Approximation algorithm for the group Steiner network problem

Penn, Michal; Rozenfeld, Stas

doi:10.1002/net.20151

Cited by 2 publications

(3 citation statements)

References 24 publications

(34 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…heuristics, LP-relaxations, polyhedral aspects and approximability, cf., e.g., Dror, Haouari and Chaouachi [2], Dror and Haouari [1], Feremans, Labbe, and Laporte [3], Pop [12,13], Salazar [14], Garg, Konjevod and Ravi [5]. See also Penn and Rozenfeld [11] for a fairly comprehensive list of existing literature.…”

Section: The Generalized Minimum Spanning Tree Problemmentioning

confidence: 99%

Approximation theory in combinatorial optimization. Application to the generalized minimum spanning tree problem

Pop,

Still,

Kern

2005

J. Numer. Anal. Approx. Theory

View full text Add to dashboard Cite

We present an overview of the approximation theory in combinatorial optimization. As an application we consider the Generalized Minimum Spanning Tree (GMST) problem which is defined on an undirected complete graph with the nodes partitioned into clusters and non-negative costs are associated to the edges. This problem is NP-hard and it is known that a polynomial approximation algorithm cannot exist. We present an in-approximability result for the GMST problem and under special assumptions: cost function satisfying the triangle inequality and with cluster sizes bounded by \(\rho\), we give an approximation algorithm with ratio \(2 \rho\).

show abstract

Section: The Generalized Minimum Spanning Tree Problemmentioning

confidence: 99%

Approximation theory in combinatorial optimization. Application to the generalized minimum spanning tree problem

Pop,

Still,

Kern

2005

J. Numer. Anal. Approx. Theory

View full text Add to dashboard Cite

show abstract

“…Halperin and Krauthgamer [17] presented a lower bound of value (log 2 k) on the approximation ratio for GMST. The study of the group Steiner network problem was initiated in [23] where approximation algorithms for solving it were developed. In this problem, given a partition of the vertices into K groups and some connectivity requirements between the different groups, the aim is to find simultaneously a set of representatives, one for each group, and a minimum cost connected subgraph that satisfies the connectivity requirements between the groups (representatives).…”

Section: Introductionmentioning

confidence: 99%

“…Our algorithms follow the general scheme of Algorithm 1 in [23] where at the first stage, a selected set of representatives is chosen by solving LP relaxation of a related ungrouped problem. Then, relative to this set, the required network is constructed using a known approximation algorithm.…”

Section: Introductionmentioning

confidence: 99%

Approximation algorithms for group prize-collecting and location-routing problems

Glicksman

Penn

2008

Discrete Applied Mathematics

Self Cite

View full text Add to dashboard Cite

a b s t r a c tIn this paper we develop approximation algorithms for generalizations of the following three known combinatorial optimization problems, the Prize-Collecting Steiner Tree problem, the Prize-Collecting Travelling Salesman Problem and a Location-Routing problem.Given a graph G = (V , E) on n vertices and a length function on its edges, in the grouped versions of the above mentioned problems we assume that V is partitioned into k + 1 groups, {V 0 , V 1 , . . . , V k }, with a penalty function on the groups. In the Group PrizeCollecting Steiner Tree problem the aim is to find S, a collection of groups of V and a tree spanning the rest of the groups not in S, so as to minimize the sum of the costs of the edges in the tree and the costs of the groups in S. The Group Prize-Collecting Travelling Salesman Problem, is defined analogously. In the Group Location-Routing problem the customer vertices are partitioned into groups and one has to select simultaneously a subset of depots to be opened and a collection of tours that covers the customer groups. The goal is to minimize the costs of the tours plus the fixed costs of the opened depots. We give a (2 − 1 n−1 )I-approximation algorithm for each of the three problems, where I is the cardinality of the largest group.

show abstract

Approximation algorithm for the group Steiner network problem

Cited by 2 publications

References 24 publications

Approximation theory in combinatorial optimization. Application to the generalized minimum spanning tree problem

Approximation theory in combinatorial optimization. Application to the generalized minimum spanning tree problem

Approximation algorithms for group prize-collecting and location-routing problems

Contact Info

Product

Resources

About