Pricing Tree Access Networks with Connected Backbones

Goyal, Vineet; Gupta, Anupam; Leonard, Stefano; Ravi, R.

doi:10.1007/978-3-540-75520-3_45

Cited by 2 publications

(4 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, Goyal, Gupta, Leonardi and Ravi [12] recently proposed a primal-dual 8-approximation algorithm for the rooted stochastic Steiner tree problem with a polynomial number of scenarios. However, in Sect.…”

Section: Related Workmentioning

confidence: 98%

See 1 more Smart Citation

Deterministic Sampling Algorithms for Network Design

Zuylen¹

2009

Algorithmica

View full text Add to dashboard Cite

For several NP-hard network design problems, the best known approximation algorithms are remarkably simple randomized algorithms called SampleAugment algorithms in Gupta et al. (J. ACM 54(3):11, 2007). The algorithms draw a random sample from the input, solve a certain subproblem on the random sample, and augment the solution for the subproblem to a solution for the original problem. We give a general framework that allows us to derandomize most Sample-Augment algorithms, i.e. to specify a specific sample for which the cost of the solution created by the Sample-Augment algorithm is at most a constant factor away from optimal. Our approach allows us to give deterministic versions of the Sample-Augment algorithms for the connected facility location problem, in which the open facilities need to be connected by either a tree or a tour, the virtual private network design problem, 2-stage rooted stochastic Steiner tree problem with independent decisions, the a priori traveling salesman problem and the single sink buy-at-bulk problem. This partially answers an open question posed in Gupta et al. (J. ACM 54(3):11, 2007).

show abstract

Section: Related Workmentioning

confidence: 98%

“…, or, if no such index exists, i(q + 1) = i(K ) = K. Equations (7)(8)(9)(10)(11)(12) in the proof of Theorem 2 in [13] state that if α > 1, β > 1 and β ≤ 3 + ρ 2 then…”

mentioning

confidence: 99%

Deterministic Sampling Algorithms for Network Design

Zuylen¹

2009

Algorithmica

View full text Add to dashboard Cite

show abstract

“…The rooted stochastic Steiner tree problem has been addressed in [14,20,21,22]. Gupta, Ravi, and Sinha [21] give a constant-factor approximation algorithm for the rooted SST problem if the number of scenarios with positive probability is polynomially bounded.…”

Section: Theoremmentioning

confidence: 99%

“…Van Zuylen [28] derandomized the algorithm and obtained a deterministic 8-approximation algorithm for the rooted SST problem in the independent decision model. Furthermore, Goyal et al [14] recently gave a deterministic primal-dual 8-approximation algorithm for the rooted SST problem with a polynomial number of scenarios. All known approximation algorithms for the SST problem without a root in the black-box model are based on the adaptation of the boost-and-sample framework given by Gupta and Pál [19].…”

Section: Theoremmentioning

confidence: 99%

Strict Cost Sharing Schemes for Steiner Forest

Fleischer¹,

Könemann²,

Leonardi³

et al. 2010

SIAM J. Comput.

Self Cite

View full text Add to dashboard Cite

Abstract. Gupta et al. [J. ACM, 54 (2007), article 11] and Gupta, Kumar, and Roughgarden [in Proceedings of the ACM Symposium on Theory of Computing, ACM, New York, 2003, pp. 365-372] recently developed an elegant framework for the development of randomized approximation algorithms for rent-or-buy network design problems. The essential building block of this framework is an approximation algorithm for the underlying network design problem that admits a strict cost sharing scheme. Such cost sharing schemes have also proven to be useful in the development of approximation algorithms in the context of two-stage stochastic optimization with recourse. The main contribution of this paper is to show that the Steiner forest problem admits cost shares that are 3-strict and 4-group-strict. As a consequence, we derive surprisingly simple approximation algorithms for the multicommodity rent-or-buy and the multicast rent-or-buy problems with approximation ratios 5 and 6, improving over the previous best approximation ratios of 6.828 and 12.8, respectively. We also show that no approximation ratio better than 4.67 can be achieved using the sampleand-augment framework in combination with the currently best known Steiner forest approximation algorithms. In the context of two-stage stochastic optimization, our result leads to a 6-approximation algorithm for the stochastic Steiner tree problem in the black-box model and a 5-approximation algorithm for the stochastic Steiner forest problem in the independent decision model. 1. Introduction. In the multicommodity rent-or-buy (MRoB) problem we are given an undirected graph G = (V, E) with nonnegative costs c e for all edges e ∈ E, a set of k terminal pairs R = { (s 1 , t 1 ), . . . , (s k , t k )} ⊆ V × V , a positive demand d i for every terminal pair (s i , t i ) ∈ R, and a parameter M ≥ 1. The goal is to install capacities on the edges of G such that for all (s i , t i ) ∈ R we can simultaneously route d i units of flow from s i to t i . We can either rent capacity on an edge e at cost λ(e) · c(e), where λ(e) is the flow traversing edge e, or buy infinite capacity on edge e at cost M · c(e). Bought edges have no incremental, flow-dependent cost. The overall objective is to find a feasible solution of smallest total cost.The MRoB problem generalizes a number of fundamental optimization problems that are NP-hard. For M = 1 and unit demands, the MRoB problem reduces to the

show abstract

Pricing Tree Access Networks with Connected Backbones

Cited by 2 publications

References 26 publications

Deterministic Sampling Algorithms for Network Design

Deterministic Sampling Algorithms for Network Design

Strict Cost Sharing Schemes for Steiner Forest

Contact Info

Product

Resources

About