Spider covers for prize-collecting network activation problem

Fukunaga, Takuro

doi:10.1137/1.9781611973730.2

Cited by 11 publications

(8 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3 [13], and β k = O(k ln k) for k ≥ 4 [11]. We also have β ′ k = O(k 2 ln n) by [11] and the correction of Vakilian [14] to the algorithm and the analysis of [11]; see also [6].…”

Section: Rooted Subset K-connectivitymentioning

confidence: 89%

Improved approximation algorithms for k-connected m-dominating set problems

Nutov

2018

Information Processing Letters

View full text Add to dashboard Cite

A subset S of nodes in a graph G is a k-connected mdominating set ((k, m)-cds) if the subgraph G[S] induced by S is k-connected and every v ∈ V \ S has at least m neighbors in S. In the k-Connected m-Dominating Set ((k, m)-CDS) problem the goal is to find a minimum weight (k, m)-cds in a node-weighted graph. For m ≥ k we obtain the following approximation ratios. For general graphs our ratio O(k ln n) improves the previous best ratio O(k 2 ln n) of [9] and matches the best known ratio for unit weights of [11]. For unit disc graphs we improve the ratio O(k ln k) of [9] to min m m−k , k 2/3 · O(ln 2 k) -this is the first sublinear ratio for the problem, and the first polylogarithmic ratio O(ln 2 k)/ǫ when m ≥ (1 + ǫ)k; furthermore, we obtain ratio min m m−k , √ k ·O(ln 2 k) for uniform weights. These results are obtained by showing the same ratios for the Subset k-Connectivity problem when the set T of terminals is an m-dominating set with m ≥ k.

show abstract

“…3 [13], and β k = O(k ln k) for k ≥ 4 [11]. We also have β ′ k = O(k 2 ln n) by [11] and the correction of Vakilian [14] to the algorithm and the analysis of [11]; see also [6].…”

Section: Rooted Subset K-connectivitymentioning

confidence: 89%

Improved approximation algorithms for k-connected m-dominating set problems

Nutov

2018

Information Processing Letters

View full text Add to dashboard Cite

show abstract

“…, t}. Applying these conditions, the present author obtained a new approximation algorithm for solving a problem generalizing some prize-collecting graph covering problems [12].…”

Section: Lp Relaxationsmentioning

confidence: 96%

“…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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…We borrow several ideas from work on Elem-SNDP [10,15,25,32] and VC-SNDP [11,32]. Some variants of the SNDP problem such as Prize-collecting SNDP, Budgeted SNDP, and Network Activation have been studied in node-weighted setting and we refer readers to [2,9,17,31,36] for developments in these directions, several of which have happened after the conference version of this article appeared.…”

Section: Overview Of Technical Ideas and Contributionmentioning

confidence: 99%

Node-weighted Network Design in Planar and Minor-closed Families of Graphs

Chekuri

Ene

Vakilian

2021

ACM Trans. Algorithms

View full text Add to dashboard Cite

We consider node-weighted survivable network design (SNDP) in planar graphs and minor-closed families of graphs. The input consists of a node-weighted undirected graph G = ( V , E ) and integer connectivity requirements r ( uv ) for each unordered pair of nodes uv . The goal is to find a minimum weighted subgraph H of G such that H contains r ( uv ) disjoint paths between u and v for each node pair uv . Three versions of the problem are edge-connectivity SNDP (EC-SNDP), element-connectivity SNDP (Elem-SNDP), and vertex-connectivity SNDP (VC-SNDP), depending on whether the paths are required to be edge, element, or vertex disjoint, respectively. Our main result is an O ( k )-approximation algorithm for EC-SNDP and Elem-SNDP when the input graph is planar or more generally if it belongs to a proper minor-closed family of graphs; here, k = max uv r ( uv ) is the maximum connectivity requirement. This improves upon the O ( k log n )-approximation known for node-weighted EC-SNDP and Elem-SNDP in general graphs [31]. We also obtain an O (1) approximation for node-weighted VC-SNDP when the connectivity requirements are in {0, 1, 2}; for higher connectivity our result for Elem-SNDP can be used in a black-box fashion to obtain a logarithmic factor improvement over currently known general graph results. Our results are inspired by, and generalize, the work of Demaine, Hajiaghayi, and Klein [13], who obtained constant factor approximations for node-weighted Steiner tree and Steiner forest problems in planar graphs and proper minor-closed families of graphs via a primal-dual algorithm.

show abstract

Spider covers for prize-collecting network activation problem

Cited by 11 publications

References 24 publications

Improved approximation algorithms for k-connected m-dominating set problems

Improved approximation algorithms for k-connected m-dominating set problems

Covering problems in edge- and node-weighted graphs

Node-weighted Network Design in Planar and Minor-closed Families of Graphs

Contact Info

Product

Resources

About