Survivable Network Activation Problems

Nutov, Zeev

doi:10.1007/978-3-642-29344-3_50

Cited by 13 publications

(15 citation statements)

References 12 publications

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“…Our results give the first non-trivial algorithms for the PC-NAP. We also recall that, besides our algorithms, no algorithms are known even for the element-and nodeconnectivity network activation problems because the analysis of the algorithms claimed by Nutov [13,15] contains an error. For wireless networks, it is natural to consider node-connectivity, which represents tolerance against node failures, rather than edge-connectivity, which represents tolerance against link failures.…”

Section: Our Resultsmentioning

confidence: 99%

“…We consider three definitions of the connectivity: edge-connectivity, nodeconnectivity, and element-connectivity. The edge-connectivity between two nodes u and v is the maximum number of edge-disjoint paths between u and v, and the node-connectivity between u and v is the maximum number of inner disjoint paths between u and v. The element-connectivity is defined only for pairs of research [15,16] studied the network activation problem under this assumption. In this paper, we proceed on the same assumption and design algorithms that run in polynomial time of |W | and the size of G.…”

Section: Problemmentioning

confidence: 99%

“…Concerning the network activation problem, Panigrahi [16] gave O(log |V |)-approximation algorithms for k ≤ 2 and proved that it is NP-hard to obtain an o(log |V |)-approximation algorithm even when activated edges are required to be a spanning tree. Nutov [15] presented approximation algorithms for higher connectivity requirements, including O(k log |V |)-approximation for the edge-and element-connectivity and O(k 4 log 2 |V |)-approximation for the node-connectivity. He also discussed special node-connectivity requirements such as rooted and subset requirements.…”

Section: Related Workmentioning

confidence: 99%

“…The former instance can be approximated within a factor of O(k 2 log(kd)) as above. Each of the latter instances admits a constant factor approximation using the algorithm presented in [15]. These give O(k 2 log(kd))-approximation for the original augmentation unless k = |T |−o(|T |).…”

Section: Corollarymentioning

confidence: 99%

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Spider covers for prize-collecting network activation problem

Fukunaga

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

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In the network activation problem, each edge in a graph is associated with an activation function that decides whether the edge is activated from weights assigned to its end nodes. The feasible solutions of the problem are node weights such that the activated edges form graphs of required connectivity, and the objective is to find a feasible solution minimizing its total weight. In this paper, we consider a prize-collecting version of the network activation problem and present the first nontrivial approximation algorithms. Our algorithms are based on a new linear programming relaxation of the problem. They round optimal solutions for the relaxation by repeatedly computing node weights activating subgraphs, called spiders. For the problem with element-and nodeconnectivity requirements, we also present a new potential function on uncrossable biset families and use it to analyze our algorithms. v∈V w(v), denoted by w(V ). We assume throughout the paper that G is undirected even though the problem

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Section: Our Resultsmentioning

confidence: 99%

Section: Problemmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Corollarymentioning

confidence: 99%

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Spider covers for prize-collecting network activation problem

Fukunaga

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…Naor, Panigrahi, and Singh [24] established an online algorithm for the Steiner tree problem with node weights which was extended to the Steiner forest problem by Hajiaghayi, Liaghat, and Panigrahi [16]. The survivable network design problem with node weights has also been extended to a problem called the network activation problem [28,27,12].…”

Section: Related Workmentioning

confidence: 99%

Covering problems in edge- and node-weighted graphs

Fukunaga

2016

Discrete Optimization

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This paper discusses the graph covering problem in which a set of edges in an edge-and nodeweighted graph is chosen to satisfy some covering constraints while minimizing the sum of the weights. In this problem, because of the large integrality gap of a natural linear programming (LP) relaxation, LP rounding algorithms based on the relaxation yield poor performance. Here we propose a stronger LP relaxation for the graph covering problem. The proposed relaxation is applied to designing primal-dual algorithms for two fundamental graph covering problems: the prize-collecting edge dominating set problem and the multicut problem in trees. Our algorithms are an exact polynomial-time algorithm for the former problem, and a 2-approximation algorithm for the latter problem, respectively. These results match the currently known best results for purely edge-weighted graphs.

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Minimum shared‐power edge cut

et al. 2020

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We introduce a problem called minimum shared‐power edge cut (MSPEC). The input to the problem is an undirected edge‐weighted graph with distinguished vertices s and t, and the goal is to find an s‐t cut by assigning “powers” at the vertices and removing an edge if the sum of the powers at its endpoints is at least its weight. The objective is to minimize the sum of the assigned powers. MSPEC is a graph generalization of a barrier coverage problem in a wireless sensor network: given a set of unit disks with centers in a rectangle, what is the minimum total amount by which we must shrink the disks to permit an intruder to cross the rectangle undetected, that is, without entering any disk. This is a more sophisticated measure of barrier coverage than the minimum number of disks whose removal breaks the barrier. We develop a fully polynomial time approximation scheme for MSPEC. We give polynomial time algorithms for the special cases where the edge weights are uniform, or the power values are restricted to a bounded set. Although MSPEC is related to network flow and matching problems, its computational complexity (in P or NP‐hard) remains open.

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Survivable Network Activation Problems

Cited by 13 publications

References 12 publications

Spider covers for prize-collecting network activation problem

Spider covers for prize-collecting network activation problem

Covering problems in edge- and node-weighted graphs

Minimum shared‐power edge cut

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