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Book announcement

1992 Discrete Applied Mathematics  
Lagrangian relaxation (An example: Steiner trees. The Lagrangian dual and its optimization (Subgradient optimization. Solving the Lagrangian dual with linear programming)). Simple integer programs).  ...  The track graph (Construction of the track graph). Summary). Steiner tree heuristics in sequential routing (Steiner tree heuristics for maze running.  ... 
doi:10.1016/0166-218x(92)90299-p fatcat:kkkpojidyvgifm6vpfwb5c2epi

Solving the generalized minimum spanning tree problem by a branch-and-bound algorithm

M Haouari, J Chaouachi, M Dror
2005 Journal of the Operational Research Society  
Lower bounds are derived by relaxing, in a Lagrangian fashion, complicating constraints to yield a modified minimum cost spanning tree problem.  ...  In this paper, the GMST is formulated as a minimum spanning tree problem with side constraints and solved exactly by a branch-and-bound algorithm.  ... 
doi:10.1057/palgrave.jors.2601821 fatcat:bxrnozstp5cpfcdhoxdtuqd35y

Page 8353 of Mathematical Reviews Vol. , Issue 2004j [page]

2004 Mathematical Reviews  
Steiner tree problems in graphs with Lagrangian relaxation.  ...  Summary: “This paper presents an algorithm to obtain near opti- mal solutions for the Steiner tree problem in graphs.  ... 

Page 4534 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
For these problems, the so-called Shor relaxation involves taking the Lagrangian dual of the Lagrangian dual and results in the semidefinite programming (SDP) relaxation.  ...  It is shown that the associated sep- aration problem can be solved in O(n*) time when the subgraph induced by the edges is planar, where n is the number of vertices in the graph. H. T. Lau (St.  ... 

Algorithmic expedients for the Prize Collecting Steiner Tree Problem

Mohamed Haouari, Safa Bhar Layeb, Hanif D. Sherali
2010 Discrete Optimization  
This paper investigates the Prize Collecting Steiner Tree Problem (PCSTP) on a graph, which is a generalization of the well-known Steiner tree problem.  ...  plus the penalties associated with the nodes that are not included in the subtree.  ...  Acknowledgements This research has been supported in part by the National Science Foundation under grant CMMI-0552676.  ... 
doi:10.1016/j.disopt.2010.01.001 fatcat:itls3nefkzgqfc3mbdtg5rjgzu

Combining Lagrangian Decomposition with an Evolutionary Algorithm for the Knapsack Constrained Maximum Spanning Tree Problem [chapter]

Sandro Pirkwieser, Günther R. Raidl, Jakob Puchinger
2007 Lecture Notes in Computer Science  
We present a Lagrangian decomposition approach for the Knapsack Constrained Maximum Spanning Tree problem yielding upper bounds as well as heuristic solutions.  ...  or with a very small remaining gap in reasonable time.  ...  They described a Lagrangian relaxation approach in which the knapsack constraint (3) is relaxed, yielding the simple maximum spanning tree problem which can be solved efficiently.  ... 
doi:10.1007/978-3-540-71615-0_16 fatcat:k4m3oeeseferjavcw2h33yw2ki

Page 5974 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews  
The Lagrangian heuristic uses a Lagrangian relaxation to obtain easily solved subproblems and solves the Lagrangian dual by subgradient optimization.  ...  MacGregor] (1-MA-MIE; Amherst, MA) Geometric optimization problems for Steiner minimal trees in E>.  ... 

Page 6964 of Mathematical Reviews Vol. , Issue 2002I [page]

2002 Mathematical Reviews  
Summary: “We study a bottleneck Steiner tree problem: given a set P= { pj), p2,..., Pn} Of n terminals in the Euclidean plane and a positive integer k, find a Steiner tree with at most k Steiner points  ...  tree problem in the Euclidean plane.  ... 

Global routing with crosstalk constraints

Hai Zhou, D. F. Wong
1998 Proceedings of the 35th annual conference on Design automation conference - DAC '98  
" on net i; the Lagrangian subproblem becomes the minimum crosstalk Steiner tree problem, hence can be solved by the same algorithm.  ...  Rip-up and Reroute Based on Lagrangian Relaxation Given an initial solution constructed by the minimum crosstalk Steiner tree algorithm, nets with crosstalk violations are ripped up.  ... 
doi:10.1145/277044.277147 dblp:conf/dac/ZhouW98 fatcat:74dsbzwfhfavpepspamzs4odja

Global routing with crosstalk constraints

Hai Zhou, D.F. Wong
1999 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
" on net i; the Lagrangian subproblem becomes the minimum crosstalk Steiner tree problem, hence can be solved by the same algorithm.  ...  Rip-up and Reroute Based on Lagrangian Relaxation Given an initial solution constructed by the minimum crosstalk Steiner tree algorithm, nets with crosstalk violations are ripped up.  ... 
doi:10.1109/43.806813 fatcat:o6sjjmq6o5e6rmxemavowyiau4

Lagrangian Decomposition, Metaheuristics, and Hybrid Approaches for the Design of the Last Mile in Fiber Optic Networks [chapter]

Markus Leitner, Günther R. Raidl
2008 Lecture Notes in Computer Science  
We consider a generalization of the (Price Collecting) Steiner Tree Problem on a graph with special redundancy requirements for customer nodes.  ...  The problem occurs in the design of the last mile of real-world communication networks.  ...  As already the classical Steiner tree problem on a graph is NP-hard [5] , this obviously also holds for both of our problem variants.  ... 
doi:10.1007/978-3-540-88439-2_12 fatcat:apkl4qvs5vgkhkxktykeddeyny

A relax-and-cut algorithm for the prize-collecting Steiner problem in graphs

Alexandre Salles da Cunha, Abilio Lucena, Nelson Maculan, Mauricio G.C. Resende
2009 Discrete Applied Mathematics  
Accordingly, the Prize Collecting Steiner Problem in Graphs (PCSPG) is to find a PCS tree with the lowest weight.  ...  Given an undirected graph G with penalties associated with its vertices and costs associated with its edges, a Prize Collecting Steiner (PCS) tree is either an isolated vertex of G or else any tree of  ...  PCSPG is closely related with both the Steiner Problem in Graphs (SPG) [3] and the Steiner Tree Problem in Graphs (STP) [13] .  ... 
doi:10.1016/j.dam.2008.02.014 fatcat:iitix62orza6fj4p2btumjup2u

A Lagrangian Decomposition/Evolutionary Algorithm Hybrid for the Knapsack Constrained Maximum Spanning Tree Problem [chapter]

Sandro Pirkwieser, Günther R. Raidl, Jakob Puchinger
2008 Studies in Computational Intelligence  
can be either solved to provable optimality or with a very small remaining gap in reasonable time.  ...  We present a Lagrangian decomposition approach for the Knapsack Constrained Maximum Spanning Tree problem yielding upper bounds as well as heuristic solutions.  ...  NICTA is funded by the Australian Government's Backing Australia's Ability initiative, in part through the Australian Research Council.  ... 
doi:10.1007/978-3-540-70807-0_5 fatcat:bto46x4ginebrc4fdp4qjefd2i

A Layered Graph Model and an Adaptive Layers Framework to Solve Delay-Constrained Minimum Tree Problems [chapter]

Mario Ruthmair, Günther R. Raidl
2011 Lecture Notes in Computer Science  
We present a layered graph model for delay-constrained minimum tree problems with a polynomial number of constraints which can be solved well for instances with low-to medium-sized sets of achievable delay  ...  Layered graph models have been recently shown to frequently yield tight bounds in the context of hopor delay-constrained network design problems.  ...  There are many existing approaches for efficiently solving the Steiner tree problem on graphs, e.g. [7, 14, 1] .  ... 
doi:10.1007/978-3-642-20807-2_30 fatcat:5ue6u2y7l5bqbbwutfcrtxxsdy

Page 383 of The Journal of the Operational Research Society Vol. 56, Issue 4 [page]

2005 The Journal of the Operational Research Society  
Tree problem.  ...  approximation schemes unless A=.1-), while there is plenty of evidence that the Steiner Tree problem is one of the P-hard problems.  ... 
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