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## Filters

##
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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. ...

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

2005
*
Journal of the Operational Research Society
*

Lower bounds are derived by

doi:10.1057/palgrave.jors.2601821
fatcat:bxrnozstp5cpfcdhoxdtuqd35y
*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. ...##
###
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

2010
*
Discrete Optimization
*

This paper investigates the Prize Collecting

doi:10.1016/j.disopt.2010.01.001
fatcat:itls3nefkzgqfc3mbdtg5rjgzu
*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. ...##
###
Combining Lagrangian Decomposition with an Evolutionary Algorithm for the Knapsack Constrained Maximum Spanning Tree Problem
[chapter]

2007
*
Lecture Notes in Computer Science
*

We present a

doi:10.1007/978-3-540-71615-0_16
fatcat:k4m3oeeseferjavcw2h33yw2ki
*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. ...##
###
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

1998
*
Proceedings of the 35th annual conference on Design automation conference - DAC '98
*

" on net i; the

doi:10.1145/277044.277147
dblp:conf/dac/ZhouW98
fatcat:74dsbzwfhfavpepspamzs4odja
*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. ...##
###
Global routing with crosstalk constraints

1999
*
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

" on net i; the

doi:10.1109/43.806813
fatcat:o6sjjmq6o5e6rmxemavowyiau4
*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. ...##
###
Lagrangian Decomposition, Metaheuristics, and Hybrid Approaches for the Design of the Last Mile in Fiber Optic Networks
[chapter]

2008
*
Lecture Notes in Computer Science
*

We consider a generalization of the (Price Collecting)

doi:10.1007/978-3-540-88439-2_12
fatcat:apkl4qvs5vgkhkxktykeddeyny
*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. ...##
###
A relax-and-cut algorithm for the prize-collecting Steiner problem in graphs

2009
*
Discrete Applied Mathematics
*

Accordingly, the Prize Collecting

doi:10.1016/j.dam.2008.02.014
fatcat:iitix62orza6fj4p2btumjup2u
*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] . ...##
###
A Lagrangian Decomposition/Evolutionary Algorithm Hybrid for the Knapsack Constrained Maximum Spanning Tree Problem
[chapter]

2008
*
Studies in Computational Intelligence
*

can be either

doi:10.1007/978-3-540-70807-0_5
fatcat:bto46x4ginebrc4fdp4qjefd2i
*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. ...##
###
A Layered Graph Model and an Adaptive Layers Framework to Solve Delay-Constrained Minimum Tree Problems
[chapter]

2011
*
Lecture Notes in Computer Science
*

We present a layered

doi:10.1007/978-3-642-20807-2_30
fatcat:5ue6u2y7l5bqbbwutfcrtxxsdy
*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] . ...##
###
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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