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Multi-level Steiner Trees

Reyan Ahmed, Joseph Watkins, Alexander Wolff, Patrizio Angelini, Faryad Darabi Sahneh, Alon Efrat, David Glickenstein, Martin Gronemann, Niklas Heinsohn, Stephen G. Kobourov, Richard Spence
2019 ACM Journal of Experimental Algorithmics  
In this paper, we study a natural generalization, the multi-level Steiner tree (MLST) problem: given a nested sequence of terminals T 1 ⊂ · · · ⊂ T k ⊆ V , compute nested edge sets E 1 ⊆ · · · ⊆ E k ⊆  ...  The MLST problem and variants thereof have been studied under names such as Quality-of-Service Multicast tree, Grade-of-Service Steiner tree, and Multi-Tier tree.  ...  graphs to related problems (such as the node-weighted Steiner tree problem).  ... 
doi:10.1145/3368621 fatcat:xrb473shhrdu7axlsa2qrradp4

Multi-Level Steiner Trees [article]

Reyan Ahmed, Patrizio Angelini, Faryad Darabi Sahneh, Alon Efrat, David Glickenstein, Martin Gronemann, Niklas Heinsohn, Stephen G. Kobourov, Richard Spence, Joseph Watkins, Alexander Wolff
2018 arXiv   pre-print
The MLST problem and variants thereof have been studied under various names including Multi-level Network Design, Quality-of-Service Multicast tree, Grade-of-Service Steiner tree, and Multi-Tier tree.  ...  In this paper, we study a natural generalization, the multi-level Steiner tree (MLST) problem: given a nested sequence of terminals T_ℓ⊂...⊂ T_1 ⊆ V, compute nested trees E_ℓ⊆...⊆ E_1⊆ E that span the  ...  Top-Down and Bottom-Up Approaches We present top-down and bottom-up approaches for computing approximate multi-level Steiner trees.  ... 
arXiv:1804.02627v2 fatcat:wc6tfd5epjb75o4bct3r4aabry

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
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.  ...  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.  ...  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  
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.  ...  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.  ...  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)).  ... 
doi:10.4230/lipics.esa.2020.4 dblp:conf/esa/AhmedSHKS20 fatcat:ivlsmltfubgt3nqvocppa5lvoi

Multi-layer chip-level global routing using an efficient graph-based Steiner tree heuristic

Le-Chin Eugene Liu, C. Sechen
Proceedings European Design and Test Conference. ED & TC 97  
We present a chip-level global router based on a new, more accurate global routing model for the multi-layer macro-cell technology.  ...  We developed an improved Steiner tree heuristic algorithm suitable for large routing graphs and able to generate high quality Steiner tree routing.  ...  Tree program.  ... 
doi:10.1109/edtc.1997.582376 dblp:conf/date/LiuS97 fatcat:raofmld6hbe5lbxf7zrzi6sb2m

Multi-level tree based approach for interactive graph visualization with semantic zoom [article]

Felice De Luca, Iqbal Hossain, Kathryn Gray, Stephen Kobourov, Katy Börner
2019 arXiv   pre-print
With this in mind, we propose the Zoomable Multi-Level Tree (ZMLT) algorithm for multi-level tree-based, map-like visualization of large graphs.  ...  of details; (2) The embedded trees represent the underlying graph appropriately at different levels of details; (3) At every level of detail we show real vertices and real paths from the underlying graph  ...  The abstract trees are created using an algorithm for computing multi-level max Steiner tree.  ... 
arXiv:1906.05996v2 fatcat:z4g6l2c6xbal5pxznxglbmnfya

Multi-Level Graph Sketches via Single-Level Solvers [article]

Reyan Ahmed, Keaton Hamm, Mohammad Javad Latifi Jebelli, Stephen Kobourov, Faryad Darabi Sahneh, Richard Spence
2019 arXiv   pre-print
This paper gives a flexible procedure for computing a broad class of multi-level graph sketches, which encompasses multi-level graph spanners, Steiner trees, and k–connected subgraphs as a few special  ...  Examples include Steiner trees (preserving connectivity among T) and subsetwise spanners (preserving shortest path distances up to a stretch factor).  ...  Multi-level or priority Steiner trees have been studied in [3, 16, 18] . Charikar et al.  ... 
arXiv:1905.00536v2 fatcat:ynptxpg3engvdlsxww6kb66ar4

An enhanced multilevel routing system

Jason Cong, Min Xie, Yan Zhang
2002 Computer-Aided Design (ICCAD), IEEE International Conference on  
Our contributions include: (1) resource reservation for local nets during the coarsening process, (2) congestion-driven, graph-based Steiner tree construction during the initial routing and the refinement  ...  process and (3) multi-iteration refinement considering the congestion history.  ...  tree heuristic and a history-based multi-iteration scheme.  ... 
doi:10.1145/774572.774580 dblp:conf/iccad/CongXZ02 fatcat:t5lt3i7gtzbippddbfcgnp6ydu

Multi-terminal nets do change conventional wire length distribution models

Dirk Stoobandt
2001 Proceedings of the 2001 international workshop on System-level interconnect prediction - SLIP '01  
of Steiner tree lengths for applications related to routing resource estimation.  ...  The e ects of including multi-terminal nets in the estimations are highlighted. Experiments show that the new estimated wire length distributions are close to the measured ones.  ...  To calculate the average Steiner tree length `st, we do not need to consider the complex addition of segment lengths to Steiner lengths.  ... 
doi:10.1145/368640.368679 dblp:conf/slip/Stoobandt01 fatcat:nlkhobhxk5hcpgrce2ycwugljm

A Steiner tree based approach for the efficient support of multipoint communications in a multi-domain context

Lunde Chen, Slim Abdellatif, Thierry Gayraud, Pascal Berthou
2017 2017 IEEE Symposium on Computers and Communications (ISCC)  
aggregated networks as well as the global Steiner tree.  ...  This work proposes an approach based on Steiner trees to efficiently support multipoint communications in a multidomain context, where each domain exposes a synthetic and aggregated view of its network  ...  Fig. 1 : 1 A multi-domain network and the minimum cost global Steiner tree Fig. 2: Topology aggregation in full mesh and in Steiner tree III.  ... 
doi:10.1109/iscc.2017.8024549 dblp:conf/iscc/ChenAGB17 fatcat:vcrruyqoofhnbeqaylw2illq6u

A Decentralized Storage Scheme for Multi-Dimensional Range Queries over Sensor Networks

Lei Xie, Lijun Chen, Daoxu Chen, Li Xie
2009 2009 15th International Conference on Parallel and Distributed Systems  
This paper presents the design of a decentralized storage scheme to support multi-dimensional range queries over sensor networks.  ...  We build a distributed k-d tree based index structure over sensor network, so as to efficiently map high dimensional event data to a two-dimensional space of sensors while preserving the proximity of events  ...  Assume the root of the k-d tree is at level 0, and the k-d tree indexes the cell unit at level h, (apparently h should be an even number), thus at level i (0 ≤ i ≤ h), we have: N (S i ) = 2 h−i (9) And  ... 
doi:10.1109/icpads.2009.24 dblp:conf/icpads/Xie0CX09 fatcat:a52dglvlr5ehjiub4x6svqmcdi

Multilayer chip-level global routing using an efficient graph-based Steiner tree heuristic

L.-C.E. Liu, C. Sechen
1999 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
We present a chip-level global router based on a new, more accurate global routing model for the multi-layer macro-cell technology.  ...  We developed an improved Steiner tree heuristic algorithm suitable for large routing graphs and able to generate high quality Steiner tree routing.  ...  Tree program.  ... 
doi:10.1109/43.790621 fatcat:fgona6pdljbuthin34l6yznhnm

Towards Design of System Hierarchy (research survey) [article]

Mark Sh. Levin
2012 arXiv   pre-print
., minimum spanning tree, minimum Steiner tree, maximum leaf spanning tree problem; (4) design of organizational 'optimal' hierarchies; (5) design of multi-layer (e.g., three-layer) k-connected network  ...  ; (6) modification of hierarchies or networks: (i) modification of tree via condensing of neighbor nodes, (ii) hotlink assignment, (iii) transformation of tree into Steiner tree, (iv) restructuring as  ...  spanning tree [80] 1.3.Minimum spanning forest [75],[173] 1.4.Minimum spanning multi-tree [77],[103],[198] 1.5.Multicriteria spanning tree [9],[33],[51],[96] 2.Steiner tree 2.1.Bottleneck Steiner  ... 
arXiv:1212.1735v1 fatcat:3kdzux4plbha3oajtkp6yq6zwm

Multi-Agent Steiner Tree Algorithm Based on Branch-Based Multicast

Hiroshi MATSUURA
2016 IEICE transactions on information and systems  
The Steiner tree problem is a nondeterministic-polynomial-time-complete problem, so heuristic polynomial-time algorithms have been proposed for finding multicast trees.  ...  The advantage of the proposed multi-agent BBMC algorithm is its covering of discarded effective branch candidates to seek the optimal multicast tree.  ...  Therefore, it can drastically reduce the processing time of intelligence algorithms for finding a Steiner tree, despite its same level of Steiner tree costs, compared with intelligence algorithms.  ... 
doi:10.1587/transinf.2015edp7417 fatcat:dl2achz2afhfbfza4jlwohabjm

Opportunistic Overlay Multicast in Wireless Networks

Tan Le, Yong Liu
2010 2010 IEEE Global Telecommunications Conference GLOBECOM 2010  
In MSTOR, the source and receivers are connected by an overlay Steiner tree. The source multicasts packets along the overlay links of the Steiner tree to reach all receivers.  ...  In this paper, we propose an opportunistic overlay multicast design for wireless networks, named Minimum Steiner Tree with Opportunistic Routing (MSTOR).  ...  For wireless multicast, we build an overlay Steiner tree to connect the source with all receivers. At the overlay level, packets are multicast to all receivers along the Steiner tree.  ... 
doi:10.1109/glocom.2010.5683489 dblp:conf/globecom/LeL10 fatcat:sye5ukhudfanfnkk64f5bs43zq
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