Approximation Algorithms for Directed Steiner Problems

Charikar, Moses; Chekuri, Chandra; Cheung, Tsang; Dai, Zhineng; Goel, Ashish; Guha, Sudipto; Li, Ming

doi:10.1006/jagm.1999.1042

Cited by 365 publications

(392 citation statements)

References 19 publications

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“…Above, we discussed the solutions to GST-1. As also pointed in [22], all the algorithms [19,5,16,8,23] can not be directly used to compute GST-k, because they all need to compute/sort all group Steiner trees, in order to find the minimum cost GST-k. They cannot terminate any early and report GST-k in a progress manner [22].…”

Section: Spanning and Cleanupmentioning

confidence: 99%

“…So in the time complexity given in Table 1, the l components are less important (l log n), but the n components are very important, even more important than the m components (m n 2 ). Regarding the n components (for fixed l), the time complexity of all the algorithms [19,5,16,8,9,15] is at least O(n 2 ), which makes them difficult to be efficiently applied to a large graph G with millions of nodes. The exemption is [23], but its performance ratio is unbounded.…”

Section: A New Parameterized Solutionmentioning

confidence: 99%

“…The optimal substructure holds as specified in Eq. (5)- (8). One more point need be clarified: Consider Eq.…”

Section: -Eq (8) By Examining Heightsmentioning

confidence: 99%

“…(5)- (8). The only difference is that they do not specify height h. Again, we can prove the following theorem by the induction on |p|.…”

Section: A New Best-first Dp Solutionmentioning

confidence: 99%

“…We do not report our DPH-1, because DPBF outperforms DPH-1. We do not compare our results with the work in [19,5,16,8,9,15], because their time complexity is higher than O(n 2 ), which make them difficult to handle large database graphs.…”

Section: Experimental Studiesmentioning

confidence: 99%

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Finding Top-k Min-Cost Connected Trees in Databases

Ding

Wang

et al. 2007

2007 IEEE 23rd International Conference on Data Engineering

275

274

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It is widely realized that the integration of database and information retrieval techniques will provide users with a wide range of high quality services. In this paper, we study processing an l-keyword query, p 1 , p 2 , · · · , p l , against a relational database which can be modeled as a weighted graph, G(V, E). Here V is a set of nodes (tuples) and E is a set of edges representing foreign key references between tuples. Let V i ⊆ V be a set of nodes that contain the keyword p i . We study finding top-k minimum cost connected trees that contain at least one node in every subset V i , and denote our problem as GST-k. When k = 1, it is known as a minimum cost group Steiner tree problem which is NPComplete. We observe that the number of keywords, l, is small, and propose a novel parameterized solution, with l as a parameter, to find the optimal GST-1, in time complexity O(3 l n + 2 l ((l + log n)n + m)), where n and m are the numbers of nodes and edges in graph G. Our solution can handle graphs with a large number of nodes. Our GST-1 solution can be easily extended to support GST-k, which outperforms the existing GST-k solutions over both weighted undirected/directed graphs. We conducted extensive experimental studies, and report our finding.

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Section: Spanning and Cleanupmentioning

confidence: 99%

Section: A New Parameterized Solutionmentioning

confidence: 99%

“…The optimal substructure holds as specified in Eq. (5)- (8). One more point need be clarified: Consider Eq.…”

Section: -Eq (8) By Examining Heightsmentioning

confidence: 99%

“…(5)- (8). The only difference is that they do not specify height h. Again, we can prove the following theorem by the induction on |p|.…”

Section: A New Best-first Dp Solutionmentioning

confidence: 99%

Section: Experimental Studiesmentioning

confidence: 99%

See 3 more Smart Citations

Finding Top-k Min-Cost Connected Trees in Databases

Ding

Wang

et al. 2007

2007 IEEE 23rd International Conference on Data Engineering

275

274

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References

2017

Provisioning, Recovery, and In‐operation Planning in Elastic Optical Networks

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Energy‐efficient Link Scheduling in Time‐variant Dual‐Hop 60GHz Wireless Networks

Chen

et al. 2020

Concurrency and Computation

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Dual-hop 60 GHz wireless networks which support relay-assisted dual-hop transmission have been widely adopted in the recent years, aiming to prolong communication distance and bypass obstacles in 60 GHz band. However, it is very challenging to perform link scheduling in such dual-hop architecture while considering several factors, i.e., reducing network power consumption, avoiding overloaded APs/relays and adapting to network dynamics. To this end, we investigate the problem of energy-efficient link scheduling with load constraints (ELL), and propose solutions to deal with network dynamics. First, we present a fine-grained energy model for dual-hop 60 GHz networks, and formulate the ELL problem as an integer linear programming model that aims to minimize the network power consumption, while satisfying AP/relay load constraints. Then, we propose a polynomial-time global scheduling algorithm that obtains a near-optimal link scheduling solution via iterative relaxation, and the load constraint at each AP/relay can only be violated by at most an additive constant of two. Moreover, we present a local adjustment algorithm to adjust link-scheduling solutions efficiently, such as client arrival/departure and link blockage, and design a hybrid algorithm that combines global scheduling and local adjustment. Finally, we conduct simulation experiments that validate our algorithms' effectiveness and efficiency.

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Approximation Algorithms for Directed Steiner Problems

Cited by 365 publications

References 19 publications

Finding Top-k Min-Cost Connected Trees in Databases

Finding Top-k Min-Cost Connected Trees in Databases

References

Energy‐efficient Link Scheduling in Time‐variant Dual‐Hop 60GHz Wireless Networks

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