

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