An Algorithmic Framework for the Exact Solution of the Prize-Collecting Steiner Tree Problem

Ljubić, Ivana; Weiskircher, René; Pferschy, Ulrich; Klau, Gunnar W.; Mutzel, Petra; Fischetti, Matteo

doi:10.1007/s10107-005-0660-x

Cited by 189 publications

(237 citation statements)

References 17 publications

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“…We then developed a problem reduction procedure, three heuristics, and a post-optimizer (that tries to reduce the cost of the solution by replacing two regenerator locations by one) for the RLP. We showed that the regenerator location problem can be modeled as a unit degree SAP (which is an interesting observation in its own right as it implies that the MLSTP can be modeled as a unit degree SAP), and used this observation to adapt a branch-and-cut algorithm originally developed for the prize collecting Steiner tree problem [10] to the unit degree SAP (thereby allowing us to find exact solutions and lower bounds to the RLP).…”

Section: Resultsmentioning

confidence: 94%

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The regenerator location problem

2009

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In this paper we introduce the regenerator location problem (RLP), which deals with a constraint on the geographical extent of transmission in optical networks. Specifically, an optical signal can only travel a maximum distance of d max before its quality deteriorates to the point that it must be regenerated by installing regenerators at nodes of the network. As the cost of a regenerator is high we wish to deploy as few regenerators as possible in the network, while ensuring all nodes can communicate with each other. We show that the RLP is NP-Complete. We then devise three heuristics for the RLP. We show how to represent the RLP as a max leaf spanning tree problem (MLSTP) on a transformed graph. Using this fact we model the RLP as a Steiner arborescence problem (SAP) with a unit degree constraint on the root node. We also devise a branch-and-cut procedure to the directed cut formulation for the SAP problem. In our computational results over 740 test instances, the heuristic procedures obtained the optimal solution in 454 instances, while the branch-and-cut procedure obtained the optimal solution in 536 instances. These results indicate the quality of the heuristic solutions are quite good, and the branch-and-cut approach is viable for the optimal solution of problems with up to 100 nodes. Our approaches are also directly applicable to the MLSTP indicating that both the heuristics and branch-and-cut approach are viable options for the MLSTP.

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Section: Resultsmentioning

confidence: 94%

“…The general framework follows the description given in Ljubić et al [10]. Therefore we only mention the basic concepts that make our method computationally efficient:…”

Section: Branch-and-cut Algorithmmentioning

confidence: 99%

The regenerator location problem

2009

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“…Previous types of algorithms have included support vector machines [2], graph diffusion [3,4,5], and Steiner trees [6,7]. Algorithms represented this year include set cover (Przytycka and coworkers), color-coded paths (Kahveci and coworkers), and regularized regression (Gevart and Plevritis).…”

Section: Overviewmentioning

confidence: 99%

Identification of Aberrant Pathway and Network Activity From High-Throughput Data

et al. 2012

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“…Our first contribution is the formulation of the detection task as an undirected node-and edge-weighted graphical structure called Part Bricolage (PB), where the node weights represent the type of features along with their importance, and edge weights incorporate the probability of the features belonging to a known activity class, while also accounting for the trustworthiness of the features connecting the edge. Prize-Collecting-SteinerTree (PCST) problem [19] is solved for such a graph that gives the best connected subgraph comprising the activity of interest. Our second contribution is a novel technique for robust body part estimation, which uses two types of state-of-the-art pose detectors, and resolves the plausible detection ambiguities with pre-trained classifiers that predict the trustworthiness of the pose detectors.…”

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confidence: 99%

Part Bricolage: Flow-Assisted Part-Based Graphs for Detecting Activities in Videos

Shankar

Badrinarayanan

Cipolla

2014

Computer Vision – ECCV 2014

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Abstract. Space-time detection of human activities in videos can significantly enhance visual search. To handle such tasks, while solely using low-level features has been found somewhat insufficient for complex datasets; mid-level features (like body parts) that are normally considered, are not robustly accounted for their inaccuracy. Moreover, the activity detection mechanisms do not constructively utilize the importance and trustworthiness of the features.This paper addresses these problems and introduces a unified formulation for robustly detecting activities in videos. Our first contribution is the formulation of the detection task as an undirected node-and edge-weighted graphical structure called Part Bricolage (PB), where the node weights represent the type of features along with their importance, and edge weights incorporate the probability of the features belonging to a known activity class, while also accounting for the trustworthiness of the features connecting the edge. Prize-Collecting-SteinerTree (PCST) problem [19] is solved for such a graph that gives the best connected subgraph comprising the activity of interest. Our second contribution is a novel technique for robust body part estimation, which uses two types of state-of-the-art pose detectors, and resolves the plausible detection ambiguities with pre-trained classifiers that predict the trustworthiness of the pose detectors. Our third contribution is the proposal of fusing the low-level descriptors with the mid-level ones, while maintaining the spatial structure between the features.For a quantitative evaluation of the detection power of PB, we run PB on Hollywood and MSR-Actions datasets and outperform the state-of-the-art by a significant margin for various detection paradigms.

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An Algorithmic Framework for the Exact Solution of the Prize-Collecting Steiner Tree Problem

Cited by 189 publications

References 17 publications

The regenerator location problem

The regenerator location problem

Identification of Aberrant Pathway and Network Activity From High-Throughput Data

Part Bricolage: Flow-Assisted Part-Based Graphs for Detecting Activities in Videos

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