Approximating Minimum-Power k-Connectivity

Nutov, Zeev

doi:10.1007/978-3-540-85209-4_7

Cited by 22 publications

(16 citation statements)

References 21 publications

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“…The previous best ratio for MPkOS was O(log n) + 4 = O(log n) [5] for large values of k = Ω(log n), and k + 1 for small values of k [9]. From Theorem 1 we obtain the following.…”

Section: Our Resultsmentioning

confidence: 73%

“…In [2] it is proved that an α-approximation for MPEMC and a β-approximation for Min-Cost k-Connected Subgraph implies a (α+2β)-approximation for MPkCS. Thus the previous best ratio for MPkCS was 2β + O(log n) [3], where β is the best ratio for MCkCS (for small values of k better ratios for MPkCS are given in [9]). The currently best known value of β is O log k log n n−k [7], which is O(log k), unless k = n − o(n).…”

Section: Our Resultsmentioning

confidence: 99%

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Approximating Minimum Power Edge-Multi-Covers

Cohen

Nutov

2012

Computer Science – Theory and Applications

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Abstract. 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). We give two approximation algorithms for MPEMC, with ratios O(log k) and k + 1/2, where k = maxv∈V r(v) is the maximum degree bound. This improves the previous ratios O(log n) and k + 1, and implies ratios O(log k) 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.

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“…The previous best ratio for MPkOS was O(log n) + 4 = O(log n) [5] for large values of k = Ω(log n), and k + 1 for small values of k [9]. From Theorem 1 we obtain the following.…”

Section: Our Resultsmentioning

confidence: 73%

Section: Our Resultsmentioning

confidence: 99%

Approximating Minimum Power Edge-Multi-Covers

Cohen

Nutov

2012

Computer Science – Theory and Applications

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“…We consider classic problems in the power model, that were already vastly studied, see [7,21,3,16,1,5,18,4,17,22,25,26] for only a small sample of papers in the field.…”

Section: Problems Consideredmentioning

confidence: 99%

On minimum power connectivity problems

Lando

Nutov

2010

Journal of Discrete Algorithms

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Given a (directed or undirected) graph with edge costs, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we present polynomial and improved approximation algorithms, as well as inapproximability results, for some classic network design problems under the power minimization criteria. Our main result is for the problem of finding a min-power subgraph that contains k internally-disjoint vs-paths from every node v to a given node s: we give a polynomial algorithm for directed graphs and a logarithmic approximation algorithm for undirected graphs. In contrast, we will show that the corresponding edge-connectivity problems are unlikely to admit even a polylogarithmic approximation.

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“…For further results on other minimum-power connectivity problems, among them problems on directed graphs see [2,7,8,[12][13][14].…”

Section: Related Workmentioning

confidence: 99%

Approximating Minimum-Power Degree and Connectivity Problems

et al. 2009

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Power optimization is a central issue in wireless network design. Given a graph with costs on the edges, 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 several fundamental undirected network design problems under the power minimization criteria. Given a graph G = (V , E) with edge costs {c(e) : e ∈ E} and degree requirements {r(v) : v ∈ V }, the Minimum-Power Edge-Multi-Cover (MPEMC) problem is to find a minimumpower subgraph G of G so that the degree of every node v in G is at least r(v). We give an O(log n)-approximation algorithms for MPEMC, improving the previous ratio O(log 4 n). This is used to derive an O(log n + α)-approximation algorithm for the undirected Minimum-Power k-Connected Subgraph (MPkCS) problem, where α is the best known ratio for the min-cost variant of the problem. Currently, α = O(log k · log n n−k ) which is O(log k) unless k = n − o(n), and is O(log 2 k) = O(log 2 n) for k = n − o(n). Our result shows that the min-power and the min-cost versions of the Preliminary version appeared in LATIN, pages 423-435, 2008. G. 736 Algorithmica (2011 k-Connected Subgraph problem are equivalent with respect to approximation, unless the min-cost variant admits an o(log n)-approximation, which seems to be out of reach at the moment.

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Approximating Minimum-Power k-Connectivity

Cited by 22 publications

References 21 publications

Approximating Minimum Power Edge-Multi-Covers

Approximating Minimum Power Edge-Multi-Covers

On minimum power connectivity problems

Approximating Minimum-Power Degree and Connectivity Problems

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