A greedy approximation algorithm for the group Steiner problem

Chekuri, Chandra; Even, Guy; Kortsarz, Guy

doi:10.1016/j.dam.2005.07.010

Cited by 66 publications

(85 citation statements)

References 19 publications

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“…The objective is to find a minimum-cost subtree T of G that contains at least one node from each group gi. This problem has a γ = O(ln 2 n ln ln n ln ) approximation [6]. In fact, our problem is more complicated as we need to find an algorithm A that returns a pair (Q A , T A ) that not …”

Section: The Steiner-tree Coordination Costmentioning

confidence: 99%

“…This constraint, along with the coverage constraint cov(J, q) = 1, define a group Steiner tree problem [6,10]. Note that the connection to the group Steiner tree was also considered by Lappas et al [14] for the algorithms they developed.…”

Section: The Steiner-tree Coordination Costmentioning

confidence: 99%

“…It is easy to see that the complexity of the algorithm 1 is polynomial. This follows because (i) every invocation of findGroupForGivenLambda runs in polynomial time [6] and (ii) the function binarySearch) is invoked a polynomial number of times. To see why (ii) holds, note that the parameter upperBound in line 3 of the algorithm is set to the largest possible value of the ratio c(T )/a(Q).…”

mentioning

confidence: 97%

“…The theoretical algorithm used for the group Steiner tree problem [6], while it provides asymptotic guarantees, is not practical; it involves a probabilistic embedding of the graph to a tree, solving a linear program and appropriate rounding. Therefore, in our experiments we apply some simpler heuristics.…”

Section: Implementation and Heuristicsmentioning

confidence: 99%

“…Notice however that, although polynomial, the cost of the algorithm can be high in practice, due to the super-linear cost of the group Steiner tree algorithm [6]. For this reason, in Section 5, we consider computationally less demanding heuristics to implement findGroupForGivenLambda.…”

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confidence: 99%

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Online team formation in social networks

Anagnostopoulos

Becchetti

Castillo

et al. 2012

Proceedings of the 21st International Conference on World Wide Web

269

206

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We study the problem of online team formation. We consider a setting in which people possess different skills and compatibility among potential team members is modeled by a social network. A sequence of tasks arrives in an online fashion, and each task requires a specific set of skills. The goal is to form a new team upon arrival of each task, so that (i) each team possesses all skills required by the task, (ii) each team has small communication overhead, and (iii) the workload of performing the tasks is balanced among people in the fairest possible way.We propose efficient algorithms that address all these requirements: our algorithms form teams that always satisfy the required skills, provide approximation guarantees with respect to team communication overhead, and they are online-competitive with respect to load balancing. Experiments performed on collaboration networks among film actors and scientists, confirm that our algorithms are successful at balancing these conflicting requirements. This is the first paper that simultaneously addresses all these aspects. Previous work has either focused on minimizing coordination for a single task or balancing the workload neglecting coordination costs.

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Section: The Steiner-tree Coordination Costmentioning

confidence: 99%

Section: The Steiner-tree Coordination Costmentioning

confidence: 99%

mentioning

confidence: 97%

Section: Implementation and Heuristicsmentioning

confidence: 99%

mentioning

confidence: 99%

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Online team formation in social networks

Anagnostopoulos

Becchetti

Castillo

et al. 2012

Proceedings of the 21st International Conference on World Wide Web

269

206

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Approximation algorithm for the group Steiner network problem

Penn¹,

Rozenfeld²

2006

Networks

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In this article we study the group Steiner network problem, which is defined in the following way. Given a graph G ‫؍‬ (V,E), a partition of its vertices into K groups and 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). This problem is a generalization of the Steiner network problem and the group Steiner tree problem, two known NP-complete problems. We present an approximation algorithm for a special case of the group Steiner network problem with an approximation ratio of min {2(1 ؉ 2x),2I}, where I is the cardinality of the largest group and x is a parameter that depends on the cost function.

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