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Kruskal-based approximation algorithm for the multi-level Steiner tree problem [article]

Reyan Ahmed, Faryad Darabi Sahneh, Keaton Hamm, Stephen Kobourov, Richard Spence
2020 arXiv   pre-print
In this paper, we describe a natural generalization to the multi-level case of the classical (single-level) Steiner tree approximation algorithm based on Kruskal's minimum spanning tree algorithm.  ...  We study the multi-level Steiner tree problem: a generalization of the Steiner tree problem in graphs where terminals T require varying priority, level, or quality of service.  ...  Motivated by multi-level graph visualization, we refer to this problem as the multi-level Steiner tree problem. Definition 1 (Multi-level Steiner tree (MLST)).  ... 
arXiv:2002.06421v2 fatcat:tnw2nbmq6vf4lpfmfpbatqaxfm

Kruskal-Based Approximation Algorithm for the Multi-Level Steiner Tree Problem

Reyan Ahmed, Faryad Darabi Sahneh, Keaton Hamm, Stephen Kobourov, Richard Spence, Peter Sanders, Fabrizio Grandoni, Grzegorz Herman
2020 European Symposium on Algorithms  
In this paper, we describe a natural generalization to the multi-level case of the classical (single-level) Steiner tree approximation algorithm based on Kruskal's minimum spanning tree algorithm.  ...  We study the multi-level Steiner tree problem: a generalization of the Steiner tree problem in graphs where terminals T require varying priority, level, or quality of service.  ...  problem with non-proportional edge costs. 4:14 Kruskal-Based Approximation Algorithm for the Multi-Level Steiner Tree Problem A Proof of Theorem 6 Proof.  ... 
doi:10.4230/lipics.esa.2020.4 dblp:conf/esa/AhmedSHKS20 fatcat:ivlsmltfubgt3nqvocppa5lvoi

Construction of Data Aggregation Tree for Multi-objectives in Wireless Sensor Networks through Jump Particle Swarm Optimization

Yao Lu, Jianping Chen, Ioan Comsa, Pierre Kuonen, Beat Hirsbrunner
2014 Procedia Computer Science  
In this case, the way how to design a tree structure subjected to multi-objectives becomes a crucial task, which is called as multi-objective steiner tree problem (MOSTP).  ...  In view of this kind of situation, a multi-objective optimization framework is proposed, and a heuristic algorithm based on jump particle swarm optimization (JPSO) with a specific double layer encoding  ...  M-REST is another approximate algorithm based on genetic algorithm proposed to solve a multi-objective relaying nodes placement problem in 7 .  ... 
doi:10.1016/j.procs.2014.08.086 fatcat:7d5mykxgmrdqvnxmzhmmqbyz7m

Local search with perturbations for the prize-collecting Steiner tree problem in graphs

S. A. Canuto, M. G. C. Resende, C. C. Ribeiro
2001 Networks  
In this paper, we describe a multi-start local search algorithm for the prize-collecting Steiner tree problem, based on the generation of initial solutions by a primal-dual algorithm using perturbed node  ...  Given an undirected graph with prizes associated with its nodes and weights associated with its edges, the prize-collecting Steiner tree problem consists in finding a subtree of this graph which minimizes  ...  We notice that if the subset of nodes X to be spanned is known, we have the Steiner tree problem, which consists in finding a minimum weighted connected subtree of G spanning all nodes in X.  ... 
doi:10.1002/net.1023 fatcat:igthsa4bcnhqbclxud2otbvkne

Approximation algorithms for constrained generalized tree alignment problem

Srikrishnan Divakaran
2009 Discrete Applied Mathematics  
In this paper, we present constant approximation algorithms for the constrained generalized tree alignment problem.  ...  For the generalized tree alignment problem, a special case of this problem, our algorithms provide a guaranteed error bound of 2 − 2/k.  ...  Acknowledgements We thank an anonymous referee for very helpful comments on a previous draft of this paper. We also would like to thank Professor Michael Saks for some useful comments and suggestions.  ... 
doi:10.1016/j.dam.2008.10.009 fatcat:z2d4i5hmyvdcxgzxmw2nlvwi2e

Spanning Trees With Edge Conflicts and Wireless Connectivity

Magnús M. Halldórsson, Guy Kortsarz, Pradipta Mitra, Tigran Tonoyan, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility.  ...  We also treat an extension to Steiner trees, modeling multicasting, and obtain a comparable result.  ...  Latency minimization: Bounding the time it takes for a packet to filter through the tree from a leaf to a root (and back).  ... 
doi:10.4230/lipics.icalp.2018.158 dblp:conf/icalp/HalldorssonKMT18 fatcat:6am2qyxyljdrznb36xhzyzavva

Evolutionary multiobjective combinatorial optimization (EMCO)

Rajeev Kumar
2008 Proceedings of the 2008 GECCO conference companion on Genetic and evolutionary computation - GECCO '08  
The Steiner minimum tree T={(a,d),(b,d),(c,d)} which is shown in Figure b.Minimum Steiner tree problem is NP-complete.  ...  unsupported Pareto-optimal solutions **/ Use λ on edge costs to aggregate and generate tree using standard Kruskal algorithm Update PF Output PF 73 Pareto-ranking based MOEA Complete Elitism Parameter  ... 
doi:10.1145/1388969.1389079 dblp:conf/gecco/Kumar08 fatcat:acsog2ea35eijaww2ai7ozm4qi

Global and detailed routing [chapter]

Huang-Yu Chen, Yao-Wen Chang
2009 Electronic Design Automation  
We also thank the authors of ] for their help with the formulation of the programming assignment in Exercise 12.11, and Mr.  ...  National Taiwan University students in the 2008 Physical Design class, and the EDA Laboratory for their very careful review of this chapter.  ...  A better and more natural method to route multi-pin nets is to adopt the Steiner-tree-based approach.  ... 
doi:10.1016/b978-0-12-374364-0.50019-9 fatcat:ybywesjpgjgppotezavllr3vmi

Spanning Trees With Edge Conflicts and Wireless Connectivity [article]

Magnus M. Halldorsson and Guy Kortsarz and Pradipta Mitra and Tigran Tonoyan
2018 arXiv   pre-print
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility.  ...  We also treat an extension to Steiner trees, modeling multicasting, and obtain a comparable result.  ...  Our algorithm is a reduction to a multi-dimensional version of the Steiner tree (MMST) problem, recently treated by Bilò et al. [3] .  ... 
arXiv:1803.04578v1 fatcat:cfoah6xtdfg55kajdnbxy5dyui

A prize collecting Steiner tree approach to least cost evaluation of grid and off-grid electrification systems

Gizem Bolukbasi, Ayse Selin Kocaman
2018 Energy  
We model the spatial network planning problem as Prize Collecting Steiner Tree problem, which would be a base for a decision support tool for rural electrification.  ...  Comparative results for the proposed approach and a widely used heuristic method are presented based on computational experiments.  ...  Alternatively, we presented the Prize Collecting Steiner Tree model of the underlying problem, which yields the optimal solutions to the problem.  ... 
doi:10.1016/j.energy.2018.07.029 fatcat:bwdt7645w5amzb6cd5ewcwpkpe

Performance optimization of VLSI interconnect layout

Jason Cong, Lei He, Cheng-Kok Koh, Patrick H. Madden
1996 Integration  
interconnects, including the algorithms for total wire length minimization, critical path length minimization, and delay minimization; (ii) device and interconnect sizing, including techniques for efficient  ...  clock nets, non-tree clock routing, and clock schedule optimization.  ...  Acknowledgement This work is partially supported by DARPA under Contract J-FBI-93-112, NSF Young Investigator Award MIP9357582, and grants from Intel Corporation and Silicon Valley Research under the California  ... 
doi:10.1016/s0167-9260(96)00008-9 fatcat:jt7444lufzaf5hxi7vg22qvvue

SDNPS: A Load-Balanced Topic-Based Publish/Subscribe System in Software-Defined Networking

Yali Wang, Yang Zhang, Junliang Chen
2016 Applied Sciences  
In this paper, we propose an SDN-based publish/subscribe system named SDNPS, which can construct and fine-tune topic-connected overlays for the sake of disseminating events efficiently and non-redundantly  ...  However, this problem is not solved, essentially owing to the global knowledge insufficiency under the distributed management of the traditional Internet.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/app6040091 fatcat:6hbnrtxuavexpnypog4bn7dvlu

ResilientWireless Sensor Networks Using Topology Control: A Review

Yuanjiang Huang, José-Fernán Martínez, Juana Sendra, Lourdes López
2015 Sensors  
A more complete survey on the topology control based on a 3−dimension model for WSNs can be found in [133] .  ...  Multi-path routing protocols are discussed, and many NP-complete or NP-hard problems regarding topology control are identified. The challenging open issues are discussed at the end.  ...  Acknowledgments This work is supported by the European project "Design, Monitoring and Operation of Adaptive Networked Embedded Systems" (DEMANES) (project code ARTEMIS-JU:295372) and "Ministerio de Industria  ... 
doi:10.3390/s151024735 pmid:26404272 pmcid:PMC4634502 fatcat:epnq3t5g3ja4ddhqcjjnvp4x3a

Ant colony system: a cooperative learning approach to the traveling salesman problem

M. Dorigo, L.M. Gambardella
1997 IEEE Transactions on Evolutionary Computation  
.: Measuring the quality of approximate solutions to zero-one programming problems. Mathematics of Operations Research 6, 319-332 (1981) 33.  ...  .: Model based search for combinatorial optimization: a comparative study. In: Guervós, J.  ...  .: A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem. Comput. & Operations Res. 33(5), 1274-1288 (2006) 131. Magnanti, T.L., Wolsey, L.A.: Optimal trees.  ... 
doi:10.1109/4235.585892 fatcat:mo4wg7gnhzaofi4yknobao6ddy

The k-Cardinality Tree Problem: Reformulations and Lagrangian Relaxation

Frederico P. Quintão, Alexandre Salles da Cunha, Geraldo R. Mateus, Abilio Lucena
2010 Discrete Applied Mathematics  
However, a Branch-and-Bound algorithm based on the second reformulation proved much more effective and managed to obtain, for the first time, optimality certificates for a large number of KCTP instances  ...  Given an undirected defining graph for the k-Cardinality Tree Problem (KCTP), an associated directed graph involving two additional vertices is introduced in this paper and gives rise to two compact reformulations  ...  The first is based on multicommodity flows, very much in the vein of the reformulation proposed for the Steiner Problem in Graphs in [24] .  ... 
doi:10.1016/j.dam.2009.01.017 fatcat:iqpjgfbgofhtjabiw5qn3pmvoi
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